Packet Loss in Finite - Bu ered Voice Multiplexers 1

In this paper we examine three di erent approximation techniques for modeling packet loss in nite-bu er voice multiplexers. The performance models studied di er primarily in the manner in which the superposition of the voice sources (i.e., the arrival process) is modeled. The rst approach models the superimposed voice sources as a renewal process and performance calculations are based only on the rst two moments of the renewal process. The second approach is based on modeling the superimposed voice sources as a Markov Modulated Poisson Process (MMPP). Our choice of parameters for the MMPP attempts to capture aspects of the arrival process in an alternate, more intuitive, manner than previously proposed approaches for determining the MMPP parameters and is shown to compute loss more accurately. Finally, we also evaluate a uid ow approximation for computing packet loss. For all three approaches, we consider as a unifying example, the case of multiplexing voice sources over a T1-rate link. The main conclusion of this paper is that both the new MMPP model examined here and the uid ow approximation can provide accurate loss predictions for parameter ranges of practical interest; these predictions are also shown to be many orders of magnitude better than modeling the superimposed voice sources simply as a Poisson process. We also discuss the problem of modeling bu er over ow for general arrival processes and also consider modeling approaches for analyzing nite-bu er multiplexers with general arrival and service processes in a network environment. 1 This work was supported in part by the O ce of Naval Research under contract N00014-87-K-304, the Defense Advanced Research Projects Agency under contract NAG2-578 and an NSF equipment grant, CERDCR 8500332. 2 Dept. of Elect. and Comp. Engg., UMASS, Amherst. 3 COINS Dept., UMASS, Amherst.