exists and has the product form: N ~(~) = lri~i(xi) i=1 (2) [4] E. Gelenbe. "G-networks with instantaneous customer movement". Journal of Applied Probability, 30 (3), 742-748, 1993. [5] Erol Gelenbe. "G-Networks with signals and batch removal". Probability in the Engineering and lnformatonal Sciences, 7, pp 335-342, 1993. [6] E. Gelenbe. "G-networks: An unifying model for queuing networks and neural networks". Annals of Operations Research, Vol. 48, No. 1-4, pp 433-461, 1994. [7] J.M. Fourneau, E. Gelenbe, R. Suros. "G-networks with multiple classes of positive and negative customers". Theoretical Computer Science, Vol. 155 (1996), pp.141-156. [8] E. Gelenbe, A. Labed. "G-networks with multiple classes of signals and positive customers". European Journal of Operations Research, Vol. 108 (2), pp. 293-305, July 1998. [9] M. Pinedo, X. Chao, M. Miyazawa. "Queuing Networks: Customers, Signals and Product Form Solutions", J. Wiley, 1999. where the marginal probabilifies ~i follow a geometric distribution of rate Pi. References [ 1] E. Gelenbe. "Queuing networks with negative and posifive customers". Journal of Applied Probability, Vol. 28, 656663 (1991). [2] E. Gelenbe, P. Glynn, K. Sigman. "Queues with negative arrivals". Journal of Applied Probability, Vol. 28, pp 245-250, 1991. [3] E. Gelenbe, M. Schassberger. "Stability of product form G-Networks". Probability in the Engineering and Informational Sciences, 6, pp 271-276, 1992. Queueing Analysis for Polling and Prioritized Service of Aggregated Regenerative Variable Rate ON-OFF Traffic Sources Michael Shalmon University of Quebec INRS -Telecommunications 1 Technical Overview We examine polling and priority service of aggregated variable rate ON-OFF regenerative traffic sources (M-G'V) where regenerative means that the source process regenerates at any instant inside an OFF period. The polling and priority service of the aggregates is relevant to IP differentiated services. The service within an aggregate is assumed to be FCFS. We also assume, for analysis purposes, that the service release is continuous (fluid approximation) or slotted and that each ON rate is never smaller than the service rate. The aggregate of M-G*V sources is also M-G*V. We examine first how to characterise the ON period of the aggregate, how to calculate the mgf of the output ON period for a single aggregate, and how to carry out the FCFS queueing analysis within an aggregate. The analysis is based on sample path reductions to an M/G/1 queue and we carry it out in important special cases. We then examine polling and priority service of several aggregates. The analysis is based on sample path decompositions for foreground/background service of M-G*V sources. The output of a multiplexor of M-G*V sources is M-G'D, where D points to the deterministic rate of the (fluid, slotted) output. By iterating, the (endogenous) traffic on each link of a unidirectional tree multiplexing with equal (more generally non increasing) link capacities is MG*D. We present reduction and regenerative properties of the network andshow how the analysis at an isolated station extends to the multiplexing network We present both moment generating functions and tail probabilities of the delays.

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