The main contributions of this paper are two-fold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing system's capacity as determined by the number of admissible sources for given cell loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on Large Deviations theory. The main assumption is that the sources are Markovian and time-reversible. Our approximation to the steady state buffer distribution is called "Chernoff-Dominant Eigenvalue" since one parameter is obtained from Chernoff's theorem and t...

We propose a new way for evaluating the performance of packet switching communication networks under a fixed (session based) routing strategy. Our approach is based on properly bounding the probability distribution functions of the system input processes. The bounds we suggest, which are decaying exponentials, possess three convenient properties: When the inputs to an isolated network element are all bounded, they result in bounded outputs, and assure that the delays and queues in this element have exponentially decaying distributions; In some network settings bounded inputs result in bounded outputs; Natural traffic processes can be shown to satisfy such bounds. Consequently, our method enables the analysis of various previously intractable setups. We provide sufficient conditions for the stability of such networks, and derive upper bounds for the interesting parameters of network performance. 1 Introduction In this paper we consider data communication networks, and the problem of ev...

Even though ATM seems to be clearly the wave of the future, one performance analysis indicates that the combination of stringent performance requirements (e.g., 10 - 9 cell blocking probabilities), moderate-size buffers and highly bursty traffic will require that the utilization of the network be quite low. That performance analysis is based on asymptotic decay rates of steady-state distributions used to develop a concept of effective bandwidths for connection admission control. However, we have developed an exact numerical algorithm that shows that the effective-bandwidth approximation can overestimate the target small blocking probabilities by several orders of magnitude when there are many sources that are more bursty than Poisson. The bad news is that the appealing simple connection-admissioncontrol algorithm using effective bandwidths based solely on tailprobability asymptotic decay rates may actually not be as effective as many have hoped. The good news is that the statistical multiplexing gain on ATM networks may actually be higher than some have feared. For one example, thought to be realistic, our analysis indicates that the network actually can support twice as many sources as predicted by the effectivebandwidth approximation. That discrepancy occurs because for a large number of bursty sources the asymptotic constant in the tail probability exponential asymptote is extremely small. That in turn can be explained by the observation that the asymptotic constant decays exponentially in the number of sources when the sources are scaled to keep the total arrival rate fixed. We also show that the effective-bandwidth approximation is not always conservative. Specifically, for sources less bursty than Poisson, the asymptotic constant grows exponentially in the numbe...

Consider an aggregate arrival process A N obtained by multiplexing N On-Off processes with exponential Off periods of rate and subexponential On periods ø on . As N goes to infinity, with N ! , A N approaches an M=G=1 type process. Both for finite and infinite N , we obtain the asymptotic characterization of the arrival process activity period. Using these results we investigate a fluid queue with the limiting M/G/1 arrival process A 1 t and capacity c. When On periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q P t observed at the beginning of the arrival process activity periods P[Q P t ? x] ¸ r + ae \Gamma c c \Gamma ae Z 1 x=(r+ae\Gammac) P[ø on ? u]du x !1; where ae = EA 1 t ! c; r (c r) is the rate at which the fluid is arriving during an On period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions on On periods than reg...

This paper demonstrates a new, efficient, and general approach for providing end-to-end performance guarantees in integrated services networks. This is achieved by modeling a traffic source with a family of bounding interval-dependent (BIND) random variables and by using a rate-controlled service discipline inside the network. The traffic model stochastically bounds the number of bits sent over time intervals of different length. The model captures different source behavior over different time scales by making the bounding distribution an explicit function of the interval length. The service discipline, RCSP, has the priority queueing mechanisms necessary to provide performance guarantees in integrated services networks. In addition, RCSP provides the means for efficiently extending the results from a single switch to a network of arbitrary topology. These techniques are derived analytically and then demonstrated with numerical examples. 1 This research was supported by the National ...

Over the last few years, a substantial number of call admission control (CAC) schemes have been proposed for ATM networks. In this article, we review the salient features of some of these algorithms. Also, we quantitatively compare the performance of three of these schemes.

Abstract—Network performance evaluation through traditional packetlevel simulation is becoming increasingly difficult as today’s networks grow in scale along many dimensions. As a consequence, fluid simulation has been proposed to cope with the size and complexity of such systems. This study focuses on analyzing and comparing the relative efficiencies of fluid simulation and packet-level simulation for several network scenarios. We use the “simulation event ” rate to measure the computational effort of the simulators and show that this measure is both adequate and accurate. For some scenarios, we derive analytical results for the simulation event rate and identify the major factors that contribute to the simulation event rate. Among these factors, the “ripple effect ” is very important since it can significantly increase the fluid simulation event rate. For a tandem queueing system, we identify the boundary condition to establish regions where one simulation paradigm is more efficient than the other. Flow aggregation is considered as a technique to reduce the impact of the “ripple effect ” in fluid simulation. We also show that WFQ scheduling discipline can limit the “ripple effect”, making fluid simulation particularly well suited for WFQ models. Our results show that tradeoffs between parameters of a network model determines the most efficient simulation approach. Keywords—fluid simulation, performance evaluation, traffic model I.

We consider an ATM system with an architecture which is designed to accommodate users with very different quality of service requirements. In the base case with only two services, sources which require low loss belong to a High Priority class, and share a FCFS buffer, which has priority access to the trunk. A Low Priority class of sources with typically less stringent requirements on loss have a separate FCFS buffer, which receives the time-varying, residual bandwidth, if any, of the trunk. By administering admission control and restricting the combination of sources to an admissible set, the service guarantees for both classes may be satisfied. The sources are bursty and stochastic fluid models are used to handle burst-scale congestion effects. Our contributions are: (i) we develop simple, fast and robust analytic approximations for the queue distributions in the two buffers; (ii) for admission control, we calculate the admissible set by using our analytic approximations and find that...

We address the issue of call acceptance and routing in ATM networks. Our goal is to design an algorithm that guarantees bounds on the fraction of cells lost by a call. The method we propose for call acceptance and routing does not require models describing the traffic. Each switch estimates the additional fraction of cells that would be lost if new calls were routed through the switch. The routing algorithm uses these estimates. The estimates are obtained by monitoring the switch operations and extrapolating to the situation where more calls are routed through the switch. The extrapolation is justified by a scaling property. To reduce the variance of the estimates, the switches calculate the cell loss that would occur with virtual buffers. A way to choose the sizes of the virtual buffers in order to minimize the variance is discussed. Thus, the switches constantly estimate their spare capacity. Simulations were performed using Markov fluid sources to test the validity of our approach. ...

We consider the efficient estimation, via simulation, of very low buffer overflow probabilities in certain acyclic ATM queueing networks. We apply the theory of effective bandwidths and Markov additive processes to derive an asymptotically optimal simulation scheme for estimating such probabilities for a single queue with multiple independent sources, each of which may be either a Markov modulated process or an autoregressive processes. This result extends earlier work on queues with either independent arrivals or with a single Markov modulated arrival source. The results are then extended to estimating loss probabilities for intree networks of such queues. Experimental results show that the method can provide many orders of magnitude reduction in variance in complex queueing systems that are not amenable to analysis.