Efficient simulation of delay threshold probabilities in ATM switches with heterogeneous traffic

Akyamac, Ahmet A.; Townsend, J.K.

doi:10.1109/icc.1997.610062

Cited by 3 publications

(15 citation statements)

References 9 publications

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“…Here, we assume that MPl is the entry point into the switch and MP2 is the exit point from the switch. Thus, in this context, the two-point CDV defined in Section 2 is identical to the delay threshold probability considered in [8]. Since we assumed that the routing within the switch is instantaneous, the delay between points M A and MP2 is a result of the queueing.…”

Section: S I M U L a T I O N Proceduresmentioning

confidence: 97%

“…The randomness in the simulation is in the connection In [8], we developed efficient simulation methods to estimate the aggregate delay threshold probability for heterogeneous traffic consisting of two classes, namely CBR and VBR, using the same ATM switch model shown in Fig. 1.…”

Section: S I M U L a T I O N Proceduresmentioning

confidence: 99%

“…MC simulation is not feasible due t o the very low probabilities involved. In [8], we developed a three-part IS simulation procedure to efficiently estimate PTH. We use the simulation procedure in [8] t o form the estimate the aggregate delay threshold probability, P .…”

Section: S I M U L a T I O N Proceduresmentioning

confidence: 99%

“…Since we assumed that the routing within the switch is instantaneous, the delay between points M A and MP2 is a result of the queueing. We use the techniques developed in [8] to generate the two-point CDV for the individual classes. Note that we consider the two-point CDV for both the CBR and VBR classes.…”

Section: S I M U L a T I O N Proceduresmentioning

confidence: 99%

“…Thus, we use Importance Sampling (IS) as a means of generating efficient simulations. For the 2-Point CDV results, we extend the techniques we used previously in [8] for the case of aggregate delay threshold probabilities with heterogeneous traffic. For the 1-Point CDV results, we present a new IS procedure to generate efficient simulations.…”

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confidence: 97%

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Efficient simulation of rare jitter probabilities in ATM switches

Akyamac

Townsend²

GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record

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A b s t r a c t The ATM Forum has defined two different types of cell delay variation (CDV) measures: The 1-Point CDV, which is a measure of jitter, is typically specified for constant bit rate (CBR) sources and the 2-Point CDV, which can be specified for both CBR and variable bit rate (VBR) sources. In this paper, we model traffic using the ATM Forum standardized traffic descriptors and consider dispersion as a measure of jitter. The events associated with excessive jitter in ATM networks are typically rare (< IOv6), hence Monte Carlo simulation is not feasible. We extend our previous work on remote delay quantiles for heterogeneous systems to generate efficient simulation techniques using Importance Sampling t o estimate the 2-Point CDV for mixed CBR and VBR sources. Subsequently, we present a novel Importance Sampling simulation methodology to estimate the 1-Point CDV for CBR sources in the presence of background VBR traffic. For both cases, we observe from experimental results that the improvement in simulation efficiency is inversely proportional to the probability being estimated 1. Introduction Cell Delay Variation (CDV), or jitter, is an important Quality of Service (QoS) measure that will be provided in Asynchronous Transfer Mode (ATM) Networks. The ATM Forum [l] has defined two different types of CDV measures: The 1-Point CDV is typically specified for constant bit rate (CBR) sources and the 2-Point CDV can be specified for both CBR and variable bit rate (VBR) sources. The events associated with excessive jitter in ATM networks are typically rare-we focus on probabilities on the order of lo-' and below.In this paper, we consider cell delay variation through a single stage ATM switch with CBR traffic multiplexed with background VBR traffic. We use the ATM Forum connection traffic descriptors to generate 1-Point CDV results for CBR traffic in the presence of background VBR traffic and 2-Point CDV results for mixed CBR and VBR traffic. These descriptors are the peak cell rate, (Mbps), and the maximum burst duration, B (cells), a t the peak rate.Cell delay variation has been studied before in the literature. The departure process of VBR cells has been considered in [2]. CBR sources multiplexed with Possion background VBR traffic are considered in [3, 41, where jitter is defined as the tail probability of the queueing delay, which corresponds to the 2-Point CDV. The Poisson assumption is not realistic for bursty traffic sources, such as the ones in ATM. Approximate solutions are given for more sophisticated 2-state Markov models in [5]. The above do not employ the ATM Forum standardized traffic descriptors, which are used in [6] t o generate tail probabilities. (Mbps), the mean cell rate, -~ 'This research was supported by the Center for Advanced Computing and Communication, North Carolina State University.But, as in the above, the service rate is assumed to be equal to the transmission rate of a cell. The 1-Point CDV definition is used in [7], which assumes VBR traffic to consist of independent and identica...

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Section: S I M U L a T I O N Proceduresmentioning

confidence: 97%

Section: S I M U L a T I O N Proceduresmentioning

confidence: 99%

Section: S I M U L a T I O N Proceduresmentioning

confidence: 99%

Section: S I M U L a T I O N Proceduresmentioning

confidence: 99%

mentioning

confidence: 97%

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Efficient simulation of rare jitter probabilities in ATM switches

Akyamac

Townsend²

GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record

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Efficient simulation of QoS in ATM switches using connection traffic descriptors

Akyamac

Freebersyser

Townsend

1999

Performance Evaluation

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Conditional importance sampling and its application to ATM switch analysis

Akyamac

Townsend²

ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated With SUPERCOMM'98 (Cat. No.98CH362

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In communication systems and networks, important performance measures include the error or fault probabilities related to the inability of the system to sustain a desirable operating state. These probabilities are typically low, in the range of 10 ;6 or less. In many cases, it is not possible to nd analytical expressions for such probabilities. Monte Carlo simulation quickly becomes intractable due to the low probabilities involved, although Importance Sampling (IS) techniques have been used as a means of increasing simulation e ciency. P arametric IS methods are not very e ective in cases where the input processes are characterized by uniform input distributions (e.g., random delays), which arise frequently in communication systems and networks. In this paper, we present a conditional IS scheme for systems with input processes that can be characterized by uniform input distributions. The scheme adaptively modi es an initial biasing strategy as samples are taken and also incorporates a problem speci c component that enables the algorithm to be applied to a diverse set of problems. The overall approach i s m o r e e e c t i v e than parametrically biasing the uniform input distributions. We use the conditional biasing algorithm to estimate rare jitter probabilities in ATM switches for CBR sources multiplexed with heterogeneous background VBR and CBR sources. For the experimental systems considered, we observe that the improvement in simulation e ciency is inversely proportional to the probability being estimated. 1

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Efficient simulation of delay threshold probabilities in ATM switches with heterogeneous traffic

Cited by 3 publications

References 9 publications

Efficient simulation of rare jitter probabilities in ATM switches

Efficient simulation of rare jitter probabilities in ATM switches

Efficient simulation of QoS in ATM switches using connection traffic descriptors

Conditional importance sampling and its application to ATM switch analysis

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