A Relation between Queue-Length Distributions during Server Vacations in Queues with Batch Arrivals, Batch Services, or Multiclass Arrivals: An Extension of Burke’s Theorem

Kilhwan Kim

doi:10.17485/ijst/2015/v8i25/80226

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A Relation between Queue-Length Distributions during Server Vacations in Queues with Batch Arrivals, Batch Services, or Multiclass Arrivals: An Extension of Burke’s Theorem

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i25/80226

Year: 2015, Volume: 8, Issue: 25, Pages: 1-5

Original Article

A Relation between Queue-Length Distributions during Server Vacations in Queues with Batch Arrivals, Batch Services, or Multiclass Arrivals: An Extension of Burke’s Theorem

Kilhwan Kim^*

Department of Management Engineering, Sangmyung University, Republic of Korea; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

This paper presents a relation between queue-length distributions during vacations and those at vacation start and end times, in M/G/1 vacation queues with batch arrivals, batch services or multi-class arrivals. In order to obtain the relation, we develop a new approach that extends Burke’s theorem to queues with batch arrivals, batch services or multi-class services. We also give an example to demonstrate how to apply the proposed relation to the analysis of such a queue.
Keywords: Batch Arrivals and Services, Burke’s Theorem, Multi-class Arrivals, Queue-length Distributions, Vacation Queues