Time dependence of queues with semi-Markovian services
- 1 August 1967
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 4 (2) , 356-364
- https://doi.org/10.2307/3212029
Abstract
A single server queueing system with Poisson input is considered. There are a finite number of types of customers and the service time of the nth customers depends on the types of the nth and the (n – l)th customers. The time dependence of the queue size process will be studied, (it will be clear how the methods of the paper can be applied to other processes of interest,) and limiting as well as transient results will be 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
- Stationary Waiting-Time Distributions for Single-Server QueuesThe Annals of Mathematical Statistics, 1962
- 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