Vacation models in discrete time

被引:46
作者
Alfa, AS [1 ]
机构
[1] Univ Manitoba, Dept Elect & Comp Engn, Winnipeg, MB R3T 5V6, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
discrete time; matrix-geometric method; matrix-product problem; vacation queues; gated and ungated systems;
D O I
10.1023/A:1024028722553
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
A class of single server vacation queues which have single arrivals and non-batch service is considered in discrete time. It is shown that provided the interarrival, service, vacation, and server operational times can be cast with Markov-based representation then this class of vacation model can be studied as a matrix-geometric or a matrix-product problem-both in the matrix-analytic family-thereby allowing us to use well established results from Neuts(1981). Most importantly it is shown that using discrete time approach to study some vacation models is more appropriate and makes the models much more algorithmically tractable. An example is a vacation model in which the server visits the queue for a limited duration. The paper focuses mainly on single arrival and single unit service systems which result in quasi-birth-and-death processes. The results presented in this paper are applicable to all this class of vacation queues provided the interarrival, service, vacation, and operational times can be represented by a finite state Markov chain.
引用
收藏
页码:5 / 30
页数:26
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