A Discrete Queue with the Markovian Arrival Process and Phase Type Primary and Secondary Services
Document Type
Article
Publication Date
1994
Publication Title
Stochastic Models
Abstract
A discrete time queueing model with Markovian arrival process in which jobs require primary and possibly secondary service, is analysed. Under the assumptions of infinite waiting room for the primary queue and no waiting room for the secondary queue we show that the steady state queue length density is of the matrix-geometric type. Stationary waiting time distribution of an arriving job is derived explicitly. Efficient algorithmic procedures for the computation of the rate matrix and the waiting time distribution are given.
Volume
10
Issue
2
First Page
437
Last Page
451
DOI
10.1080/15326349408807303
ISSN
Print ISSN: 1532-6349 Online ISSN: 1532-4214
Rights
© 1994 Taylor & Francis
Recommended Citation
Sule, Attahiru Alfa and Chakravarthy, Srinivas R., "A Discrete Queue with the Markovian Arrival Process and Phase Type Primary and Secondary Services" (1994). Industrial & Manufacturing Engineering Publications. 92.
https://digitalcommons.kettering.edu/industrialmanuf_eng_facultypubs/92
