Queues with semi-Markovian arrivals

A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue s...

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Bibliographic Details
Published in:Journal of applied probability 1967-08, Vol.4 (2), p.365-379
Main Author: Çinlar, Erhan
Format: Article
Language:English
Subjects:
Absolute value
Adjoints
Eigenvalues
Eigenvectors
Ergodic theory
Markov chains
Matrices
Network servers
Polynomials
Research Papers
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Summary:A queueing system with a single server is considered. There are a finite number of types of customers, and the types of successive arrivals form a Markov chain. Further, the nth interarrival time has a distribution function which may depend on the types of the nth and the n–1th arrivals. The queue size, waiting time, and busy period processes are investigated. Both transient and limiting results are given.
ISSN:0021-9002
1475-6072
DOI:10.2307/3212030