Comput Syst Sci & Eng (2015) 2: 1–14 © 2015 CRL Publishing Ltd

International Journal of

Computer Systems Science & Engineering

Optimal WiMax backhauling solutions for WiFi traffic Glaucio H.S. Carvalho Faculty of Computing, Federal University of Pará, Belém, Pará, Brazil E-mail: [email protected]

WiMax network arises as one of the most prominent last mile alternatives for broadband wireless access. Offering quality of service (QoS) by design, WiMax supports advanced services while enabling wireless backhaul support for WiFi traffic. However, to successfully exploit that scenario, an effective and efficient call admission control (CAC) for WiMax and WiFi traffic should be put in place. This paper addresses this issue by formulating the CAC mechanism as a Semi-Markov Decision Process (SMDP) model and presenting a comprehensive analysis where different design aspects are critically analyzed in order to achieve the target operation. Keywords: Wireless Backhaul; WiMax; WiFi; Call Admission Control; Semi-Markov Decision Process, Decision Making Process in Telecommunications

1.

INTRODUCTION

Undoubtedly, the building of a broadband telecommunication infrastructure is a keystone in the development process in any country. Initially, service providers made use of wired-based solutions such as xDSL and T1 in this regard. Over the last decades, 2.5G and 3G, in which G stands for generation, cellular mobile networks (GSM/GPRS/EDGE, WCDMA, CDMA2000) have strongly contributed to that achievement by providing pervasive and mobile wireless access. For in-building broadband coverage - homes,offices, and public hotspot locations, WiFi (Wireless Fidelity)networks, based on IEEE 802.11 standards, became the most popular technology thanks to features such as affordable prices, easy and fast deployment, high data rates, etc. In an attempt to reach the same success, a number of municipalities and local communities invested in a WiFi ecosystems for outdoor environments such as downtowns areas, rural and under served areas. However, because of the WiFi small coverage, one soon realized that this solution lacks scalability requiring a dense deployment of access points,which made it impractical for large-scale ubiquitous deployment [1]. More recently, WiMax (Worldwide Interoperability for Microwave Access) network or IEEE 802.16 standard has received a great deal of attention in literature by providing high peak rate (up to 100 Mbps), QoS (Quality of Service) support by design,

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and wide-metropolitan-coverage area. Comparing to the wired counterpart-T1, DSL, and cable-modem, WiMax is cheaper and less time consuming to deploy [1, 2]. These characteristics are essential especially in developing countries,rural areas, and under served regions where there is a poor wired infrastructure or even a complete lack of one. In these circumstances, WiMax arises as one of the better choices to deliver broadband services. Based on previous presentation, the combination of WiFi and WiMax allows the delivery of broadband services in a large coverage area while supporting indoor users by enabling backhauling capabilities in the WiMax system [1, 3, 4].Consequently, WiFi networks may rely on ubiquitous wireless access for Internet access rather than wired solution (traditionally DSL) while a WiMax service provider may extend its coverage with highdata rates by using WiFi networks. In order to fully exploit that combination, an effective and efficient Call Admission Control (CAC) method has to be designed for WiMax radio resource optimization where the QoS profiles of both WiFi and WiMax subscribers are met. This is the main contribution of this paper. CAC is fundamentally a network QoS mechanism [5]whose the main characteristic is to provide QoS isolation for ongoing connections while controlling the admission of incoming requests.While the specific used criterion is technology-and application-dependent, generally the number of ongoing connections and bandwidth allocated to each one [6] is used to com-

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OPTIMAL WIMAX BACKHAULING SOLUTIONS FOR WIFI TRAFFIC

pute the residual wireless capacity. The design of CAC methods for a holistic wireless networks operation with the goal of taking exploiting their complementary features have been focus of some papers in literature. The synergy between UMTS/WLAN wireless networks is evaluated by simulation in [7] whose goal is to restrict the occurrences of hard handover between WLAN and UMTS cells. A two-tier wireless architecture considering UMTS and WiMax cooperation is studied in [8]. As a QoS enabler, CAC is used in the overlapping areas. The work in [9] follows the same direction. Considering a pricing standpoint, the work in[10] analyzes the GPRS/WiFi integration. The main feature of this paper is to address the radio resource allocation issue from an economic point of view. A 3D-continuous time Markov chain model is used in [11] to a CAC method that allows a service provider to manage the WiMax cell bandwidth between WiFi networks and its Subscribers Station (SS). This scheme follows the multi-threshold idea, which has been recently studied in cellular mobile networks (see [12–14]). In[3] and [15], the authors proposed a game theory-based approach to model for WiMax/WiFi integration in point-to-multi point (PMP) and mesh networks, respectively. In [16], an wireless backhaul is presented. The authors resort to the concept of multiple wireless networks to increase the backhaul capacity. A Metro-Ethernet-based solution is evaluated in [17] as a backhauling alternative for WiMax networks. The solutions aim at improving end-to-end QoS parameters. Simulation and analytical approaches are used to assess the system performance. Performance study is conducted in [18] to evaluate the application of WiMax/WiFiintegration in Malaysia. By means simulation, the authors conclude that the proposed architecture may play an important role in empowering rural areas with broadband services. In [19],a fuzzy-based vertical handoff mechanism is proposed to ensure seamless communication in WiMax/WiFi networks. The model takes into account various criteria to support the decision making as signal strength, mobile user speed and signal to noise ratio. The model is implemented in the NS software. The work in[20] follows the same direction, but using a larger set of criteria considering monetary price, power consumption,security to name a few to assist the decision making process. In this paper, we exploit the complementary features of WiMax and WiFi networks to design a holistic CAC method that ensures the backhaul support for WiFi traffic. The problem is formulated as a Semi-Markov Decision Process model whose objective is to minimize WiMax and WiFi realtime blocking probabilities while taking into consideration the preemption of ongoing data calls. Preemptive priority is a service discipline that allows a higher priority service class being directly put in service as soon as it arrives into the system [21]. This way, it arises as an important mechanism for resource assurance in communication networks. For example, the preemptive priority is often employed to keep the high performance of voice traffic [13, 22–26]. In order to mitigate the impact of the preemptive priority on data service provisioning,data service elasticity, by means a degradation and compensation mechanism [12, 13], is assumed in the proposed model.Besides, to avoid the abusive employment of the preemptive priority, a preemption cost is included in the optimal control formulation, so that by properly setting this parameter, the optimal CAC may control the relative importance of WiMax or WiFi real time calls and data calls into the system and, this way,offer different designing alternatives for

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network designers. The treatment given to the preemptive priority completely distinguishes our proposal from previous works in literature (see [27–30]), which optimize the system behavior without considering the preemptive priority.Comparing to more recent works such as [16] where the wireless backhaul is analyzed in multiple wireless system, our model still stands out since it optimizes the radio resource allocation taking into consideration the preemption operation.Despite not considering the user mobility as in [19, 20], our model may be easily extended to cover such scenario by modifying its traffic model. For instance,in a wireless cellular network, the service time in a base station is formed by the composition of call holding time and dwell time.Since both distributions are exponentially distributed, the channel holding time is also exponential distributed. In this regard, the proposed model may be quickly adjusted to provide insights in such scenario. Furthermore, the model allows specifying different bandwidth requirements for a real time service to fulfill its QoS profile. Thus, it may be used to design situation in which service providers can supply their clients with applications like: telephony, Digital TV, Tele medicine, Distance Education, Surveillance applications, Environment monitoring, and so forth. We study optimal policy for the unconstrained case and compute it by using the value iteration algorithm considering the data-transformation method under the criterion of the long-run expected average cost per time unit.

2.

WIMAX FRAMEWORK

The IEEE 802.16 standard or WiMax (Worldwide Interoperability for Microwave Access) is last mile solution for broadband wireless access. With the QoS support explicitly established in WiMax design, service providers are invited to deliver the following services [4]: Unsolicited Grant Service (UGS) for constant bit-rate (CBR) traffic, Real-Time Polling Service (rtPS) for delay-sensitive real-time traffic, Non-Real-Time Polling Service (nrtPS) for delay-tolerant traffic, and Best-Effort Service for less stringent data services applications. This QoS framework allows WiMax Service Providers to offer a variety of applications such as: FTP, HTTP, email, voice, and video by mapping each one, accordingly its QoS demands, in a particular service class. The WiMAX physical layer (PHY) is based on orthogonal frequency division multiplexing (OFDM), which enables highspeed data, video, and multimedia communications and is used by a variety of commercial broadband systems, including DSL, Wi-Fi, Digital Video Broadcast-Handheld (DVB-H), and MediaFLO [1]. OFDM is a scheme that offers good resistance to multipath and allows WiMAX to operate in non-line-of-sight conditions. At MAC level, WiMax offers two basic topologies: pointto-multi point (PMP) and mesh. The first mode resembles a cellular wireless network structure where each cell has its own Base Station that routes its traffic among its SSs. On the other hand, in the mesh mode, traffic may be routed through other SSs [31]. Thus, a PMP is a centralized topology where the BS is the system center while in a mesh topology, it is not. Since the PMP topology is the option for the last mile wireless access [2, 4], we consider it as the MAC topology in our proposed CAC method.

computer systems science & engineering

G. H.S. CARVALHO

3.

SYSTEM AND TRAFFIC ASSUMPTIONS

The PMP topology illustrated in Fig.1 prevails in the current analysis. In this array, the WiMax wireless link (represented by B radio channels) is shared by SS (WiMax) and WiFi networks traffic flows. Each traffic flow fall into one the following service classes: WiMax real time connections, WiFi real time connections, and data connections. Due to their delay-intolerant nature, WiMax and WiFi incoming request connections require constant bandwidths to fulfil their QoS profiles. Conversely, because of the elasticity, a data service tolerates variations in the service rate thanks to the TCP flow control mechanism. Additionally, as best-effort application it equally shares the residual bandwidth not used by WiMax and WiFi real time connections. In this respect, each data call service rate can change over time, depending on the number of ongoing WiMax and WiFi real time connections and data connections. Like [11], we do not differentiate WiFi data traffic from WiMax data traffic. As shown in Fig. 1 the optimal CAC resides on the WiMax BS. As usually assumed in performance evaluation of wireless networks, WiMax real time connections, WiFi real time connections, and data connections follow Poisson processes mutually independents with parameters λx , λf , and λd , respectively. Additionally, they require negative exponential service times with mean rates 1/µx , 1/µf , and 1/µd , respectively. We define ρx = λx /µx , ρf = λf /µf , and ρd = λd /µd as the WiMax real time connection, WiFi real time connection, and data connection intensities, respectively.

4.

PROPOSED CAC METHOD

Figure 2 outlines the flowchart of the proposed CAC method. As can be seen, when an event is detected by the optimal controller, it first identifies the type of traffic class. It further determines the type of event, i.e. if a call departure or an incoming service request. This assessment is necessary because the optimal CAC determines the type of action to be taken based on this knowledge. Thus, for a real-time call arrival, it verifies, based on the proposed cost function (to be defined later), whether or not the incoming service request will be accepted and apply the data call preemption. In this case, the transmission parameters (ongoing bandwidth) of data calls are updated considering the admission of a new real-time call. On the other hand, for data service, the optimal controller always accepts the incoming service request as long as there is room to accommodate it according to its bandwidth requirement. Again, the data service transmission parameters are re-computed to conform the call to the residual radio resources. After the end of their services, real-time calls and data-services leave the system releasing their radio resources. The proposed CAC method is quite general and cover the two major scenarios: i) when the WiMax Service Providers implement their own WiFi networks, which is a profitable business strategy; ii) when the WiFi networks are owned by third-party operators. In this case, a Service Level Agreement (SLA) must be established between the involved parties. The proposal model does not cover the situation in which users migrate between WiFi and WiMax networks. In fact, we

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assume that they are stationary. This consideration represents the primary WiMax deployment goal in many regions around the world, mainly, in early stages in which the goals are the last mile wireless access with QoS support. A practical example of this is the Amazonian region. The lack of telecommunications infrastructure is latent in several cities. Additionally, the cities are, in many cases, surrounded by forest and lakes. These factors contribute to their almost total isolation and with them, their hospitals, schools, government offices, and so on. Currently, in many cities in such region, a WiMax network is being deployed aiming at, in this crucial moment, solely providing the last mile access. In a second moment, it is intended to interconnect all the cities with a fiber optical backbone forming digital cities. With this infrastructure implemented, several services are envisioned to be deployed.

5. 5.1

SMDP MODEL FORMULATION State Space

The set  of all feasible states is defined as
  B  = (mx , mf , d, e) : 0 ≤ mx ≤ , Bx      B B 0 ≤ mf ≤ , 0≤d≤ , e = [0 1 2] , (1) Bf Bmin where mx , mf , and d denote the number of in-progress WiMax real time connections, WiFi real time connections, and data connections. Ongoing WiMax and WiFi real time connections require Bx and Bf radio channels to fulfill their QoS profile. In Eq. (1), [g] means the largest integer not greater than g. In the proposed CAC method, the preemptive priority provides resource assurance for (WiMax and WiFi) real time services over data calls. In order to prevent bandwidth monopolization of realtime services, we provide means of mitigating the preemption impact on the network performance. The first is degradation and compensation mechanism, which captures the elastic characteristic of data traffic. This way, a data connection can quickly finish its service by using as much radio resources as it can. Some works in literature have implemented this feature, see for example[32]; however, it is unfeasible in practice to assume that a connection can use all the available bandwidth. It is our belief that it is more suitable to assume [12, 13] that the bandwidth allocated to a data connection varies within the following limits: minimal bandwidth (Bmin ) and maximum bandwidth (Bmax ). In a nutshell, the degradation and compensation mechanism assumes that a data connection is accepted and served with the maximum bandwidth Bmax if possible. However, due to the resource dynamic occupancy, the CAC method will reassess the system load after any system state changes (motivated by call arrivals or departures) and adjust the actual bandwidth values between the minimal bandwidth and the maximum bandwidth accordingly. To model this traffic elasticity, the concept of ideal departure rate [12, 13] applies in which the real instantaneous departure rate of data connections is proportional to the actual bandwidth of each connection. So,with mx and mf real time connections into the system, each data connection will receive

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OPTIMAL WIMAX BACKHAULING SOLUTIONS FOR WIFI TRAFFIC

Figure 1 Scenario under analysis: WiMax and WiFi wireless networks integration

Figure 2 Flowchart of the proposed optimal admission control.

the bandwidth of    B − m x Bx − m f Bf bw (i) = min Bmax max 1, , d

(2)

and will be served with service rate of µd  =

bw (i) µd . Bmax

(3)

departure rate when a data connection receives the maximum bandwidth, Bmax , its mean service rate will also be maximized and equal to µd  = µd . In Eq. (1), the random variable e is the last event occurred. This information is introduced in the state space in order to define the set of possible actions in each state. Accordingly the system dynamics, the values of e ∈ e may be: 0, 1, 2; where the former means either an arrival (departure) of data connection or

It is noteworthy to realize that inside the concept of ideal

4

computer systems science & engineering

G. H.S. CARVALHO

a departure of a real time connections (WiMax or WiFi). The second means an arrival of WiMax real time connection and the latter means an arrival of WiFi real time connection.

5.2

Decision Epochs and Actions

We assume that each state means the system’s configuration just after an event occurrence and just before a decision making. The “real” decision epochs are the arrivals of real time connections, i.e., WiMax and WiFi real time connections; while the service completion epochs and arrival of data connection are defined as “fictitious” decision epochs, e = 0. In each state i ∈ , the admission controller can choose one out of the possible actions:
a = 1, e = 1, 2 and σ ≤ B A(i) = (4) a = 0, e = 0, 1, 2;  where σ = Bj + (mx + Bx + mf Bf ) is the amount of bandwidth used by real time call plus the bandwidth required by the new connection request of type j , which is determined by the value of e = 1, 2. In the set of actions a ∈ A(i), i ∈ , the action a = 0 denotes the rejection, a = 1 denotes acceptance. After admittance, a WiMax real time connection or a WiFi real time connection may preempt the bandwidth being used by data calls or even some data calls. Since there is a minimum bandwidth requirement for a data call, it is needed to determine if the remainder bandwidth is enough to accommodate all the existing data calls. Therefore, after an admission, the remainder bandwidth can support   B − mx B x − m f B f θ= , Bmin data calls with bandwidth Bmim . Thus, if d < θ , then the system can support all the existing data calls with bandwidth more than Bmim ; otherwise, ζ = d − θ data calls will be preempted and the system will reduce the bandwidth of the remainder ones θ to Bmim . Mathematically, the number of data calls into the system after the admission will be given by min(d, θ ).

5.3

Expected Time Until the Next Decision Epoch

If the system is in the state i ∈ , and the action a ∈ A(i) is chosen, then the expected time until the next decision epoch, τi (a), is given by: ti (a) =

λx + λ f + λ d +



1   mx µx + mf µf + dµd  (5)

                                

λx τi (a), i = (mx , mf , d, 1), a = 1, j = (mx + 1, mf , min(d, θ ), e), λx τi (a), i = (mx , mf , d, 1), a = 0, j = i, λf τi (a), i = (mx , mf , d, 2), a = 1, j = (mx , mf + 1, min(d, θ ), e), λf τi (a), i = (mx , mf , d, 2), a = 0, j = i, λd τi (a), i = (mx , mf , d, 0), a = 0, pij (a) = j = (m  x , mf , d + 1, e),  B−mx Bx −mf Bf   , d<   Bmin    m µ τ (a), i = (m , m a = 0,  x x i x f , d, 0),    j = (m − 1, m , d, e),  x f    mf µf τi (a), i = (mx , mf , d, 0), a = 0,     j = (mx , mf − 1, d, e),     dµd  τi (a), i = (mx , mf , d, 0), a = 0,     j = (mx , mf , d − 1, e),    0, Otherwise. (6) Due to the complexity of the proposed SMDP model, it is quite impractical to graphically represent a complete state transition diagram even for a small-scale system. Therefore, an example displaying the transitions for the states (1,3,8,0) and (1,3,8,1) ∈  is outlined in Fig. 3. As shown, the system moves from the state (1,3,8,0) to state (1,3,8,1) or (1,3,8,2) upon an arrival of a WiMax real-time connection request or a WiFi real-time connection request with probabilities λx τi (a) or λf τi (a), respectively. With probability λd τi (a), the system moves from state (1,3,8,0) to (1,3,9,0). After its completion, a WiMax (resp. WiFi) real-time connection departures and triggers a transition from the state (1,3,8,0) to (0,3,8,0) (resp. (1,2,8,0)) with probability mx µx τi (a) (resp. 3mf µf τi (a)). Similarly, a departure of a data connection with probability 8µd  τi (a) motivates a state transition to (1,3,7,0). Since the event e = 1 is a decision making epoch, the optimal CAC has to select either the action a = 0 what implies in a connection rejection or the action a = 1 that triggers the transition to the state (2,3,8,1). By using the same approach, the remaining state transitions can be similarly obtained.

5.5

Cost Function

In the proposed CAC method, the main goal is to find out a rule for maximizing the system capacity (minimizing real-time blocking probability) while controlling the application of the preemptive priority on data calls such that the long run average cost per time unit is minimal. To this end, the following cost function is proposed: Ci (a) = Cx (i, a) + Cf (i, a) + Cp (i, a),

5.4

(7)

Transition Probabilities

The state dynamic is completely specified by stating the transition probabilities among the system states. Thus, let pij (a) be the probability that in the next decision epoch the state will be j ∈  if the present state is i ∈  and the action a ∈ A(i) is chosen. For all i and j ∈ , we have the following cases:

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where Cx (i, a), Cf (i, a), and Cp (i, a) are the WiMax, WiFi real time connections blocking costs and preemption cost,respectively. These functions are computed as:
Cx (i, a) =

cx , 0

e = 1; a = 0 ∈ A(i) Otherwise

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OPTIMAL WIMAX BACKHAULING SOLUTIONS FOR WIFI TRAFFIC

Figure 3 Transition Probabilities for the states (1,3,8,0) and (1,3,81).


Cf (i, a) =

cf , 0

e = 2; a = 0 ∈ A(i) Otherwise

  ζ cpx , ζ cpf , Cp (i, a) =  0

e = 1; a = 1 ∈ A(i); ζ > 0 e = 2; a = 1 ∈ A(i); ζ > 0 Otherwise,

(8)

where the quantities cx and cf are, respectively, the immediate cost incurred whenever an incoming WiMax or WiFi real time connection (e = 1, 2) is blocked. In this paper, the preemption cost is employed as a manner to control the importance of real time services and data service accordingly the business model of the place where the WiMax/WiFinetworks will be deployed. Thus, the higher the Cp (i, a), the higher the importance of data connection into the system and vice-versa. For the sake of simplicity, an intuitive definition of Cp (i, a) is used. In our analysis, it assumed that it is proportional to the number of preempted data calls (ζ ), where cpx and cpf are the immediate costs incurred whenever an incoming WiMax or WiFi real time connections is accepted and a data connection is preempted, respectively.However, it is noteworthy that this cost might depend on complex factors such as the signaling overhead and the amount of resource re-allocated needed to run and manager the preemption operation not only in the link under analysis, but also in others where the signaling overhead traffic is transmitted, network architecture (including the Operating System), and so forth.

5.6

Data-Transformation Method and Value Iteration Algorithm

After the specification of the SMPD model, we have to convert it into a discrete time MDP model such that for each stationary policy the average cost per time unit in the discrete-time Markov model is the same as in the semi-Markov model. This approach is referred to as data-transformation method. Next, the value

6

iteration algorithm may be applied in the transformed model to get the optimal policy. It is worth mentioning that a stationary policy R, defined by the decision rule f :  → A, prescribes the action f (i) ∈ A(i) each time the system is observed in the state i ∈ . The data-transformation method is described as follows [33]: Let i, j ∈  and a ∈ A(i), choose a number τ such that: 0 < τ < min τi (a), i,a

(9)

and redefine the process according to the following procedure: ¯ = ,  ¯ = A(i), i ∈ , ¯ A(i) Ci (a) ¯ ¯ a ∈ A(i), C¯ i (a) = , i ∈ , (10) τi (a)  τ ¯ ¯ a ∈ A(i), i  = j, i ∈ , τi (a) pij (a),

p¯ij (a) = τ τ ¯ ¯ a ∈ A(i), i = j, i ∈ , τi (a) pij (a) + − τi (a) , in which the notation i¯ means the converted component. After turning the continuous time SMDP model into a discrete time MDP model, the value iteration algorithm, outlined in the Algorithm 1, is applied to obtain the optimal policy [33]. When the value iteration algorithm stops, after finitely many iterations, the policy R(n), whose average cost function is given by gi (R(n)), satisfies: 0≤

gi (R(n)) − g ∗ ≤ ε, g∗

(11)

where g ∗ denotes the minimal average cost per time unit and ε is the tolerance used to stop the algorithm.

computer systems science & engineering

G. H.S. CARVALHO

Algorithm 1 Value Interation Algorithm Require: , pij (a), A(i), Ci (a), τi (a), τ , ε 0) For each i ∈ , set V0 (i) as Eq. 14 and set n ← 1. 0 ≤ V0 (i) ≤ min a

Ci (a) , τi (a)

(12)

1) For each i ∈ , compute Vn (i) by: 

    C (a) τ τ i Vn (i) = min  pij (a)Vn−1 (j ) + 1 − + Vn−1 (i) a∈A(i) τi (a) τi (a) τi (a)

(13)

j ∈

Let R(n) be a stationary policy whose actions minimize the right-hand side of Eq. (1.5). 2) Compute the bounds mn = min{Vn (i) − Vn−1 (i) and Mn = max{Vn (i) − Vn−1 (i)}}. The algorithm stops with policy R(n) if 0 ≤

Mn −mn mn

≤ ε.

Otherwise, go to Step 3. 3) n ← n + 1 and go to step 1.

6.

PERFORMANCE METRICS

U=

In this section, we derive the QoS performance metrics used to assess the system performance. The mean carried real-time connection (WiMax or WiFi) traffic is computed as: Oe =



(λx + λf + λd + mx µx + mf µf + dµd  ) πi

1 B



(mx Bx + mf Bf + dbw (i))πi .

i∈ mx > 0; mf > 0; d>0

The mean number of preempted data connections is given by:

i∈ e = 1, 2 a = 1 ∈ A(i)

Npd =

where π is the continuous time Markov chain steady state probability distribution vector under the optimal policy. Giving Oe , the real-time connection blocking probabilities are expressed as Oe , λe

(15)

where Pbrt depends on the e value. Thus, if e = 1 then Pbrt will be the WiMax real time connection blocking probability and λe = λx . The data connection blocking probability, Eq. (18), is given by the probability that an incoming data connection faces less than the minimum bandwidth available. 

Pdc = i∈:d≥

B−m

x Bx −mf Bf Bmin

πi .

(16)

The bandwidth utilization is defined as the ratio between the mean number of occupied channels and the total number of channels, i.e.,

vol 30 no 2 March 2015



ζ πi

(18)

i ∈ ; e = 1, 2; a = 1 ∈ A(i) ζ >0

(14)

Pbrt = 1 −

(17)

7.

RESULTS

In this section we present numerical results to assess the QoS metrics of the proposed optimal CAC for WiMax and WiFi integration developed previously. First, we present an analysis discussing how variations on the WiMax and WiFi real time connections blocking costs can impact the system performance. After that, we evaluate the effect of different WiMax and WiFi real time connections blocking costs and preemption costs on system performance. We finish the analysis by presenting a study of how variations on the preemption costs and WiMax and WiFi real time bandwidth requirements impact on system performance. Unless specified otherwise, we use the following setting in analyzing the proposed CAC method: B = 30, µ1x = µ1f = µ1d = 30 minutes, ρx = ρf = ρd = 4, Bx = Bf = 2 radio channels, [Bmin , Bmax ] = [1, 3] radio channels, and ε = 10−12 .

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OPTIMAL WIMAX BACKHAULING SOLUTIONS FOR WIFI TRAFFIC

7.1

Impact of WiMax and WiFi real time connections blocking costs on system performance

In order to characterize how WiMax and WiFi real time connections blocking costs impact on the system performance, we vary cf and cx in the range of 0.25 to 4 each and keep cpx = cpf = 1.5. This way, we can observe the optimal admission behavior in terms of QoS metrics when cf and cx approach cpx and cpf . As outlined in Fig. 4a, the proper selection of cx and cf greatly affects the system performance in such a way that for large cf and small cx , the higher the WiMax real time connection blocking probability and vice-versa. A similar analysis may be conducted to explain Fig. 4b. It is interesting to note that in each figure there is a little peak on real time blocking probability when cx and cf approach cpx and cpf . It happens because the optimal CAC method decides to reject incoming real time connection requests in order to favor ongoing data calls, keeping them into the system. This effect is not observed as real time connections blocking costs become higher than preemption costs. Figure 5 shows that the data connection blocking probability and the bandwidth utilization are higher when cx and cf approach cpx and cpf . It occurs because more ongoing data calls are kept in the system for this setting as one may realize in Fig. 6a. The optimal cost increases as the real time blocking costs increase, Fig.6b. A careful analysis from Fig. 4 to Fig. 6 supplies different design alternatives and provides network designers with valuable hints. For instance, if the design aims at deploying a WiMax network in a place with many WiFi networks and where the data service demand is high, then a possible network setup might be: cf > cx and cpx = cpf ≈ cx . We can note that this configuration privileges WiFi real time connections, which is justified by the fact that IEEE 802.11(WiFi) standard does not specify any QoS support and IEEE 802.11(WiMax) does. Furthermore, it keeps whenever possible data connections in progress.

7.2

Impact of WiMax and WiFi real time connections blocking costs and preemption costs on system performance

In doing this evaluation, we set cx = cf and cpx = cpf and vary them in the range of 0.25 to 4. Figure 7 leads to a straight forward conclusion that, in general, high cx and cf values and low cpx and cpf values yield in low real time blocking probabilities and vice-versa. As presented in Fig. 8a, the data connection blocking probability is highest when cx and cf approach cpx and cpf . It happens because in this case, the optimal CAC method balances between to accept WiMax/WiFi real time calls and to keep the ongoing data connections into the system. Thus, once an incoming data call will solely use idle radio resources (that are very few in this configuration) its blocking probability increases. A joint analysis of Fig. 8b and Fig. 9a shows that when data connections are kept into the system, (cpx = cpf > cx = cf ), the bandwidth utilization is maximized. Finally, Fig. 9b shows that the optimal cost increases as cx , cf , cpx , and cpf increase.

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One more time, the analysis under consideration provides useful insights in network designing. In this case study, it is noteworthy that the costs (blocking and preemption) suitable selection may produce results substantially distinct. For instance, working in the region cx = cf = (3 or 4) > cpx = cpf = (1 or 2) favors WiMax and WiFi real time service performances, but leads to data service QoS degradation and lowest channel utilization (due to the preemption). We must highlight that, although this configuration lowers data connection probability, an accepted data call, in this case, has more change to be preempted. The opposite case provides better results for the system (utilization) and data connection, but penalizes WiMax and WiFi real time service performances. Operating in the region cpx = cpf ≈ cx = cf seems to be the better option, except for the optimal cost and data connection blocking probability. However, data call blocking probability may be lowered by relaxing the data call bandwidth requirement condition, i.e., if the network designer chooses [Bmin , Bmax ] = [1, 5], for example; the data call service time will be reduced and the radio channel will be quickly released. These fresh free channels may then be assigned to the new data connection requests. This analysis illustrates how the proper selection of cpx and cpf values can affect the system performance. Particularly, it may establish a tradeoff between the data service and WiMax/WiFi real time performances. In terms of performance evaluation, this adjustment is another design option offered by the proposed model, supporting the network designer during the network planning and tuning phases in which the parameters must be optimally set up to improve the network performance.

7.3

Impact of preemption costs and WiMax and WiFi real time bandwidth requirements on system performance

In this study, we set cpx = cpf and vary them in the range of 0.25 to 4. Also, we set Bx = Bf and vary them in the range of 1 to 5. As shown in Fig. 10, WiMax and WiFi real time blocking probabilities are sensitive to real time bandwidth requirements and preemption costs variations except when Bx = Bf = 1. This result may be explained by looking at Fig. 12a, in which we can observe that with Bx = Bf = 1 the number of preempted data connections is low regardless of cpx and cpf values, i.e., the impact of the real-time services acceptance on the data services performance is small. Thus, the optimal CAC method opts to accept the incoming WiMax and WiFi real-time connections. In Fig. 11a it is possible to note that data connection blocking probability increases as Bx and Bf increase and becomes highest when the preemption costs are minimum and Bx = Bf = 5. As we can see, it happens because cx = cf = 2 are greater than the preemption costs and the real-time bandwidth requirements are highest, so that the optimal CAC method decides to accept incoming WiMax and WiFi real time calls. As a consequence, fewer channels are left for incoming data connections, leading to an increase in its blocking probability. Figure 11b and 12b show that the radio bandwidth utilization and the optimal cost are higher for higher real time bandwidth requirements. Figure 12a reveals that the mean number of preempted data connections is highest for higher real time bandwidth requirements and smaller preemption costs (lower than cx and cf ).

computer systems science & engineering

G. H.S. CARVALHO

(b) (a) Figure 4 Real Time Connection Blocking Probabilities versus cx and cf : (a) WiMax (b) WiFi

(b) (a) Figure 5 Performance Metrics versus cx and cf : (a) Data connection blocking probability b) Utilization.

(b) (a) Figure 6 Performance Metrics versus cx and cf : (a) Number of preempted data calls (b) Optimal Cost.

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OPTIMAL WIMAX BACKHAULING SOLUTIONS FOR WIFI TRAFFIC

(b) (a) Figure 7 Real Time Connection Blocking Probabilities versus cx , cf , cpx , and cpf : (a) WiMax (b) WiFi.

(a)

(b)

Figure 8 Performance Metrics versus cx , cf , cpx , and cpf : (a) Data connection blocking probability (b) Utilization.

(a)

(b)

Figure 9 Performance Metrics versus cx , cf , cpx , and cpf : (a) Number of preempted data calls (b) Optimal Cost.

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computer systems science & engineering

G. H.S. CARVALHO

(a)

(b)

Figure 10 Real Time Connection Blocking Probabilities versus Bx , Bf and cpx , cpf : (a) WiMax (b) WiFi.

(a)

(b)

Figure 11 Performance Metrics versus Bx , Bf and cpx , cpf : (a) Data connection blocking probability (b) Utilization.

(a)

(b)

Figure 12 Performance Metrics versus Bx , Bf and cpx , cpf : (a) Number of preempted data calls (b) Optimal Cost.

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OPTIMAL WIMAX BACKHAULING SOLUTIONS FOR WIFI TRAFFIC

This experiment may lead to a very useful case study. Particularly, it confronts the network performance in terms of real time bandwidth requirements against the preemption costs. It means that the scenery under investigation may cover situations in which the WiMax service provider offers all sort of applications ranging from traditional voice-oriented communication services to high-intensive bandwidth video-based application. At the same time, depending on the preemption costs values, the data service may or not play a central role in the business model. As a wireless last mile technology, WiMax network is very suitable for regions in development process such as Amazonian region or other parts of the world. In these places applications like Distance Education and Telemedicine are vital, and, this way, the network designer must design the WiMax CAC mechanism taking these applications into account. This way, if both real time service and data services are important in the business model, then a feasible set up might be cpx = cpf ≈ Bx = Bf ≈ 2.This configuration results in a good performance tradeoff between the two service classes.

8.

CONCLUSION

An optimal CAC method, based on the Semi-Markov Decision Process framework, has been presented. The proposed CAC method was designed to support wireless backhaul for WiFi traffic while optimally deciding whether accepting WiMax and WiFi real time calls taking data calls preemption into account.A comprehensive analysis of the numerical results has shown that by appropriately setting the cost function parameters it is possible to achieve satisfactory QoS level in the wireless backhaul. Additionally, the proposed cost function is flexible enough to cover different business mode scenarios. For future works, we plan to extend the proposed optimal CAC method to support not only WiFi networks, but also femtocells.

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