On the Effect of Finite Buffer Truncation in a Two-Node Jackson Network

Yutaka Sakuma · Masakiyo Miyazawa

15 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

Abstract

We consider a two-node Jackson network in which the buffer of node 1 is truncated. Our interest is in the limit of the tail decay rate of the queue-length distribution of node 2 when the buffer size of node 1 goes to infinity, provided that the stability condition of the unlimited network is satisfied. We show that there can be three different cases for the limit. This generalizes some recent results obtained for the tandem Jackson network. Special cases and some numerical examples are also presented.

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References

2014Introduction to Stochastic Processes 1984Matrix-Geometric Solutions to Stochastic Models 1957Networks of Waiting Lines 1985Matrix-geometric solutions in stochastic models 2004The stationary tail asymptotics in the GI/G/1-type queue with countably many background states 2004Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process 2001GEOMETRIC DECAY OF THE STEADY-STATE PROBABILITIES IN A QUASI-BIRTH-AND-DEATH PROCESS WITH A COUNTABLE NUMBER OF PHASES 1999Asymptotics of first passage times for random walk in an orthant

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