A UNIFIED QUEUE LENGTH FORMULA FOR BMAP/G/1 QUEUE WITH GENERALIZED VACATIONS

Seok Ho Chang · Tetsuya Takine · Kyung Chul Chae · Ho Woo Lee

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

The main purpose of this article is to demonstrate a unified queue length formula for the BMAP/G/1 queue with generalized server vacations. We also present two unified formulas; one for the distribution of the workload, and the other for the joint distribution of the queue length and the remaining service time. Some factorizations, which are previously known for M/G/1 queues with vacations and for MAP/G/1 queue with multiple vacations, are now recast in this new framework. Further, based on these formulas, we provide general recursions for the performance measures of interest.

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References

1986Queueing systems with vacations ? A survey 1991New results on the single server queue with a batch markovian arrival process 1995Queueing analysis: A foundation of performance evaluation 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 1987Pseudo-conservation laws in cyclic-service systems 2005The BMAP/G/1 queue: A tutorial 1994The workload in theMAP/G/1 queue with state-dependent services:its application to a queue with preemptive resume priority

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