The Remaining Busy Period of a Finite Queue

Terrell J. Harris

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

Abstract

In the M/G/1/N queuing system where no more than N < ∞ customers are allowed in the system, define the remaining busy period from state i = 0, 1, …, N as the time spent in transition from state i to state 0, i.e., until the server becomes idle for the first time. The purpose of this paper is to derive the Laplace-Stieltjes transform of the distribution of this time and the generating function of the number of customers served in this time.

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References

1963Introduction to the Theory of Queues.1967Stream of Overflows from a Finite Queue

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1985On the busy-period distributions ofM/G/1/Kqueues by state-dependent arrivals and FCFS/LCFS-P service disciplines 2008Consecutive customer losses in regular and oscillating M X /G/1/n systems 2006Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems 2008Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates

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