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Level crossing analysis of priority queues and a conservation identity for vacation models
Author(s) -
Shanthikumar J. George
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198912)36:6<797::aid-nav3220360605>3.0.co;2-w
Subject(s) - queue , computer science , identity (music) , operations research , mathematics , computer network , physics , acoustics
The two purposes of this article are to illustrate the power and simplicity of level crossing analysis and to present a conservation identity for M / G /1 priority queues with server vacations. To illustrate the use of level crossing analysis we apply it to preemptive (resume) priority M / G /1 queues with single‐ and multiple‐server vacations considered by Kella and Yechiali (1986) and to non‐preemptive priority M / M / c queues considered by Kella and Yechiali (1985). The conservation identity presented here states that the ratios of mean waiting times in an M / G /1 queue with and without server vacation policies are independent of the service discipline for first come first served, shortest processing time, shortest processing time within generations and non‐preemptive priority service disciplines.