Conditional stochastic decompositions in the M/M/c queue with server vacations

Naishuo Tian · Quan‐Lin Li · Jinhua Gao

69 citations0/0 files storedStochastic Models

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

Abstract

We consider the M/M/c queue with server multiple vacations, where each of the c servers leaves for a vacation of an exponentially distributed duration when it finds no waiting units in line. If the server returns to an empty waiting line, it immediately takes another vacation. This paper is concerned with the upper triangular structure of the rate matrix R and the determination of the stationary distributions of queue length and waiting time. The emphasis is on obtaining the conditional stochastic decompositions of the stationary queue length and waiting time conditioned by the event , where denotes the event that all of the c servers are busy

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References

1984Matrix-Geometric Solutions to Stochastic Models 1986Queueing systems with vacations ? A survey 1985Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations 1990A single-server queue with server vacations and a class of non-renewal arrival processes 1976An M/M/s Queue With Servers’ Vacations 1985A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times

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2003Analysis of Queueing Systems with Synchronous Single Vacation for Some Servers 2016Exact solutions for M/M/c/Setup queues 2014Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward 2022A multi-station unreliable machine model with working vacation policy and customers’ impatience 2013Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward 2005Analysis of multi-server queue with a single vacation (e, d)-policy 2020Analysis and Performance Evaluation of Markovian Feedback Multi-Server Queueing Model with Vacation and Impatience

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