Two queues in series with a finite, intermediate waitingroom

Marcel F. Neuts

87 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

A service unit I, with Poisson input and general service times is in series with a unit II, with negative-exponential service times. The intermediate waitingroom can accomodate at most k persons and a customer cannot leave unit I when the waitingroom is full. The paper shows that this system of queues can be studied in terms of an imbedded semi-Markov process. Equations for the time dependent distributions are given, but the main emphasis of the paper is on the equilibrium conditions and on asymptotic results.

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References

1963Introduction to the Theory of Queues.1967A General Class of Bulk Queues with Poisson Input 1965A Sequence of Two Servers with No Intermediate Queue 1966The single server queue with Poisson input and semi-Markov service times

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