Single server queues with modified service mechanisms
- 1 December 1962
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 2 (4) , 499-507
- https://doi.org/10.1017/s144678870002749x
Abstract
Summary: This paper considers a generalisation of the queueing system M/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.Keywords
This publication has 3 references indexed in Scilit:
- A probability limit theorem with application to a generalisation of queueing theoryActa Mathematica Hungarica, 1959
- Investigation of waiting time problems by reduction to Markov processesActa Mathematica Hungarica, 1955
- The theory of queues with a single serverMathematical Proceedings of the Cambridge Philosophical Society, 1952