Sojourn times in closed queueing networks

Frank P. Kelly · Philip K. Pollett

79 citations0/0 files storedAdvances in Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Petri Nets in System Modeling

Abstract

This paper obtains the stationary joint distribution of a customer's sojourn times along an overtake-free path in a closed multiclass Jackson network. The distribution has a simple representation in terms of the product form distribution for the state of the network at an arrival instant.

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References

1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1985Queues and Point Processes.1975Parametric Analysis of Queuing Networks 1981The Distribution of Queuing Network States at Input and Output Instants 1957Waiting Times When Queues are in Tandem 1980Stationary state probabilities at arrival instants for closed queueing networks with multiple types of customers 1962Mathematical Methods in the Theory of Queueing 1980Sojourn times and the overtaking condition in Jacksonian networks

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2002Passage time distributions in large Markov chains 1991Some new results on queueing networks with batch movement 1990Laplace transform inversion and passage-time distributions in Markov processes 1983Asymptotic expansions of moments of the waiting time in closed and open processor-sharing systems with multiple job classes 1993The mathematics of product form queuing networks 1992Regenerative closed queueing networks

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