Statistical Multiplexing, Bandwidth Allocation Strategies and Connection Admission Control in ATM Networks *

Statistical Multiplexing, Bandwidth Allocation Strategies and Connection Admission Control in ATM Networks* N.M. Mitrou, K.P. Kontovasilis+, H. Kröner...
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Statistical Multiplexing, Bandwidth Allocation Strategies and Connection Admission Control in ATM Networks* N.M. Mitrou, K.P. Kontovasilis+, H. Kröner++, V.B. Iversen+++ Abstract This paper gives a brief description and the main results of work done within the RACE 1022 project on bandwidth allocation and Connection Admission Control in ATM-based networks. Additionally, and before presenting these two main issues, some important facets of statistical multiplexing are highlighted. The key question which is answered by a bandwidth allocation algorithm is "how much bandwidth is required by a group of connections (e.g., within a VP), with certain traffic characteristics, in a certain multiplexing environment". Answers to this question are given for specific traffic classes and mixing conditions. The advantages and the limitations of the proposed strategies are indicated. In cases where the proposed bandwidth allocation strategies fail to fulfil the specified objectives (e.g., in highly heterogeneous traffic mixes), sophisticated CAC algorithms are required. In particular, the hierarchically organised CAC strategy implemented within the RACE 1022 ATD Technology Testbed will be described in detail. This CAC scheme is based on a simple real-time processing algorithm which provides a quick acceptance decision. This decision will be refined by a precise but numerically complex background algorithm. Simulation studies confirm the potential of this concept.

1 Introduction The exploitation of the salient features of the ATM, such as the flexibility to provide (potentially) for any bit rate and to support services with divergent traffic characteristics and Quality of Service (QoS) requirements, has its price: a rich set of rather sophisticated Traffic and Congestion Control (T&CC) functions, [7], is required to cope with the divergent demands of connections, while optimising network resource utilisation through statistical multiplexing. Developing such a set of control functions is not an easy job. Some first difficulties arise from the fact that we do not exactly know the services of the future, nor their traffic characteristics, of course. A second obstacle is related to the nature of the statistical multiplexing and the rather complicated problem of maximising the multiplexing gain, while maintaining the desired QoS for each of the multiplexed connections. Thirdly, this problem has to be answered on-line within a very limited time, during the connection admission phase.

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This work was partially funded by the EEC (project R1022, "Technology for ATD") National Technical University of Athens, Division of Computer Science, Heroon Polytechniou 9, GR-15773 Zografou 9, Greece ++ University of Stuttgart, Institute of Communications Switching and Data Technics, Seidenstr. 36, D-70174 Stuttgart, FRG +++ Technical University of Denmark, Institut for Teleteknik, Build. 343, DK-2800 Lyngby, Denmark

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Of primary importance within the T&CC function set are the Connection Admission Control (CAC) and the Network Resource Management (NRM) procedures. CAC addresses those control functions that give an answer to a connect request whether there are sufficient resources to support the new connection or not. NRM, on the other hand stands between Network Provisioning (NP) (a long-term configuration of the network resources, mainly at the physical level, e.g. assigning trunk capacity between nodes) and CAC, by providing for a short- or medium-term planning of resource allocation to classes of connections in a way that the CAC within a particular class becomes much simpler. As the main mechanism of grouping connections together in an ATM network is by using Virtual Paths (VPs), establishing VPs and allocating bandwidth to them is the primary NRM function. The hierarchy of NP, NRM and CAC functions, as well as their interaction is shown schematically in Figure 1. Routing is also shown in this figure, as part of all three levels of the hierarchy. This paper aims at presenting in short the work done within the RACE 1022 project on CAC and Bandwidth Allocation and giving the basic results out of this work [7]. Section 2 highlights some important facets of statistical multiplexing, which can be useful for understanding the basic properties of this issue and devising sensible and efficient traffic control strategies. Some guidelines for buffer dimensioning are also included in this section. Section 3 deals with the problem of bandwidth allocation to VPs. Central in this section is the linear or effective-ratebased approach, which can be used in nearly homogeneous traffic mixes. Alternative strategies are suggested for non-homogeneous mixes. The main question which is related to bandwidth allocation and answered here is "how much bandwidth is required by a group of connections (e.g., within a VP) of a certain traffic class", or its inverse, i.e. "how many connections of a certain class can be accommodated within a VP, which has been allocated a certain amount of bandwidth". The application of bandwidth allocation to VPs simplifies CAC. There are cases, however, where resource management alone is not sufficient to fulfil simultaneously both objectives, i.e. respecting the QoS for each connection and maximising the multiplexing gain. The heterogeneous traffic mix within a VP, or among different VPs that share the same link, is an example where the proposed bandwidth allocation strategies might be either, too optimistic (e.g. the linear approach), or too pessimistic (the partitioning approach). In such cases a sophisticated CAC algorithm is required on a connection-by-connection basis. Section 4 presents a hierarchically organised CAC strategy comprising two different computation levels. The first level of the CAC function accepts a connection request if the bit rate, which is required to maintain an adequate network performance for all connections in progress including the new one, remains below the link capacity. This required bit rate is the sum of the bit rate necessary for the new connection request and the bit rate which has been already allocated to the connections in progress. The allocated bit rate is refined by the precise but complex background algorithm which is based on the so-called convolution approach. The performance characteristics of three different schemes will be compared. Another approach based on tables which contain the admissible number of connections for each traffic class will be discussed, too. This table which provides the basis for the admission decision of the first level algorithm will be adjusted to the current load situation by the background algorithm.

3 Network Provisioning (4)

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Figure 1: Relation between NP, NRM and CAC functions

2 Statistical Multiplexing in ATM Networks Statistical Multiplexing (SM) of traffic streams addresses the sharing of a resource among many statistically varying sources, where the peak demand of all of them may exceed the available resource capacity. Such a peak, however, should occur with a small probability. The SM is quantified by means of the multiplexing gain, defined as the ratio of the resource utilisation with SM and the resource utilisation with peak demand allocation to each source. Exploitation of the statistical multiplexing gain is of prime importance for the successful introduction of ATM networks, because it is the only way to obtain efficient operation under significant and diverse traffic demands. Understanding the multiplexer's behaviour is a basic prerequisite for designing efficient traffic control procedures with the above objective. An ATM multiplexer is equipped with two resources: the output link capacity and the buffer space. A variety of different approaches for the analysis of its performance have been proposed in the literature [7,7,7,7,7,7,7,14,7,7,7,7,7,7,7,7,7,7,7]. They can be divided into three general categories: (i) Exact methods, based on the formulation of the (discrete) state space and the description of the dynamics (usually) by a Markov chain, which can be solved numerically or otherwise. In this class belong also variants of the above methods that introduce some kind of approximation, either at the problem formulation stage or at the computation stages. (ii) Fluidflow and Asymptotic methods, which ignore the short-term dynamics arising from the discrete nature of the cells and their asynchronous arrivals, taking only into account the long-term (burst level) statistics. (iii) Decomposition methods, which use different sub-models for the different time scales. Exact methods, apart from very few cases of trivially small systems, suffer from huge state spaces, with all the subsequent difficulties it means for getting a solution (long computation times, instability of the results, etc.). In many cases, even the formulation of a solvable Markov chain is questionable. Fluid-flow methods ignore the discrete nature of the cells and the cell-level fluctuations and consider each stream as a continuous flow of information [7,7,7,7,7]. The case of homogeneous ON/OFF traffic is solved analytically in [7], while the more general case of Markov Modulated Rate Processes is handled in [7]. On the extreme of this approach, asymptotic methods offer a substantial simplification by keeping only one term (or a few terms) of the

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spectral decomposition sum, corresponding to the dominant eigenvalue(s) [7,7]. The drawback with such an approach is that we are not able to mark a range out where the fluid-flow model (or the dominant terms of it) offer the required accuracy. Finally, the decomposition methods [7,7,7,7,7,7,7], stand between the two approaches and, usually, give rather accurate results in all ranges. However, as in the fluid-flow (including the asymptotic) approach, it is difficult to delineate the different sub-regions where one submodel prevails with the required accuracy. In the remainder of this section, analytical results will be presented which indicate the characteristic performance behaviour of a statistical multiplexer. Furthermore, some basic guidelines for the traffic control framework will be deduced. The results within Figure 1(a) refer to a multiplexing of 8 ON/OFF (sporadic) sources. These sources generate a geometrically distributed number of equally spaced cells (referring to a certain peak bit rate) during a burst period. Bursts are separated by silence phases with a geometric distribution. Within Figure 1(a), the peak to mean bit rate ratio has been chosen as 5, the peak to link bit rate ratio is fixed to 0.25, and the mean number of cells within a burst, denoted by V, is varying. A more detailed description of the modelling, the related analytical methods, and the results illustrated within Fig. 1(a) can be found in [7]. Similar results can be obtained for a multiplexing of general MMDP sources: the results depicted in Fig. 1(b) correspond to a multiplexing of eight 3-state MMDP traffic sources. These sources alternate between three different states, referring to the bit rates 3, 6, and 30 Mbit/s. The net link capacity has been chosen as 135.85 Mbit/s. Within each state a geometrically distributed number of cells is generated. The mean state durations have been fixed to 70, 20, and 10 ms. The transitions among the different states are governed by a Markov chain. If a state transition occurs, another state will be selected with equal probability (=0.5).

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Grafikname: Erstellt in: Erstellt am:

Title: FIG_2 Creator: Picasso, Kimon CreationDate: 10-MAR-1992

(a)

(b) Figure 1: Cell loss probability vs. buffer size for (a) sporadic and (b) 3-state MMDP sources

The results demonstrate that, if we exclude the trivial case of Continuous Bit Rate (CBR) sources, at least two scales are present in the queueing behaviour of an ATM multiplexer: the cell level, due to the discrete nature of the ATM cells and their asynchronous arrivals, and the burst level, due to the rate variations of the information sources. These two scales are distinguishable if the bursts are quite larger than one cell. The queuing behaviour in the first region (resulting from short-term fluctuations of the cell arrival process) can be well approximated by elementary queuing models such as M/D/1-S, GEO/D/1-S or (N×D)/D/1-S models [7,7,7,7,7,7]. The results from an M/D/1-S queuing model provides an upper bound for cell scale fluctuations, because the short-term variations of the arrival and queueing process include a slight negative correlation [7]. The long-term queuing behaviour (governed by the burst level characteristics of the traffic streams) is covered by a fluid flow approximation [7,7,7,7,7,7,7,7,7,7,7] and dominates for long buffers.

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Obviously, the asymptotic slope of the fluid flow part of the curves depends on the mean burst length and tends to zero if the mean burst length approaches infinity (cf. Fig. 1(a)). Furthermore, from the different slopes referring to short- and long-term fluctuations, it can be concluded that a buffering of a short-term overload is possible with small buffers, whereas the buffering of a longterm overload requires larger buffers. This is due to the difference of the time scales referring to burst and cell level fluctuations. From these results it becomes obvious, that the gain resulting from statistical multiplexing can be subdivided into two different parts: One part can be obtained from the mutual compensation of the bit rate requirements of different connections. This gain can be even achieved for long burst and silence durations and represents the significant part of the multiplexing gain if the source peak bit rate to link bit rate ratio is small. If the buffers are able to buffer long-term fluctuations caused by the burst level fluctuations of the traffic streams (number of cells within a burst less than queue size), there is an additional gain resulting from buffering of bursts or parts of bursts. This gain is only significant for large buffers and high peak bit rates of the traffic sources. Furthermore, this gain depends on the distribution of burst and silence periods as well as their correlation [7]. However, the declaration and enforcement of these parameters seems not to be feasible. It has to be stressed that both components are necessary to determine the multiplexing performance for any buffer size. Indeed, even if the long-term dynamics are so slow-varying that could be considered constant for any buffer size of practical interest, they are necessary for the determination of the maximal multiplexing gain that can be achieved. This point is illustrated by the examples depicted in the following two figures. log(CPDF(x)) 0

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Figure 2: Complementary probability distribution function of the buffer contents for a multiplexing of sporadic sources (a) with varying burstiness vs. number of sources (N) (b) with varying peak rate vs. number of sources (N)

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Figure 2(a) considers the superposition of a number of identical sporadic sources each of which featuring a very large mean burst length. V=1000 and a peak to link rate ratio of c/C=0.1. The number of sources multiplexed, N, varies along with the burstiness of each source so that the total mean load remains fixed to 0.24. Plots of the overflow probability versus buffer size, as derived from the fluid approximation, for various configurations are presented, along with the M/D/1-S curve (which applies to all curves, since the mean load of the superposition is kept fixed). It is obvious that the variation of the parameters results in widely differing potential for multiplexing gain. This is illustrated by the different values for the probability of overflow that can be achieved with reasonable buffer sizes, the particular values being located close to the intersection of the curves for the long-term dynamics with the common curve of the fastdynamics. A similar situation is depicted in Figure 2(b). There, V is as in Figure 2(a), the burstiness is kept fixed to 10 and the number of sources varies with the peak-to-link rate ratio, so that the mean load remains fixed to 0.24 again. The results are of the same flavour as in Figure 2(a). The conclusion is that a control mechanism should take into account both fast and slow dynamics, if a reliable criterion for the multiplexing performance is to be achieved. Another point that needs clarification is related to the belief that when the multiplexed streams feature very long burst lengths (compared to the buffer size), then the burst-level dynamics remain practically invariant for all buffer sizes of interest and, hence, can be well represented by the overload probability as derived from the stationary bit-rate distribution of the aggregate stream (computable by convolution by requiring only peak and mean rates). This argumentation is usually safe on the grounds of homogeneous multiplexing (where all burst lengths are large) but may produce erroneous results in a heterogeneous multiplexing environment. This is illustrated in Figure 3 where mixes of traffic belonging to two classes of sporadic sources are considered. The mean and peak rates are kept the same for both classes which differ widely in the mean burst lengths of the sources in them. The total number of sources is kept fixed for all plots, resulting in a constant total mean load. Notice that while the same curve of M/D/1-S would apply to all curves and same holds true for the overload probability as derived from the stationary bit rate distribution, the behaviour of the mixes varies widely even for short buffer sizes (relative to the highest mean burst length).

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Figure 3: Traffic mixes composed from two-classes traffic From this figure it can be concluded that the fluid flow approximation results in an additional multiplexing gain besides the multiplexing gain exploited by the convolution approach even if some of the sources exhibit large bursts, if at least some of the burst lengths of the superposed sources are small. This phenomenon appears when the total load of the sources with the very large bursts is small enough so that the part of the input stream with the smaller burst sizes dominate in the long-term dynamics of the superposition. In particular, this gain is relevant if the small bursts are smaller than the buffer size as stated previously.

Buffer Dimensioning Buffer dimensioning is part of the Network Provisioning functions. The results presented in the previous section imply that in some cases of large mean burst lengths, only the short-term dynamics can be accommodated by reasonable buffer sizes. Dimensioning via the M/D/1-S model can then be applied. This is performed by fixing an upper bound for the maximum admissible value for the mean load of the aggregate stream and using the M/D/1-S model to find the smallest buffer that can accommodate this load. It is then the responsibility of the control functions to ensure that this limit is not exceeded and that the long term dynamics respect the network performance. At the same time, it must be taken into account that the end-to-end delay should not exceed a maximum tolerable limit beyond which service quality would be distorted. This poses an upper bound to the buffer size, otherwise complicated time-priority mechanisms would have to be introduced to avoid unacceptable delays for delay sensitive services. It happens, though, that in many cases the dimensioning via the M/D/1-S method results in smaller buffers than what is imposed by the delay requirements. An alternative approach is to determine the buffer size by the delay (and maybe other technological) constraints to an upper limit. Then M/D/1-S can be used to determine the maximum load that can be fed to the multiplexer without violating the network performance. Then, the control functions should have to assure that this limit is not exceeded (control of the fast dynamics) and apply a criterion to ensure that the long term dynamics are such that the

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network performance requirements are respected. This alternative approach may result in somewhat larger buffers that can be used to obtain a better multiplexing gain in cases like the one of Figure 3. The trade-off between the costs of larger buffers and smaller link requirements is in benefit of the second method, if significantly better multiplexing gain values are obtained, compared with the M/D/1-S dimensioning method. Otherwise, the first method is preferable. This latter issue can only be answered when loading conditions and profiles can be anticipated.

3 Bandwidth Allocation Strategies In this section, the problem of bandwidth allocation to connections (or groups of connections, e.g. VPs), which are multiplexed on the same link, is considered. Bandwidth allocation to a VP can be conceived either as a calculation procedure, which answers the question "how much bandwidth is required by the VP in order to maintain a certain QoS (cell loss probability or delay percentile)" and decides whether this bandwidth is available on the link, or even further, as a physical implementation that offers the VP ATM slots at the required rate. The latter may require special multiplexing or switching hardware, possibly supporting priorities (if the multiplexed VPs have different QoS requirements), which is not considered here. Central in our consideration is the linear or effective-rate-based approach to bandwidth allocation, which, if applicable, extremely simplifies the problem of Connection Admission Control (CAC). The main idea behind the notion of an 'Effective Rate (ER)' is the representation of the bandwidth requirements of a source in a single figure, which, once found, would be used for a simple CAC scheme in an add-and-compare, circuit-switched-like fashion. Despite this very simple outline of the ER principle, a full development of the idea presents some difficult problems. Firstly, it is not a figure that characterises a traffic stream by itself. It depends not only on the traffic characteristics, but also on the multiplexing environment (link capacity, buffer space, traffic homogeneity conditions) as well as on the required QoS. Secondly, given the above dependencies, efficient methods for the ER calculation under particular multiplexing conditions should be devised. The advantages and the limitations of an effective-rate based approach to bandwidth allocation is the subject of paragraph 3.2. Before embarking on that, however, some preliminary material is presented in the next section, 3.1.

3.1 Definition, Properties and Calculation of the Effective Rate (ER) Several definitions of the ER are found in the literature [7,7,7,7,7], differing in the multiplexer model (bufferless or with buffers) and/or the analysis method used (fluid flow approximation, discrete-space approaches, etc.). Here we follow the developments in [7] by considering the more general multiplexing model, i.e. taking into account the buffer, and by using the fluid-flow approximation for its performance analysis. This specialisation, however, does not affect the definition lines, nor it harms the generality of the respective bandwidth allocation methods. For the sake of completeness, we outline here the basic assumptions, the definition and the properties of the ER. For more details see [7]. Modelling and analysis assumptions: Suppose that the multiplexer is fed by a homogeneous traffic, consisting of N independent and statistically identical streams, each with a mean rate r

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and a peak rate c. The condition for the existence of a non-trivial Complementary Probability Distribution Function (CPDF) for the queue length (not zero, nor 1) is that the output rate, C, is between the total mean and the total peak of the aggregate input stream, i.e. Nr

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