Queues with semi-Markovian arrivals
- 1 August 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (02), 365-379
- https://doi.org/10.1017/s0021900200032113
Abstract
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.Keywords
This publication has 5 references indexed in Scilit:
- The single server queue with Poisson input and semi-Markov service timesJournal of Applied Probability, 1966
- Markov Renewal Processes with Finitely Many StatesThe Annals of Mathematical Statistics, 1961
- Regenerative stochastic processesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1955
- Unzerlegbare, nicht negative MatrizenMathematische Zeitschrift, 1950
- Recherches sur les chaînes de Markoff: Premier MémoireActa Mathematica, 1936