MITSIMLab for Stockholm Enhancements, Calibration and Validation

Moshe Ben-Akiva Angus Davol Tomer Toledo Intelligent Transportation Systems Program, MIT Haris N. Koutsopoulos VOLPE National Transportation Systems Center Wilco Burghout Ingmar Andréasson Centre for Traffic Simulation Research, KTH Tobias Johansson Christer Lundin Gatu- och Fastighetskontoret

Stockholm, December 2000

Foreword The report describes the findings from a research project sponsored by Gatu- och Fastighetskontoret (GFK) of the City of Stockholm and jointly undertaken with the Massachusetts Institute of Technology (MIT), VOLPE National Transportation Systems Center and Royal Institute of Technology (KTH). The MIT/VOLPE team consisted of Professor Moshe Ben-Akiva, Dr. Haris N. Koutsopoulos (VOLPE), Tomer Toledo and Angus Davol. Professor Ben-Akiva, Director of the MIT Intelligent Transportation Systems (ITS) Program, was the Principal Investigator. Dr. Koutsopoulos was the technical manager. Tomer Toledo and Angus Davol, developed and implemented the MITSIMLab enhancements, calibrated the models and assisted in the fine-tuning of the network and control logic. Other researchers at the MIT ITS program assisted with the project. They include, in particular, Dr. Mithilesh Jha who was instrumental in developing the research approach and Ramachandran Balakrishnan who contributed to the enhancement of the User’s Manual for MITSIMLab and RNE. Research at KTH was conducted at the Centre for Traffic Simulation Research (CTR) and directed by Adjunct Professor Ingmar Andréasson. Wilco Burghout performed the validation test of MITSIMLab. Eugene Merritt of the Traffic and Transport Planning division was responsible for the floating car data collection and comparisons of simulation results with aerial photographs. Tobias Johansson of GFK coded the Brunnsviken network, processed detector data, and implemented the control logic at the various intersections. Christer Lundin was the GFK project monitor. Work continues with applications around Hornsgatan and the South Link in Stockholm. Centre for Traffic Simulation Research Ingmar Andréasson Adj.prof.

2

Contents FOREWORD

2

OVERVIEW OF MITSIMLAB

5

General

5

Model descriptions & general calibration approach Driving Behaviour Models General acceleration Lane Changing and Gap Acceptance Models Route Choice Model

8 8 8 10 12

Calibration

13

ENHANCEMENTS TO MITSIMLAB

15

Modelling of intersections and roundabouts A proactive anticipatory gap acceptance model

15 17

Modelling of driver’s path awareness (“look-ahead”) A “look-ahead” awareness model Bus Lane Enhancements

18 20 21

Bibliography

21

MITSIMLAB CALIBRATION FOR STOCKHOLM

22

Calibration of MITSIMLab for the Brunnsviken network

22

Available Data

22

Calibration of general parameters

24

Calibration of driving behaviour parameters Desired speed distribution The calibration sub-network Boss/Quattro calibration

25 25 26 28

Calibration of travel behaviour parameters Path choice set generation Habitual Travel Times Route Choice parameters

29 30 31 32

3

OD Estimation

33

Conclusions

37

EVALUATION OF MITSIMLAB

39

Introduction

39

Criteria

40

Method Network Data collection set-up Floating Cars Detector Loops

40 40 41 41 42

Analysis Introduction Number of replications Goodness of fit measures Comparison method Flows Travel times

42 42 42 43 44 44 44

Comparison Results Flows Travel times Clockwise Counter-clockwise

46 46 49 51 55

Evaluation of Queue Lengths

57

Discussion

61

Conclusion

62

Bibliography

64

4

Overview of MitsimLab

General MITSIMLab is a simulation-based laboratory that was developed for evaluating the impacts of alternative traffic management system designs at the operational level and assisting in subsequent refinement. Examples of systems that can be evaluated with MITSIMLab include advanced traffic management systems (ATMS) and route guidance systems. MITSIMLab is a synthesis of a number of different models and has the following characteristics: • Represents a wide range of traffic management system designs; • Models the response of drivers to real-time traffic information and controls; • Incorporates the dynamic interaction between the traffic management system and the drivers on the network. The various components of MITSIMLab are organized in three modules: • Microscopic Traffic Simulator (MITSIM) • Traffic Management Simulator (TMS) • Graphical User Interface (GUI) The interactions among the various MITSIMLab modules are shown in Figure 1. A microscopic simulation approach, in which movements of individual vehicles are represented, is adopted for modelling traffic flow in the traffic flow simulator (MITSIM). This level of detail is necessary for an evaluation at the operational level. The Traffic Management Simulator (TMS) represents the candidate traffic control and routing logic under evaluation. The control and routing strategies generated by the traffic management module determine the status of the traffic control and route guidance devices. Drivers respond to the various traffic controls and guidance while interacting with each other.

5

TRAFFIC MANAGEMENT SIMULATOR (TMS)

TRAFFIC SURVEILLANCE SYSTEM

MICROSCOPIC TRAFFIC SIMULATOR (MITSIM)

TRAFIIC CONTROL AND ROUTING DEVICES

Graphical User Interface (GUI)

Figure 1. Elements of MITSIMLab and their interactions

Traffic Flow Simulator (MITSIM). The role of MITSIM is to represent the “world”. The traffic and network elements are represented in detail in order to capture the sensitivity of traffic flows to the control and routing strategies. The main elements of MITSIM are: • Network Components: The road network along with the traffic controls and surveillance devices are represented at the microscopic level. The road network consists of nodes, links, segments (links are divided into segments with uniform geometric characteristics), and lanes. • Travel Demand and Route Choice: The traffic simulator accepts as input time-dependent origin to destination trip tables. These OD tables represent either expected conditions or are defined as part of a scenario for evaluation. A probabilistic route choice model is used to capture drivers' route choice decisions. • Driving Behaviour: The origin/destination flows are translated into individual vehicles wishing to enter the network at a specific time. Behaviour parameters (such as desired speed, aggressiveness, etc.) and vehicle characteristics are assigned to each vehicle/driver combination. MITSIM moves vehicles according to car-following and lane-changing models. The car-following model captures the response of a driver to conditions ahead as a function of relative speed, headway and other traffic measures. The lane-changing model distinguishes between mandatory and discretionary lane changes. Merging, drivers' responses to traffic signals, speed limits, incidents, and tollbooths are also captured.

6

Traffic Management Simulator (TMS). The traffic management simulator mimics the traffic control system in the network under consideration. A wide range of traffic control and route guidance systems can be simulated, such as: • Ramp control • Freeway mainline control • Lane control signs (LCS) • Variable speed limit signs (VSLS) • Portal signals at tunnel entrances (PS) • Intersection control • Variable Message Signs (VMS) • In-vehicle route guidance TMS has a generic structure that can represent different designs of such systems with logic at varying levels of sophistication (from pre-timed to responsive). Graphical User Interface (GUI). The simulation laboratory has an extensive graphical user interface that is used for both, debugging purposes and demonstration of traffic impacts through vehicle animation.

7

Model descriptions & general calibration approach

Driving Behaviour Models In MITSIMLab vehicles move according to the following models (which are a function of the traffic environment around the subject vehicle, vehicle’s individual characteristics, and driver’s characteristics). • General acceleration • Lane changing and gap acceptance • Merging • Forced merging • Intersection models

General acceleration A vehicle accelerates (decelerates) in order to: • React to the vehicles ahead; • Perform a lane changing or merging manoeuvre; • Respond to events (e.g. red signals and incidents); The most constraining of these situations determines the acceleration (deceleration) rate to be implemented in the next simulation cycle. Depending on the degree of interaction with the vehicle ahead, the subject vehicle can be in free-flowing, car-following, or emergency regime. The degree of interaction is determined by the time headway between the two vehicles. The acceleration in the free-flowing regime is a function of the vehicle's desired speed, while in the car-following and emergency regimes, the acceleration is a function of traffic conditions and relative position and speed of the two interacting vehicles. Free-flowing regime: In the free-flowing regime, the vehicle accelerates if its current speed is different from the driver's desired speed. The acceleration applied by a driver in this regime is assumed to have the following functional form:

[

]

α nff (t ) = λ ff V n* (t − τ n ) − V n (t − τ n ) + ε nff (t ) Where, αnff(t):

acceleration of driver n at time t

8

λff:

parameter

Vn*(t):

desired speed of the driver

Vn(t):

speed of subject vehicle at time t

εnff(t):

error term

Car-following: The car-following model is used for calculating a vehicle’s acceleration or deceleration rate in various cases such as: • Car-following relationship with the leading vehicle; • Competition with other vehicles if two or more lanes merge into a single downstream lane; • Yielding to another vehicle shifting into the same lane. The car following model is a generalization of the non-linear GM model. Furthermore, the parameters of the model can be different for acceleration and deceleration situations. The general structure of the model is shown in Figure 2:

L n −1 V n −1 ( t )

Ln V n (t )

∆ x (t )

x n −1 ( t )

xn (t)

Figure 2. Car-following model

The car-following model can be expressed mathematically as:

an (t) =α cf

Vn (t −T)α

[∆x(t −T)]

β

kδ [Vn−1(t −T) −Vn (t −T)] + εncf (t) γ

Where, cf

a n (t ) :

acceleration of vehicle n at time t;

∆x(t): k: Vn(t): α, β, γ,δ: εn cf(t):

gap between vehicles at time t; density of traffic in the vicinity of the vehicle; speed of vehicle n at time t; parameters error term

9

Emergency regime: In the emergency regime, the vehicle uses an appropriate deceleration rate to avoid collision. The deceleration rate depends on the state of the front and subject vehicles. In all cases though, the applied rate guarantees that the subject vehicle will always decelerate to extend the headway to a safe range.

Lane Changing and Gap Acceptance Models The lane changing model is implemented in three steps: (a) checking if a change is necessary and defining the type of the change; (b) selecting the desired lane; and, (c) executing the desired lane change if the available gaps are acceptable. Lane changing may be mandatory (MLC) or discretionary (DLC). Mandatory lane changing is performed when the current lane ceases to be an option (due to, for example, lane use regulations, incidents, and need to take exit ramps), and thus the driver must move to another lane. Discretionary lane changing is performed when a driver is not satisfied with the driving conditions in the current lane (due to, for example, average speed of the lane as compared to the driver’s desired speed, and existence of heavy vehicles). The lane changing model structure is shown in Figure 3. In most cases the decision process is latent in nature. The latent and observable parts of the process are represented by ovals and rectangles respectively. Start

MLC

MLC

driving conditions not satisfactory

driving conditions satisfactory

other lanes

Left Lane

Right Lane

Left Lane

current lane

Right Lane

Gap Accept

Gap Reject

Gap Accept

Gap Reject

Gap Accept

Gap Reject

Gap Accept

Gap Reject

Left Lane

Current Lane

Right Lane

Current Lane

Left Lane

Current Lane

Right Lane

Current Lane

Current Lane

Figure 3. Structure of lane changing model

10

Current Lane

The Gap Acceptance Model The gap acceptance model captures drivers’ assessment of gaps as acceptable or unacceptable. Drivers are assumed to consider only the adjacent gap. An adjacent gap is defined as the gap in between the lead and lag vehicles in the target lane (see Figure 4). For merging into an adjacent lane, a gap is acceptable only when both lead and lag gaps are acceptable. X

total clear gap + vehicle length lag gap

Y

lead gap

lag vehicle

lead vehicle

subject

front vehicle

X

Y

Figure 4. Gap acceptance model

Drivers are assumed to have minimum acceptable lead and lag gap lengths (lead and lag critical gaps respectively). These critical gaps vary not only among different individuals, but also for a given individual under different traffic conditions. The value of the critical gap is a function of traffic density, distance to the point by which the driver has to complete a mandatory lane change, etc. In summary, the gap acceptance model is stated as: if available lead (lag) gap < critical lead (lag) gap ⇒ reject lead (lag)gap if available lead (lag) gap > critical lead (lag) gap ⇒ accept lead (lag) gap if both lead and lag gaps are accepted change

⇒

perform lane

Forced Merging Model In heavily congested traffic, gaps for merging and lane changing are difficult to find. In these situations the driver creates a gap by forcing another vehicle to yield. The probability of forced merging is a function of traffic conditions and characteristics of the subject drivers. The tree diagram in Figure 5 summarizes the structure of the forced merging model. As before, the ovals correspond to the latent part of the process that 11

involves decisions and the rectangles correspond to the events that are directly observable.

MLC

do not start forced merging (M)

start forced merging (M)

Same Lane

Target Lane

Same Lane

Figure 5. The forced merging model structure.

Route Choice Model In MITSIMLab drivers make route choice decisions either pre-trip or en-route (based on information received from Variable Message Signs (VMS) or in-vehicle devises). A probabilistic route choice model is used to capture route choice decisions and it has two forms: path- or link-based. The path-based model is a variation of the C-Logit model. The link-based model calculates the probabilities of choosing an outgoing link at each intersection using the formula (see Figure 6): p(l j , t ) =

[ (

exp β c$l ( t ) + C$ k ( t + c$l ( t ))

∑

C$ k ( t + c$l ( t ) ) ≤ C$ j ( t )

Where: c$l ( t ) :

[ (

)]

exp β c$l ( t ) + C$ k ( t + c$l ( t ))

)]

expected time to traverse link l for a vehicle that enters that link at time t;

12

C$ k ( t ) :

expected shortest travel time from node k to the destination for a vehicle

β:

that arrives at k at time t; model parameter.

o

Current Link

j ttl

d

l k

TTk

Figure 6: Linked-based route choice model

The expected travel time to one’s destination for each alternative downstream link at an intersection can be time dependent. The expected travel time depends on the type of information the driver has access to. If no information is available habitual travel times are used.

Calibration In general, the calibration framework for MITSIMLab is shown in Figure 7. The calibration methodology consists of two steps. At the first level, using disaggregate data individual driver behaviour models can be calibrated and estimated. Disaggregate data includes information on detailed driver behaviour such detailed vehicle trajectories (both for the subject and surrounding vehicles). At the second level aggregate data (e.g. time headways, speeds, flows, etc.) are used to fine-tune driver behaviour parameters and estimate other general parameters in the simulator.

13

Data Collection

Disaggregate Data

Model Refinement

Estimation of Individual Models

Evaluation

Aggregate Data

Validation of Model System

Evaluation

Calibrated and Validated System of Models

Figure 7. Calibration Methodology

In the absence of detailed data, aggregate data is used to calibrate the most critical parameters. Aggregate calibration uses optimisation techniques to minimize a measure of deviation between the output of the simulator and the corresponding observed values. A common measure that is used in practice is the square difference between the simulated and actual values. In this case the objective function of the optimisation is expressed as: objective function =

∑ w ∑ (X i

i

Where, wi: Xtisim: Xtiobs:

sim ti

− X tiobs

)

2

t

weight for measurement i simulated output t associated with measurement i observed output t associated with measurement I

14

Enhancements to MITSIMLab Several new features were incorporated in the MITSIMLab model as part of this project. These enhancements were needed for accurate modelling of the Brunnsviken network. In particular features that improve the capability to model urban networks were implemented. In this section we describe the enhancements to some of the models. Two new models are described in detail: • Drivers’ behaviour at intersections and roundabouts • Drivers’ path-awareness capabilities (“look-ahead”) In addition, enhancements required for proper modelling of the bus lanes on the Brunnsviken network, such as bus-priority at traffic signals and loading and unloading at bus stops, are currently underway.

Modelling of intersections and roundabouts Intersections and roundabouts are among the most important features of urban networks. Strong interaction between vehicles in the intersection area causes delays to vehicles. These delays make up significant proportions of total trip time in urban networks. Moreover, this proportion increases with the level of congestion in the network, as growing numbers of vehicles in intersecting links compete over a fixed, limited capacity of the intersection. A driver approaching an intersection is confronted with the decision of how to negotiate his manoeuvre in the intersection. To make this decision, the driver has to assess vehicle positions and speeds in other approaches to the intersection as well as its own desired speed within the intersection. Traditionally, this behaviour is modelled with gap acceptance models. These models are based on the notions of priorities in the intersection and of conflicting movements. Movements in the intersection are ranked in terms of right of way. Movements with lower priority are assumed to yield to higher priority movements. Vehicles in these movements are looking at available gaps in higher priority conflicting traffic. Gap acceptance models are used to determine their actions on the existing gaps. These models formulate a problem in which a driver is presented with a gap. The choice set is binary. The driver will either accept or reject the gap. The decision is based on

15

comparison of the existing gap with an unobserved attribute of the driver, the critical gap. Mathematically it can be written as: 1 Y= 0

if t ≥ t ct if t < t cr

1 Where Y is the decison variable  0 t cr - the critical gap

if the gap is accepted if the gap is rejected

Critical gaps are assumed to be random variables drawn from some distribution (Cohen, 1955; Miller, 1972 and others). Mahmassani and Sheffi (1981) allowed the mean of the critical gap distribution to be a function of explanatory variables. This enabled introducing impatience functions – critical gaps are decreasing functions of waiting times at the stop line (or the number of rejected gaps). Another class of models used for intersection modelling is real-estate models. One such model was implemented in the simulation package CORSIM (FHWA, 1998). These models do not explicitly model drivers’ behaviour, but used a cellular-automata-like representation of the intersection to determine the ability of a vehicle to perform its movement on which the vehicle must travel to perform its movement. The intersection area is divided into blocks of 15-20ft in which vehicles may reside. Individual vehicle movements are related directly to various real-estate blocks within the intersection. A vehicle path is defined by a sequence of blocks that it occupies as it moves through the intersection and by the time each block is occupied. Each vehicle, within or approaching an intersection, influences blocks along its path, both upstream and downstream of its position. The extent of influence varies with the speed and acceleration of the vehicle and is determined by simple rules. These influences define the status of the block at every time interval. A block may be free, occupied or under influence of a vehicle prohibiting other vehicles to occupy it. The advantage of this approach is that it does not require enumerating, a priori, all possible combinations of vehicle paths within the intersection that can create conflicts. Instead, only the status of the real estate blocks needs to be checked in order to identify conflicts. The shortcoming of this approach is in the use of simplistic occupancy rules, and even more severely the dependency of the outcome on the real estate blocks representation of the intersection. It is almost impossible to formulate a general logic for defining blocks that would be able to handle intersections with non-standard geometry. This problem caused CORSIM to drop this approach for modelling intersections, and prevents its implementation in other models.

16

A proactive anticipatory gap acceptance model The binary formulation of intersection gap acceptance decisions may be reasonably suitable for drivers standing at the stop line, however it is far less suited for moving vehicles or crawling traffic. The major deficiency is that in existing models drivers are assumed to be passive. Their choice set is restricted to a simple accept/reject decision. In reality, drivers make more complicated choices, playing a more active roll: • Drivers do not make only accept/reject decisions but also adjust their speeds and acceleration rates to maximize the probability that they would be able to accept gaps. Modelling this decision is essential for models used in a microscopic simulation context where the basic variables are speed and acceleration. • Gap evaluation process - drivers do not make their decisions based on actual gaps, which are unknown at the time the decision is made. Instead, they estimate available gaps by predicting the behaviour of vehicles in the opposing movements. • Drivers’ acceleration decisions are bounded by an upper limit value of desired manoeuvring speed. This speed is a function of the type of manoeuvre (crossing, right tern, left turn) and the geometry of the intersection. A model that explicitly addresses the above principles is implemented in MITSIMLab. In the first step of the model, the vehicle is tagged as approaching an intersection. This is done at a distance from the intersection related to the stopping distance and the visibility of the intersection. The tagging distance is randomly distributed over the population of drivers. Once a vehicle is tagged, it starts adjusting its speed to the intersection. A maximum desired manoeuvre speed is defined for each vehicle. This speed is based on the specifics of the manoeuvre the vehicle is about to undergo in the intersection and a random component. An intersection-approaching vehicle starts to consider gaps along with the other constraints (car following, traffic lights etc.) when making acceleration decisions. This primarily concerns the first vehicle in the lane approaching an intersection, but is also applied in a restricted way to following vehicles to allow several vehicles to use the same gap should the gap size allow it. The consideration of gaps consists of three components: 1. Identifying conflicting vehicles - the driver identifies conflicting vehicles that he has to yield to. The implementation is that based on the hierarchy of right-of-way in the intersection the vehicle object identifies the movements that have priority

17

over its own, identifies the lanes that these movements would be using to approach the intersection and identifies the first vehicle in each of these lanes. 2. Predicting gaps - once the conflicting vehicles were identified, the driver predicts the gap available to him. The predicted gaps are based on a prediction of his arrival time at the conflict zone and on his perception of the arrival times at the conflict zone of conflicting vehicles. Since the driver cannot know how these drivers would behave in the future, his prediction of their arrival times is based only on their current speed. The gap the driver reacts to is the minimal of gaps available to him in conflicting movements. 3. Evaluating gaps and deciding acceleration - having predicted the available gap, the driver evaluates his ability to accept the gap and makes the appropriate acceleration decision. The gap acceptance decision is based on comparison of the existing gap with a critical gap. This gap is movement specific, and randomly distributed between drivers. In the current implementation the driver tries to maximize the probability that the gap available to him will be acceptable by adjusting his speed and acceleration to create the largest possible gap. Other driving constraints set the limits of acceleration. If the gap is unacceptable, even under optimal arrival timing at the intersection, the driver will decelerate to be able to stop at the stop line.

Modelling of driver’s path awareness (“look-ahead”) Most lane changing models assume that 2 types of lane changes exist: discretionary and mandatory. A discretionary lane change is performed when the driver perceives that it will improve the driving experience (i.e. speed advantage, comfort etc.). A mandatory lane change is triggered when the driver must perform a lane change in order to follow its path (e.g. be on a lane that leads to an exit ramp from a freeway). The problem of path awareness arises in the context of mandatory lane changes. The question is when do drivers become aware of the path plan constraint that triggers a mandatory lane change. The previous approach used in MITSIMLab was that at any time drivers are only aware of the next link on their path. Therefore only lane changes required in order for the vehicle to be able to continue to the next link are considered. This approach is common to many micro-simulation models. It is mainly driven by the computational efficiency gained from the fact that at any time a vehicle only needs to know the next link on its path rather then store information on the whole path. The use of this approach may be reasonable for freeway networks, with relatively long links. However, it is problematic in an urban environment, characterized by short links and paths that may require frequent turning movements. In such cases, the one-link

18

awareness model generates excess weaving and merging manoeuvres due to many late lane changes and therefore leads to gross underestimation of the capacity of these locations. Real-world drivers may consider their path plan well in advance and adjust their position to allow for a smoother continuation of the path. This problem was encountered at several locations on the Brunnsviken network and was particularly severe at the northbound approach to Nortull-Sveavägen intersection. A simplified scheme of the site is shown in Figure 8. Vehicles travelling westbound on Sveavägen, heading to E4 (Uppsalavägen) will turn right at Norrtull. A Short distance (~50 m.) later the road splits to two: Vehicles heading to E4 northbound will take the right arm and vehicles heading to E4 southbound will take the left one. Figure 1a shows the behaviour of a southbound vehicle according to the one-link awareness model. At Sveavägen the right lane allows the vehicle to continue to the next link and therefore the driver may choose to stay on that lane. Only after crossing Norrtull the driver is aware that a lane change is required in order to take the left arm at the divergence point. This driver, as well as many others with similar behaviours, will perform lane changes in the short section before the divergence. The capacity of the section will be reduced and if demand is sufficiently large a bottleneck will be created. Eliminating the one-link awareness restriction may cause drivers to consider their intended manoeuvre in the divergence before crossing Norrtull and move to the left lane already in Sveavägen (as shown in Figure 8b).

(a)

(b)

Figure 8 – A scheme of the Norrtull intersection

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A “look-ahead” awareness model A new awareness model that overcomes the limitations of the one-link awareness has been implemented in MITSIMLab. The assumption is that a driver is aware of the pathplan up to a certain distance downstream of the current position. The driver will react to any mandatory conditions that arise within this “look-ahead” distance and ignore any such considerations beyond that distance. The look-ahead distance is a characteristic of the driver: it may depend on factors such as familiarity with the path and spatial abilities. Look-ahead distances are assumed to be randomly distributed in the population of drivers. The critical operation in the implementation of the look-ahead model is mapping the lane connectivity from the vehicle’s position to look-ahead distance downstream. This is required in order to determine whether a mandatory lane change is required and if so, in which direction. A double pass process is used for that: 1. Forward pass - starting at the position of the vehicle, the next segments on the path are accumulated up to the look-ahead distance. The lanes in the last segment within the look-ahead distance are labelled as the target lanes. The driver will want to be in a lane that is connected to any of these lanes. 2. Backward pass - starting from the target lanes and moving backwards on the path, a list of lanes connected to the target lanes is maintained. In the next step the lanes on that list will become the target lanes. The process is repeated until the connected lanes in the current segment are identified. The list of connected lanes in the current segment is used to determine whether a mandatory lane change is required. If the vehicle’s current lane is connected, no lane change is needed. Otherwise a mandatory lane-change in the direction of the connected lanes is triggered. Figure 9 shows an example of a current segment, target lanes and connected lanes (shown in red) in Norrtull. The vehicle shown in this figure will immediately initiate a mandatory lane change to either of the two left lanes.

Figure 9 – Mapping of lane connectivity in Norrtull

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Bus Lane Enhancements In previous applications of MITSIMLab, high-occupancy vehicle lanes were typically separate facilities with limited access points, as is common on freeway networks. The Brunnsviken network, however, includes arterial bus lanes that are discontinuous to allow non-HOV vehicles to use them as acceleration and deceleration lanes and which are not physically separated from adjacent unrestricted lanes. Two main enhancements of existing models were required to allow for proper modelling of these lanes. First, one enhancement was capturing the preference of the HOV lane by drivers of high-occupancy vehicles, even when the discretionary lanechanging model would not lead to a lane-change. Second, these lane-use privileges were incorporated into the “look-ahead” model discussed above in order to capture the drivers’ awareness of downstream lane restrictions. This was required in order to better model the merging of vehicles from an acceleration lane to the mainline lanes when the acceleration lane is a discontinuity in the bus lane.

Bibliography

Cohen E., Dearnaley J., and Hansel C. – The risk taken in crossing a road. Operation research quarterly 6, pp 120-128, 1955 CORSIM user manual, Federal Highway Administration, 1998. Highway Capacity Manual, Transportation Research Board, 1994. Mahamassani H. and Sheffi Y. – Using gap sequences to estimate gap acceptance functions. Transportation research part B, 15B, pp.243-248, 1981. Miller A. - Nine estimators of gap acceptance parameters. In Proceedings of the 5th International symposium on transportation and traffic theory, pp. 215-235 1972.

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MITSIMLab Calibration for Stockholm

Calibration of MITSIMLab for the Brunnsviken network The main objective of this project is to calibrate MITSIMLab parameters to capture the behaviour of Swedish drivers. Parameters in MITSIMLab are classified to 3 main groups: • Driving behaviour parameters • Travel behaviour parameters • General parameters Driving behaviour in MITSIMLab is based on car-following, lane-changing, and intersection models. The parameters of these models have been previously calibrated to Boston data. Demand inputs included the trip demand for different types of vehicles in the form of an origindestination matrix, parameters of the route choice model, and a path choice set. Some of the important general parameters are the distribution of vehicle types, lane-use privileges (i.e. bus lanes) and vehicle performance characteristics. The default values represent average US fleet characteristics.

The section is organized as follows: we begin by describing the data available for calibration. Next we detail the relevant parameters and calibration approach for each one of the groups mentioned above.

Available Data For the calibration phase, GFK provided traffic data from May 1999. Counts on the A4 motorway were obtained from MCS sensors, which gave speeds and flows in 1-minute intervals at 23 locations on 5-6 May 1999. The sensor locations are shown in Figure 10. This data was supplemented with SNRA loop counts at two other locations in the network, giving counts in 15-minute intervals for 4-9 May 1999. These locations are shown in Figure 11.

22

Figure 10 - MCS sensor locations

Figure 11 - 1999 SNRA count locations

23

An EMME/2 generated, static AM peak O-D matrix, which has been previously used for studies on the same network, was also provided by GFK. Other miscellaneous data including information about the vehicle mix by type and lane-use privileges were also available. The MITSIMLab simulation network was coded by GFK with assistance from MIT based on technical drawings and aerial photographs provided by GFK.

Calibration of general parameters This group includes parameters that affect the general performance of the traffic network but are not directly associated with a particular behaviour. An important class of parameters is the vehicle mix parameters. In particular two aspects of the vehicle mix are of importance for the Brunnsviken application: the classification of vehicles by type (i.e. passenger cars, buses, trucks etc.) and by lane-use privilege (i.e. permission to use bus lanes). The type assigned to a simulated vehicle in MITSIMLab affects its physical properties (length and width) and performance capabilities (e.g. maximum speed, maximum acceleration and deceleration). The importance of lane-use privileges in this application stems from the extensive bus lanes system in place on the Roslagsvägen corridor and on E18. The vehicle mix specified in MITSIMLab is directly based on the information provided by GFK on AM peak traffic observations for a comparable roadway stretch in June 1999 and is shown in Table 1. Vehicle Type Autos Taxis + Buses Heavy Trucks

Fraction 0.81 0.10 0.06 0.03

Table 1 - Vehicle Classification Data

The “Taxis +” classification refers to automobiles that were counted in the bus/taxi lane, which included taxis and non-authorized users. The vehicles in this class, as well as all buses, were assigned as having bus lane privileges in MITSIMLab. All other vehicles are not permitted to use the bus lanes. The Autos category was further split into two separate groups: high-performance vehicles and low-performance vehicles. The division was based on statistics about the distribution of vehicle of age and brand provided by GFK. The year 1990 was, rather arbitrarily, chosen as the cut-off point. High

24

performance vehicles account for 41% of the vehicles and low-performance vehicles for 40%. Taxis are assumed to be high-performance vehicles.

Calibration of driving behaviour parameters This category includes parameters that govern the behaviour of vehicles as they manoeuvre in traffic. Two important models affect the driving behaviour in MITSIMLab: the acceleration model and the lane-changing model. The acceleration model determines the longitudinal movement of a vehicle under 3 possible regimes: free flowing, car following and emergency. The car-following behaviour is active when the subject vehicle is directly affected by the vehicle in front of it. The free-flowing regime describes the behaviour of a vehicle that is not affected by the vehicle in front (when it is far away from it). Emergency behaviour is invoked when the driver tries to avoid a collision. The lane-changing model captures a lane changing action with three levels of decision-making: the decision to change lane, the choice of lane to change to and the gap acceptance behaviour to perform the lane change. A detailed description of the models currently implemented in MITSIMLab is presented in Ahmed (1999) and Ahmed et al. (1996). The driving behaviour parameters were calibrated in 3 stages: first, the distribution of desired speeds was inferred directly from MCS sensor data. Next, a sub-network was used to initially calibrate car-following and lane-changing behaviour parameters using Boss/Quattro, a stochastic optimisation tool. Finally, the calibrated parameters were applied to the whole network and scale parameters of the models were modified to best replicate the state of the network.

Desired speed distribution The key parameter in the free-flowing acceleration behaviour is the desired speed of the vehicle. The desired speed is defined as the speed that the driver would choose in the absence of any restrictions imposed by other vehicles or by traffic control devices. This speed is affected by the geometry of the section and by driver characteristics. MITSIMLab uses the speed limit as a basis for the distribution of desired speeds in the driver population. A set of parameters determines the distribution of desired speeds. The distribution of desired speeds is inferred from the MCS data using the speeds of unconstrained vehicles. Vehicles crossing the sensor stations at times when the flow rate was less than 600 Veh/Hr/lane are considered unconstrained. This threshold corresponds to the Highway Capacity Manual maximum flow for level of service A. The speeds of unconstrained vehicles (i.e. under flows less then 600 Veh/Hr/lane) reported by the MCS system were recorded. The speed limit in the section of E4 studied

25

is 70 Km/hr. The distribution of speeds of these unconstrained vehicles is presented in Figure 3. D e sire d Sp e e d D istrib u tio n 40 35 30

Percentage

25 20 15 10 5 0 u n d e r 70

70-80

80-90

90-100

100-110

110-120

o v e r 120

Sp e e d C a te g o ry ( k m /h r)

Figure 12 – Desired speed distribution based on 600 Veh/Hr/lane flow threshold

An analysis of the sensitivity of the desired speed distribution with respect to the changes in flow threshold was performed. The desired speed distributions obtained from using flow thresholds of 300 and 200 Veh/Hr/lane were not significantly different than the ones reported in Figure 12.

The calibration sub-network A small sub-network of the Brunnsviken network was used in order to calibrate other driving behaviour parameters. Two main considerations contributed to adopting this approach: 1. The calibration process is more manageable when performed on a sub-network. An optimisation tool, Boss/Quattro, was used. 2. The sub-network was chosen such that available MCS sensor data can be used to generate a highly accurate O-D matrix at very high time resolution (1 min. intervals). Moreover for each O-D pair in the sub-network only one path exists. Therefore most of the errors generated by O-D estimation procedures and route choice modelling were eliminated by the use of the sub-network. 26

The sub-network location that was chosen is in the north part of the E4 southbound corridor, as shown in Figure 13. A more detailed view of the sub-network including the various on- and off-ramps and MCS sensors on that network is presented in Figure 14. The numbers shown on the figure are sensor numbers in the MCS system. This subnetwork was chosen for several reasons including: 1. Minimal downstream effects – the location is far from possible spillbacks from the bottlenecks in the Norrtull area that may offset the behaviour and are not represented in the MITSIMLab model. 2. Representation of different behaviours – The calibration network contains geometric elements that are likely to demonstrate most of the behaviours that are represented in MITSIMLab. The network contains on- and off-ramps, allowing capturing mandatory and discretionary lane changing, and merging behaviour.

Figure 13 – Location of the calibration sub-network

27

Figure 14 – A detailed view of the calibration sub-network

Boss/Quattro calibration Boss/Quattro is a software environment that manages external applications. It supports analysis and optimisation of the influence of parameters on the response yielded by external software applications through a built-in engine. Running an external application may involve reading an input file, running the software program and reading the results of the run. Detailed description of Boss/Quattro and its application to optimisation of MITSIMLab parameters can be found in Kurian (1999). In this application Boss/Quattro was used to perform sensitivity analysis and calibrate the driving behaviour parameters. The calibration sub-network was coded in MITSIMLab. O-D information was extracted from MCS counts at 1 min. intervals and an appropriate input file was created. Speed data from MCS sensors was used for the calibration. The objective function defined was to minimize the square deviations of simulated sensor speeds from the observed MCS speeds:

28

min

∑∑ (V t

i ,t obs

i ,t 2 − Vsim )

(1)

i

i ,t i ,t Where, Vobs and Vsim are the observed and simulated speeds at sensor i at time t,

respectively. Next, parameters that Boss/Quattro may change in order to optimise the objective function were identified in the parameter file (paralib.dat).

Calibration of travel behaviour parameters Two major components affect travel behaviour in any traffic model: the trip generation process and the route choice model. In MITSIMLab, simulated vehicles are generated and assigned with an origin and a destination node according to a user-specified, timedependent O-D matrix. A route choice model determines the route each vehicle will follow. When using traffic count data to calibrate the two components (O-D matrix and route choice model), their impact on traffic flow cannot be separated. To see that we may look at the inputs required for each one of the models: O-D estimation methods require an assignment matrix as input. The entries in this matrix are fraction contributions of each O-D flow to each one of the sensor readings used for the estimation. Usually the assignment matrix is not readily available and needs to be generated from the model. However, the assignment matrix generated by a MITSIMLab (or any other) model is a function of the route choice model that is used. On the other hand, one of the most important explanatory variables in route choice models is the travel time on the route. Traffic flow theory shows that travel times, in particular in congested networks, are flow-dependent. Flows on the network are strongly affected by the O-D matrix used. Therefore, an iterative calibration approach is called for. Several important elements are identified in the calibration process. The route choice model calibration requires two preliminary stages: determination of the choice set, a set of reasonable paths for each O-D and an array of habitual link travel times that will be used to explain the route choice behaviour. As mentioned above, the O-D estimation process requires generation of an assignment matrix. The framework for calibration of travel behaviour models is shown in Figure 15. We iterate between a route choice calibration step and an O-D estimation step. At each iteration, based on the existing OD matrix, input for the route choice model is generated and parameters of this model are calibrated. The calibrated route choice model is used to generate an assignment matrix, which we use in the O-D estimation process. The new O-D matrix is used to re-calibrate route choice parameters and so on. In the next sections we describe the methods used in each one of these steps.

29

Path Choice Set

Driving Behavior Parameters

Habitual Travel Times

Route Choice Parameters

OD Matrix

Figure 15 – Framework for calibration of travel behaviour models

Path choice set generation The route choice model requires a set of reasonable, alternative paths for each O-D pair in the network. The following procedure was used to generate these sets: 1. Generation of a comprehensive path set – The MITSIMLab model is run using the default link based route choice model. In this route choice model a vehicle decides the next link on its path at each node. The next link choice is based on a logit model with the shortest path travel times to the destination via each one of the possible next-links as explanatory variables. 2. Unreasonable paths elimination - The myopic route choice tends to generate a large number of paths. All the paths generated this way were recorded, and judgment was used to eliminate unreasonable paths (e.g. circular paths or paths using off-ramp and on-ramp immediately after that). The “browse path” tool in the MITSIMLab graphical user interface was used to visualize paths and assist in the elimination process The structure of the Brunnsviken network is such that for each OD pair only one or two reasonable paths exist. This allowed us to perform the path generation exercise once and fix the path set. In a more general case the path set may be more dependent on traffic conditions, in which case the process should be repeated as the O-D matrix and route choice model evolve to ensure that all reasonable paths are captured.

30

Habitual Travel Times The default route choice model implemented in MITSIMLab uses habitual path travel times (i.e. expected travel times) to explain the choice of routes. In order to calibrate the parameters of the model knowledge of the habitual travel times is required. An iterative day-to-day learning model is used to develop these travel times. At each iteration (representing a day) of this process, MITSIMLab is run using the current habitual travel times estimates. Experienced travel times from the MITSIMLab run are used to update the habitual travel times by calculating a weighted average of the two sets of travel times. Mathematically, the expected travel time on next day is given by: TTitk+1 = λk ttitk + (1- λk)TTitk

(2)

Where, TTitk is the expected travel time on link i, during time period t on day k+1, ttitk is the experienced travel time on day k, and λk is the weight parameter for the experienced travel time. The day-to-day evolution of habitual travel times is shown in Figure 16. Early iterations exhibit large fluctuations in travel time, in subsequent iterations travel times are equilibrated and stationary values are reached. Ha b itu a l Tra v e l Tim e s 8.4 8.2

Average Travel Time (min.)

8 7.8 7.6 7.4 7.2 7 6.8 6.6 6.4 1

2

3

4

5

6

7

8

9

10

11

Ite ra tio n

Figure 16 – Evolution of habitual travel times

31

Route Choice parameters Parameters of the route choice model were calibrated to match the split between the two points shown in Figure 17. These points were selected because due to the ring structure of the network, all vehicles with a choice of paths pass these points. Splits rather than counts were used in order to reduce errors that stem from inaccuracies in the scale of the O-D matrix. This was particularly useful in early iterations, since it was known that the seed O-D matrix is scaled down compared to the “true” matrix.

E4 count location

Roslagsvägen count location

Figure 17 – Measurement locations for route choice calibration

32

Figure 18 shows the split resulting from calibrated model. The values shown are the percentage of all southbound traffic using the A4 instead of Roslagsvägen. The results from MITSIM are compared with actual traffic counts.

Percentage of southbound traffic on E4 100% 90% 80% 70% 60%

Actual MITSIM

50% 40% 30% 20% 10% 0% 06:45 07:00 07:15 07:30 07:45 08:00 08:15 08:30 08:45

Figure 18 – Route Split results, southbound

OD Estimation

The framework of the OD estimation procedure is shown in Figure 19. MITSIMLab, with its previously calibrated parameters, is used to generate the assignment matrix from the seed OD matrix. The estimation routine is then performed in MATLAB. These steps will be detailed below.

33

sensor counts assignment matrix

MITSIMLab

seed OD

estimated OD

MATLAB

Figure 19 – OD Estimation Framework

The assignment matrix maps time-dependent OD flows to time-dependent sensor counts within the network. Each element of the matrix represents the proportion of demand for OD pair n in period i which contributes to sensor count l in period j. Output data from MITSIMLab is used to generate this matrix. In MITSIMLab, a sensor at each count location reports the passage of each individual vehicle, recording the time of crossing, the vehicle’s origin-destination pair, and the vehicle’s departure time from its origin. This data is then post-processed in MATLAB, which adds each vehicle record to the appropriate location in the matrix. Each element is divided by the corresponding OD demand to give the fractional contribution of the total demand for that OD pair. Figure 20 shows the assignment in graphical form, with non-zero elements darkened. OD Demand Counts

6:45

7:00

7:15

7:30

7:45

8:00

8:15

8:30

8:45

6:45 7:00 7:15 7:30 7:45 8:00 8:15 8:30 8:45

Figure 20 – Assignment Matrix

The OD estimation process seeks to minimize the deviations between the estimated and the observed sensor counts while also minimizing the deviation between the estimated OD matrix and the seed matrix. The formulation of the optimisation problem is given by: min  Ax − y H x≥0  

2

+ w x − xH

2

  (3)

34

where x is the vector of estimated OD flows, xH is the vector of historical (seed) OD flows, yH is the vector of historical (measured) sensor counts, A is the assignment matrix, and w is the relative weight given to the seed matrix in the estimation. Due to the large number of OD pairs and sensor locations in the Brunnsviken network, the estimation was computationally too intensive for the optimisation routines in MATLAB. To overcome this limitation, a sequential estimation technique was employed which made use of the sparsity pattern of the assignment matrix. Because travel times in the network are typically no longer than one or two or the 15-minute time intervals, OD demand in one period rarely has an effect beyond the first or second of the subsequent periods. Furthermore, much of the effect of the OD is felt in the same time period. Therefore, estimating the OD matrix a single time period at a time is a reasonable compromise. The sequential estimation process is as follows: The seed OD is taken as fixed for the first time period, which is 6:30 in the case where the period of interest starts at 7:00. Since the simulation starts from an empty network, the counts in the first period will always be low. Therefore, estimating this first period demand would result in an artificial inflation of the OD as the procedure tried to match the counts. With the fixed OD in the first period, the assignment matrix is then used to estimate the effect of the first period demand on sensor counts in the subsequent periods. The demand in the second period is then estimated, based on the observed counts less the estimated contribution of the first period OD. Again the assignment matrix is used to estimate the effect of second period demand on subsequent periods, which are the periods of interest. This process is continued until the demand has been estimated for all periods of interest. Due to the effects of congestion within the network, the assignment matrix generated from the seed OD is not necessarily consistent with the estimated OD. Therefore, the OD estimation process must be iterative, as was shown in Figure 10. Each iteration takes the OD matrix estimated in the previous iteration as its seed matrix, and MITSIMLab is used to generate an updated assignment matrix. Figures 21 and 22 show the results of the OD estimation procedure by comparing MITSIMLab counts based on the static seed OD, MITSIMLab counts based on the estimated OD, and actual recorded counts. Figure 12 compares counts at a sensor just downstream of a network origin and shows that the estimation procedure has scaled the entry flows from that origin to match the actual counts. Figure 13 compares counts at a location within the network, where multiple origin and destination flows contribute to the counts. Again the counts generated from the estimated OD follow the dynamics of the actual counts.

35

C o u n ts a t En try Po in t to N e tw o rk 1200

M ITSIM c o u n ts - se e d O D M ITSIM c o u n ts - e stim a te d O D A c tua l c o u n ts

1000

Vehicle Count

800

600

400

200

0 6:45

7:00

7:15

7:30

7:45

8:00

8:15

8:30

8:45

Tim e In te rv a l

Figure 21 – OD estimation results (counts at entry)

C o u n ts w ith in Netw o rk 1600 MIT S IM counts - s e e d O D MIT S IM counts - e s timate d O D A c tual c o unts

1400

Vehicle Count

1200 1000 800 600 400 200 0 6:45

7:00

7:15

7:30

7:45

8:00

8:15

8:30

8:45

Time Interval

Figure 22 – OD estimation results (counts within network)

36

Conclusions

The calibration of the test network was a challenging task for several reasons, such as the: • Availability of only aggregate traffic data • Existence of heavily congested conditions • Combination of freeway and urban streets with a variety of facilities such as bus-lanes and rotaries. In addition, problems in the data with respect to quality, consistency and spatial coverage were also identified. Although, data problems are not atypical in applications similar to the one we undertook in this study, they nevertheless hindered the calibration and may have affected the validation task as well. Examples of data related issues include: • Possible conservation of flow violations between measurements at consecutive sensor locations • Faulty sensors • Inconsistent sensor data due to directional mislabelling • Errors in the range of ± 10 km/hr in reported MCS speed measurements (based on the report with information on the MCS system) In addition to the data issues, several other aspects were identified as impacting the process: • Limited spatial coverage of sensors for the estimation of the 1999 OD matrix • Approximate representation of traffic signals and traffic control logic • Different control logic in 2000 compared to 1999 From a methodological point of view, several problems had to be addressed. All phases of calibration are interrelated. The error in reproducing observed conditions is the result of errors in OD estimation, route choice and traffic representations. Since the results of OD estimation are input to traffic simulation, the calibration process iterated between OD estimation and calibration of driving behaviour. BOSS-Quattro provided a convenient environment to perform sensitivity analysis and calibration. However, the default algorithms may have to be replaced by algorithms that are more appropriate for optimisation of systems that involve Monte Carlo simulation. Algorithms that are not using derivatives (such as the Box COMPLEX algorithm) are good candidates. Once the data and methodological issues were resolved the calibration and estimation processes yielded sensible results. Furthermore, after the initial calibration of the driving behaviour parameters using BOSS-Quattro, the fine-tuning and subsequent calibrations with the entire network, focused only on scale parameters of the driving behaviour models. The results and the model behaviour indicate that the majority of the driving behaviour models could be transferable (to cities with similar conditions) with calibration with aggregate data only of the scale parameters. It is also useful to emphasize the importance of using all available data for both calibration and OD

37

estimation. Data, such as travel times of probe vehicles, queue conditions and lengths, can be valuable in improving the calibration and the quality of the estimated parameters.

38

Evaluation of MITSIMLab

Introduction As more and more traffic microsimulators are developed, there is a greater need to justify their use. The main reason for their application in traffic management and planning is the inability of other methods to capture important phenomena related to: the effects of ITS applications on queue dynamics; route diversion; the effects of dynamic traffic management such as route information via VMS signs; automatic incident detection and lane closure via lane use signs; etc. On the other hand a guarantee is needed to ensure that these models function something like reality, and that they correspond reasonably well with the site on which the model is based. In the case of MITSIMLab (1) an advanced microscopic traffic simulator designed to test dynamic traffic management strategies, such evaluation has taken place for applications in the Boston (MA) area. (3), (4). Since September 1999, the Stockholm City Road Authority (GFK) has decided to adopt MITSIMLab as one of their models to analyse traffic dynamics, esp. incident management, queue dynamics, dynamic traffic control. It was recognised that not only the Swedish road infrastructure, but also control logic and driver behaviour, differ greatly from their counterparts in the US. A one-year project has been undertaken to calibrate and adapt MITSIMLab to fit the conditions in and around Stockholm. Before the model could be taken into use, however, an evaluation was needed to test the suitability or resulting fit of the model to the current traffic situation in Stockholm. For GFK, certain aspects were more important than others. The applications that they have in mind for MITSIMLab in the future concern mainly the evaluation of ITS strategies such as automatic incident management, city-wide bus priority schemes, SPOT/UTOPIA (2) applications and dynamic (VMS) route and speed information, testing of ramp metering applications, and so on. This means that the model application must be validated with regard to aspects such as travel times on links, speed distributions and queue growth and dissipation.

39

Criteria The purpose of the evaluation of the MITSIMLab implementation in Stockholm was to see how well it was suited to the tasks for which it had originally been purchased. Measures considered important in accordance with the stated purpose of the package, were queue lengths, queue build-up, travel times through the network, flows and average speeds on links, and route choice. Naturally the criteria on which the package was to be evaluated would have to be based on these measures. However, not all such measures are equally suited for the purposes of evaluation. First of all, queue lengths and queue build-up are important, but both difficult to measure and highly variable from day to day even if a more qualitative general statement could be made regarding their location and average length. It is therefore not realistic to expect the micro simulation model to reproduce these types of effects exactly, although they can serve as a qualitative measure of goodness of fit. Secondly, since there was no recent and correct Origin – Destination (O/D) matrix available for the area, an approximated matrix based on link flows was created thereby limiting the use of the link flows themselves as a valid criteria for evaluation. Travel times, on the other hand, were suitable for inclusion in the evaluation criteria, since they measurable and sensitive to congestion, link speeds and flows in the network. In conclusion, the criteria selected for comparison were: 1. Flow counts 2. Travel times 3. Queue lengths

Method

Network For calibration, the “Brunnsviken” network was selected because of it’s suitability in terms of size, mix of traffic control methods, and because it contained both urban and motorway sections. For calibration, the infrastructure and signal controls were coded according to the conditions in May 1999. The base O/D matrix that was used also stems from May 1999, having been corrected for the traffic flows obtained in May 1999. For evaluation the same network was used, but in this case according to the situation in May 2000 which incorporated changes that had been made over the previous year with respect to road infrastructure, traffic control methods, etc.

40

Data collection set-up In order to collect data for comparison purposes the following criteria was established: 1. Flows: The existing structure from the Motorway Control System was completed with extra loops (see figure 2) to be able to get a good estimation of the O/D flows that serve as input to the simulation 2. Travel Times: The travel times were measured by so-called ‘floating cars’, i.e. probe cars that drive around in the network collecting data. For each marked passage spot the passage times of the floating cars were noted. 3. Queue lengths: The queue lengths were also measured by the floating cars, and complemented with aerial photographs from May 1999. See Figure 23 for locations of markings for passage points in the network, as well as locations of existing (MCS) detector loops, and extra detector loops. 1 2

Existing (MCS) detectors Passage spots Extra detectors

3 13

4 12 7

9

5

11

6

8

10

Figure 23. Brunnsviken network data collection set-up

Floating Cars Using normal vehicles in the network, passage times were noted for predefined spots. These were used to get an idea of the travel time between two consecutive passage spots during a particular period of time during the day. The floating cars were used as follows:

41

• • • • • •

Two cars per direction, circling clockwise, res. counter-clockwise through the network Passage times were recorded each time a specified point in the network was passed. Passage points were placed just before and just after major intersections in the network Estimated round-trip time was 15 minutes in non-congested traffic, 40 minutes during congested periods When a floating car joins and leaves a queue, the times are noted as well as the positions in the network. Floating car drivers received orders to follow the so-called ‘average car technique’ meaning to behave as an average driver and drive in the middle or right lane.

Detector Loops •

•

MCS detector loops on the North- and Southbound E4 road collected traffic flow data (1 min intervals). This data was logged and collected from the traffic centre (UTC). Extra loops were located by GFK at all major entry and exit points of the network, as well as between all major intersections. These loops collected flow data.

Analysis

Introduction Here the collected data is compared against the data generated from the simulation runs. In 1999 Kazi Ahmed (6) validated lane-change and acceleration models in MITSIMLab for Boston MA. A number of the notions suggested by Kazi Ahmed are also used here, such as the number of replications, and the measures of goodness of fit.

Number of replications Since MITSIM is a stochastic simulation model, the results from two or more runs with the same input data may differ. In order to get consistent and reliable predictions, the simulation needs to be replicated a certain number of times. Theoretically, on the condition that the realisations of quantities from different simulations are normally distributed, the minimum number of replications needed to obtain a certain level å of

42

accuracy with á significance for each of the quantities ys is given by the following formula:  st R =  αs / 2  yˆ ε where, yˆ s s α ε tα/2

  

2

= an unbiased estimator of ys = an estimate of the standard deviation of ys , = allowable error, = desired level of significance, = critical value of the t-distribution at a level α of significance.

In our case this value should be calculated for travel times, flows, and queue lengths, for which the most critical (highest) value of R should be taken. To get an estimate of the variance, the simulation was run 10 times. The application of the formula on the flow data resulted in R values which were lower than 10, so we continued with the output for all 10 simulations.

Goodness of fit measures Besides a graphical representation of the simulated and measured values, measures of goodness of fit can be used to quantify the relationship between the two series. A good measure to see whether the simulator is consistently over or under-predicting is the bias: 100 I y i − y i b= ∑ I i =1 y i where, I yi

= number of observations = average of measure across R replications for time-space point i

yi

= field observation of measure for time-space point i

Another measure is the Root Mean Square error Normalised (RMSN) that indicates the total percentage error of the simulator, penalising high errors at a higher rate: I

I ∑ ( yi − yi ) RMSN error =

2

i =1

I

∑y i =1

i

43

Comparison method As mentioned above, the simulated detector flows have been used to generate the O/D matrix and assignment for the MITSIM simulation runs. Therefore, technically, they cannot be used to validate the model. However, the correctness of the O/D matrix and assignment is critical not only for reproducing the flows, but also for generating the correct link speeds and travel times. Thus, before we can compare the travel times, we should see how well the simulated flows that result from the estimated O/D matrix and MITSIM assignment match their observed counterparts.

Flows As a basis for the comparison of flows, eight fifteen-minute intervals were taken. This time period was chosen based on several considerations, most importantly because the flows that were collected by the GFK detectors were aggregated to these 15-minute intervals. There were a large number of detector flows that were available for comparison, however, a large-scale comparison of flows is outside the scope of this paper. Instead the flows for a few typical spots are compared. In addition to the graphs showing these results, the bias and RMSN errors are reported.

Travel times The travel times are the main focus of the validation. However, while MITSIMLab reports stretch travel times for each passing car, there are not very many measurements of travel times from the floating cars. Moreover, since travel times generally live on a transient, increasing towards the peak hour (non-stationary) and decreasing afterwards, it not possible assume that travel times from a larger period of time are normally distributed. This prevents us from comparing these measurements against those of the simulation by statistical tests such as a Chi-squared or Kolmogorov-Smirnoff test. As an alternative it was decided to compare measured travel times per 15-minute period to the average times and their standard deviations observed in MITSIM. Even though the travel times from 15-minute periods cannot be assumed to be stable, the error is obviously much smaller and is considered to be acceptable. A shorter period for comparison would be impossible because of a lack of observations to compare such measurements.

44

B

C

A

H

E

D

F

G

Figure 24. Definition of stretches for travel time comparison

From the simulated values the means and standard deviations are calculated for the travel times for each stretch (see Figure 24) per 15-minute interval. The observed values are then compared against the mean plus or minus two times the standard deviation, and for each stretch the percentage of values within these bounds for the 15-minute periods are reported. If the values found were normally distributed (within the 15 min. periods), then it would be expected that an observation would fall within the interval with a probability of roughly 95%. In other words we would expect that roughly 95% of the observations fall within mu ±2*sd. However since it is not possible to assume that the values are normally distributed, it is necessary to resort to Chebyshev’s theorem: If a probability distribution has a mean mu and standard deviation sd, then the probability of getting a value which deviates from mu by at least k*sd is at most 1/k2 In our case k=2 so it can be assumed that at most 25% of the values should be outside the [mu-2sd, mu+2sd] interval. In other words at least 75% of the values are expected to be inside the interval. Based on the quantity and the quality of the measurements, it was decided to make this comparison for eight stretches of the network, taking four in each direction and using three to four consecutive measurement intervals. This allowed most of the missing and incorrect passage times to be corrected.

45

Comparison Results

Flows Since the detector flows were used to estimate the OD matrix, the comparison made here is for illustration purposes only. See Figure 25 for the location of the sensors in the network. The bias and RMSN errors are presented in Table 2, and Figures 26-31 show the simulated versus the measured flows in more detail. From Table 2 and the graphs in Figures 26-31 it is possible to draw a number of conclusions. In general it can be seen from the bias error that there is generally neither a large under or overestimation of the flows. The largest overestimation is found on detector 12 Southbound (Figure 29). The flows are generally 14% higher in the simulation than those actually measured. This might be due to traffic that is, in reality, turning off North prior to the detector. An underestimation of the flows by 11.8 % on location 9 Westbound (Figure 31) might indicate that a large proportion of the flows from Roslagsvägen SB (C-D) turn South in the simulation, while in reality more vehicles turn West onto Cedersdalgatan (D-A). Also, the RMSN error can be considered low, indicating that the simulated flows follow the measurements rather well. The largest error appears again at location 12 Southbound, indicating that the pattern of the simulation does not completely follow that of the measurements. In conclusion, it can be suggested that the simulated flows over these detectors correspond sufficiently well to the measurements, and therefore that the traffic volumes in the model should represent reality fairly well. 2 WB +0%

16 NB -8%

2 EB -10% 16 SB -12%

A 4 Z 7 2 .2 -11% A 4 N 7 2 .0 -8%

12 SB +14%

12 NB +9%

9 WB -12%

7 WB -6%

7 EB +1%

9 EB -1%

Figure 25. Location of compared detector flows

46

Location Bias error RMSN error 2 Westbound 0% 7% 2 Eastbound -10% 13% A4Z 72.2 (E4 Southbound) -11% 11% A4N 72.0 (E4 Northbound) -8% 9% 16 Southbound -12% 12% 16 Northbound -8% 12% 12 Southbound 14% 17% 12 Northbound 9% 11% 7 Westbound -6% 6% 7 Eastbound 1% 6% 9 Westbound -12% 12% 9 Eastbound -1% 5%

Table 2. Comparison of Flows

W B (3)

EB (4)

1 600

1 600

1 400

1 400

1 200

1 200

1 000

1 000

800

800

Actual M I T SIM

600

Actual M I T SIM

600

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0

0 06:45

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08:30

08:45

Figure 26. Location 2: Bergshamraleden E18 Westbound and Eastbound

SB (1081)

NB (1015) 1 600

1 600

1 400

1 400

1 200

1 200

1 000

1 000

800

800

A c tual M ITSIM

600

A c tual 600

400

400

200

200

0

M ITSIM

0 06:45

07:00

07:1 5

07:30

07:45

08:00

08:1 5

08:30

08:45

06:45

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Figure 27. Location E4 Southbound (A4Z 72.2) and Northbound (A4N 72.0)

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Figure 28. Location 16:Northern Roslagsvägen Southbound and Northbound

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Figure 30. Location 7: Sveavägen Westbound and Eastbound

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Figure 31. Location 9: Cedersdalgatan Westbound and Eastbound

Travel times The travel times that were measured by the floating cars are here compared to the values from the simulated floating cars. From the simulation runs all measurements of travel times were taken into account when calculating the average and standard deviation for the travel times per stretch and per 15 minute interval. For each stretch and each time interval the interval of [ì-2ó,ì+2ó] is shown in the graph, together with ì. The measurements are plotted in the same graph to illustrate the ‘goodness of fit’ indicated by the numbers in Tables 3 and 4 for the clockwise and counter-clockwise directions.

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Figure 32. Travel times section A-B. Uppsalavägen Northbound.

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Travel times Section B-C: Bergshamraleden EB 07:00 350.00

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Figure 33. Travel times section B-C. Bergshamraleden Eastbound.

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Figure 34. Travel times section C-D. Roslgsvägen Southbound

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Figure 35. Travel times section D-A. Cedersdalgatan Westbound

Stretch % inside Bias AB 88% -7% BC 78% 7% CD 53% 68% DA 23% -29%

Table 3. Comparison of Travel times in the clockwise direction.

Clockwise It can be seen that the stretches A-B (Figure 32) and B-C (Figure 33) have a fairly good fit, considering the form of the curve and variance. The values in Table 3 confirm this finding with 88% and 78% of the measurements falling within the defined interval. These stretches are relatively uncongested during the morning peak hour, which explains the flat curve. Stretch C-D (Figure 34) is especially interesting. The Roslagsvägen Southbound is normally heavily congested during the morning peak. This is shown by the steep curve in both the measurements and simulated travel times. Obviously the shape of the curve is rather well replicated, although the measurements stay high towards 8:45-9:00 while the simulated values go down. The bias of 64% and the 54 % of the measurements that fall into the defined interval should be considered with caution. While the simulation includes the buses on bus lanes, the floating car measurements are solely derived from 51

private cars that are not allowed to use those lanes. Figure 36 shows a histogram of the Roslagsvägen SB from 8:00 to 8:15. The 15% buses and taxis that use these bus lanes therefore have much shorter travel times during peak hour than the other cars. They show up clearly in the histogram as the group of travel times < 800 seconds, while the other values are much higher. Buses

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Figure 36.. Histogram of travel times on Roslagsvägen Southbound during peak quarter (8:00-8:15).

However, the cut between buses and normal cars cannot always be made, especially for the travel times of earlier periods, where the low travel times can be from either buses or normal cars. It can be concluded that the average of the MITSIM simulated values without the buses would be about 80 seconds higher. This would mean a lower bias eror, but due to lower standard deviation, there would be little change in how many values would fall inside the interval. Stretch D-A (Figure 35), the Cedersdalgatan, shows a steady underestimation of the measured values. Only 23 % of the values fall within the proposed bounds. This poor fit was also shown in the flow comparison, caused by a poor O/D flow estimation and route-choice for that location. Finally, the fact that this section consists of a roundabout and two intersections that are connected by some very short sections of road, means that the effects of the intersections dominate the behaviour of flows and travel times. The measurements from floating cars are very sensitive to such conditions.

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Figure 37. Travel times section E-F. Uppsalavägen Southbound.

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Figure 38. Travel times section F-G. Cedersdalgatan Eastbound.

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Figure 39. Travel times section G-H. Roslagsvägen Northbound.

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Figure 40. Travel times section H-E. Bergshamraleden Westbound.

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Stretch % inside Bias EF 71% 21% FG 17% 84% GH 69% 17% HE 75% 49%

Table 4. Comparison of Travel times in the counter-clockwise direction.

Counter-clockwise Section E-F Uppsalavägen Southbound, is prone to very heavy traffic. In the graph (Figure 37) both the empirical measurements and those generated by the simulation, show that travel times increase greatly as flows increase from 7:45 onwards. But while the travel times remain high for the empirical measurements, the simulation values for the last quarter (8:45-9:00) are significantly lower. The same was noticed for section CD Roslagsvägen Southbound (Figure 34). It seems that the peak continues in reality, while in the simulation the flows and travel times decrease. According to Table 4. 71% of the measurements fall within the projected interval indicating a fairly good fit, with a bias error of 21%, which is mainly caused by the under-prediction of the simulator in the last quarter. Section F-G , Cedersdalgatan Eastbound (Figure 38) looks much like section D-A, which is the same road in the Westbound direction. The travel times from the simulation are much lower than those from the measurements. Table 4 confirms this with only 17% of the measurements falling within the defined interval and a bias of 84 % meaning that the measurements are on average 84% higher than the simulated values. This rather poor fit might be caused by the same reasons as mentioned for section D-A. Possible causes include the instable nature of the short road sections between the intersections, incorrect signal settings coding, to little traffic coming in from the Uppsalavägen Southbound and too much exiting traffic turning onto Valhallavägen instead of going onto Roslagsvägen Northbound, where the friction caused by the roundabout would be much greater. The measured travel times in section G-H Roslagsvägen Northbound (Figure 39) show a larger spread than the measurements. This is probably due to outliers in the measurement data. Apart from this value the other values match rather well. So the 69% falling into the designed interval of simulated data can be considered conservative. With more measurements this would probably be higher. The bias error of 17% is also largely

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because of this outlier. As in the case of section C-D, there is a bus lane, but since we are in a more or less free-flow situation, the buses and taxies on the bus lane do not generate significantly lower travel times than the normal cars. In conclusion, it is possible to suggest that this section is well represented in the simulation. Finally section H-E Bergshamraleden Westbound (Figure 40) is an important part of our discussion. This part of the network gets heavily congested during the morning peak with queues starting at the Järva Krog intersection for traffic turning onto the Uppsalavägen (E4) Southbound (Figure 37), and growing all the way to the onramp of the Roslagsvägen Southbound, and even upwards on the Roslagsvägen southbound. This queue normally interlocks with the queue on the Roslagsvägen southbound that starts at Roslagstull. The combined queue normally grows a kilometre or more upstream of the northern boundary of the network. The graph and Table 4 indicate a fairly good fit with an underestimation of the values between 8:15 and 8:30 and to some extent even afterwards. The resulting 75% of values within the projected interval is a positive finding, but a bias value of 49% indicates a definite underestimation. As mentioned previously, the setting of the Northern boundary of the network might be the main cause for this effect. Since queues are growing upstream of this boundary it is possible to suggest that this section should have been modelled within MITSIM. Another reason might again be the bus lane on the right-hand side. Figure 41 shows the histograms of the travel times from MITSIM for two time periods. In the first histogram from 7:307:45 (Figure 41a), the travel times from buses and taxis seem indistinguishable from those from normal cars. However as the queue grows the differences increase, as can be seen in Figure 41b. where the travel times from buses and taxies are visibly lower. This period from 8:15-8:30 also shows up in the graph as the period with the biggest underestimation of travel times.

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Figure 41. Effects of buslane on Bergshamraleden Westbound on travel times. 41a. Left: 7:30-7:45

41b. Right: 8:15-8:30

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Evaluation of Queue Lengths The study period was chosen for the calculated rush hour 0730 – 0830 am, as this period proved to have the highest traffic flows in the test area Brunnsviken. From Figure 42 it can be observed that a good correlation between simulated and measured values has been obtained for the intersection Frescativägen in the southbound approach. The time and intensity of the queue build up is also very realistic. The nature of the floating car study and aerial photography allow only a small number of observations in comparison to the number of simulated.

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Figure 42. Mitsim Queue Length Comparison with Aerial Photography and Floating Car Measurements at Frescativägen

The next approach to be studied was that of the intersection Björnäsvägen (Figure 43) in the southbound direction and directly after and in line with the Frescati approach. This approach fills up very quickly in the morning rush-hour traffic and causes spill-back into the Frescati intersection, which can be observed from both Figures 42 and 43. No field data was available for this link (approx. 500m). It may be assumed that this picture of the link being completely saturated for most of the studied time period is realistic.

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Queue Lengths at Björnäsvägen

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Figure 43. Mitsim Queue Lengths at Björnäsvägen

Figures 44a and 44b represent the Bergshamraleden road section at the north end of the test site. These links are mainly very congested in the morning rush hour and over saturated for most of the rush hour period. The simulation results show queuing on the approaches (Figure 44a) that almost fills the link, but not completely while the field data reveals a queue length of 1352m, which basically means that the link is completely full.

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Mitsim Queue lengths at Bergshamraleden Aerial Snapshot Floating Car Queue Length Figure 44a. Mitsim Queue Length Comparison with Aerial Photography and Floating Car Measurements at Bergshamraleden West Bound

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Figure 44b. Aerial Photograph of the Bergshamraleden Westbound

The Northern approach from Roslagsvägen , which is the northern boundary of the simulation, shows no queue at all from the simulation, except for a short period while field data and local knowledge of the area reveals a queue length of up to 1400m and possibly more in extreme situations. This queue extends to north of the boundary of our test network. The approach (Figures 45a and 45b) at Norrtull, south bound is more difficult to compare with field measurements as there is only one aerial photo to compare it with and no good observations from the floating cars. However local knowledge and the available photograph seem to agree with the results from the simulation.

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Queue lengths at Norrtull

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Figure 45a. Mitsim Queue Length Comparison with Aerial Photography at Norrtull (traffic entering from the north)

Figure 45b. Aerial Photograph of the E4 Uppsalavägen at Norrtull

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Discussion

While we have made efforts to make this evaluation of MITSIMLab in Stockholm as precise and concise as possible, we should discuss the limitations as well. There are different kinds of problem we encountered during this validation exercise, some because of time or money limitations, some because of available equipment and some because of the nature of traffic data itself.. A common source of difficulty in validation of simulation models is the data quality. In our case we had several such problems. First of all the number of floating cars was limited and therefore the number of datapoints for comparison with the simulation as well. Although we would like to have had a larger fleet of floating cars, this would have been prohibitively expensive, as well as requiring the cooperation of a large number of people. Moreover, a too large number of –artificially inserted – floating cars would disrupt the normal flow of traffic, thereby decreasing the accuracy of the measurements. Secondly, the floating cars tend to cluster when there are queuing situations. The cars end up spending most of their time in the same queue. These queues also make the number of observations for congested areas very limited. Alternatives to the floating car method for travel time measurements include number plate registration. Due to amongst others privacy legislation this can be problematic and requires a large number of participants. It would be extremely expensive to implement. Another interesting alternative might be an experiment by mobile phones. The experiment will assess the viability of using mobile phones of road users for travel time measurements. By using the polling of the mobile phones and the known position of base stations travel times could be measured for all passing cars with a mobile phone. Should this prove reliable, legal and practical, then this would be a candidate for replacing floating cars. Another problem with data quality originates from the quality of flow counts from sensors and the associated software. They are renown to have error percentages up to 25% and a significant probability of malfunctioning. In our case a number of detectors did not report any data at all, some only worked for one day (for instance because loops get torn loose) and some reported extremely low values likely indicating an error. In addition, although we planned to measure speeds, this equipment proved not capable of measuring and /or registering speeds. Apart from the loop counts, the MCS data has been shown to be far from error-free. Since this data is the basis for estimating the OD matrix, the resulting OD matrix and traffic flows in the simulation can be expected to deviate considerably from reality. An altogether different source of difficulties was the problem of applying statistical tests to validate the simulation. Some problems are intrinsic in the nature of the data. Traffic data such as flows, speeds and especially travel times are generally changing

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greatly over time during the morning peak hour. When congestion sets in the tangent to the time series of measurements is especially steep. In addition to this non-stationary nature of the data, the consecutive time-space data points are autocorrelated. Finally, the distribution observed for travel times is non-symmetric since extremely long travel times can occur during queuing situations, but the extremely short travel times don’t. This means that the data can’t be assumed to be normally distributed. The non-normal, non-stationary and autocorrelated nature of the data means that assumptions necessary for statistical tests do not hold. The only alternative would be to acquire many data points so that the intervals for tests can be short enough for the mentioned assumptions to (approximately) hold.

Conclusion In this report we described the evaluation of the MITSIMLab simulation package applied to the Brunnsviken network in Northern Stockholm. Given the goal of GFK to use the package to analyse proposed changes to road infrastructure, traffic controls and traffic management strategies, we identified three major criteria for evaluation: flows, travel times and queues. For the datacollection, during two days an extensive set of detectors were set out to complement the data collected on the E4 by the MCS system. In addition a number of floating cars collected travel time data around the network. The comparison period was determined to be 7:00-9:00 with a 15 minute warm-up period to gradually fill the model with the required traffic volumes. Using the flow data from the detectors and a seed matrix from 1999, a new OD matrix was estimated and used for the input of traffic to the model. Several replications of runs of the simulation model were aggregated and the mean values were used for comparison with the measurements. In addition to graphs, measures of goodness of fit were calculated and used in the comparison. The comparison of flows showed a relatively good fit of the model to reality. The travel times on the other hand, showed a fairly good fit on most sections, reproducing the peaking seen in the measurements to a good level of accuracy. One of the sections where not such a good fit was achieved is the Cedersdalgatan/Sveavägen. Possible reasons include errors in route choice that in its turn maybe caused by incorrect and /or missing data. Also the coding of signals can be a source of error in the model, especially since the settings around this area change often as do the systems controlling them. This makes it difficult to determine which settings are operating at which time. The conclusion that can be drawn about the representation of queue lengths is that the Roslagsvägen section is simulated to a high level of accuracy while the Bergshamraleden section underestimates the queue length slightly. In reality there are extensive queues on the approach leading unto it, but this was beyond the boundary of

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the model. In order to model this queue the boundary of the network should have been extended to include the whole queue (about 1.5 km). Not much can be said about the Norrtull approach (due to lack of field data) only that extensive queues appear here in the morning rush hour and Mitsim shows considerable queues from the simulation. Limitations to the validation process as such were determined and discussed. Most of them rested on the limited amount of validation data, the statistical problems intrinsic in the nature of traffic data and especially travel times and errors and gaps in the collected data. It can be concluded that with respect to flows and travel times and queues, the MITSIMLab model of Brunnsviken fits the measurements rather well. An interesting note is that the effect of buslanes and buses and taxis using them can be shown clearly in the MITSIMLab model and showed up in the distribution of travel times. With the future extension of bus-priority modelling in MITSIM in mind, this indicates a promising area of application.

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Bibliography

(1) Ben-Akiva M, Koutsopoulos H N, Mishalani R G and Yang Q (1997) Simulation Laboratory for Evaluating Dynamic Traffic Management Systems, Journal of Transportation Engineering, Vol. 123, No. 4 (2) Yang Q and Koutsopoulos H N .(1996) A microscopic traffic simulator for evaluation of dynamic traffic management systems. Transportation Research-C, Vol. 4, No. 3, pp113-129 (3) Yang Q (1997) A Simulation Laboratory for Evaluation of Dynamic Traffic Management Systems, Ph.D. Thesis (Department of Civil and Environmental Engineering, Massachusetts Institute of Technology) (4) Johnson R A (1994) Miller and Freund’s probability and statistics for engineers, (Prentice-Hall) (5) Centre of Traffic Simulation (CTR) (1999) DYMO project final report, Modelling of ITS Applications, Test of four dynamic models (Centre of Traffic Simulation (CTR), Royal Institute of Technology (KTH) in co-operation with TRANSEK, ISSN 1104683X) (6) Ahmed K I (1999) Modeling Drivers' Acceleration and Lane Changing Behavior, Sc.D. Thesis, Department of Civil and Environmental Engineering (Massachusetts Institute of Technology) (8) Averill M. Law, (2000) Simulation Modeling and Analysis, Third Edition, (McGraw-Hill)

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