An Elementary Method of Solution of the Queueing Problem with a Single Server and Constant Parameters
- 1 January 1956
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 18 (1) , 125-128
- https://doi.org/10.1111/j.2517-6161.1956.tb00217.x
Abstract
Summary: The queueing problem, in which the input and service time have independent negative exponential distributions with constant parameters, is studied for the single server case. The “simple” problem with constant parameters, dealt with first by W. Ledermann and G. E. H. Reuter (1954), and by A. B. Clarke (1953) was considered by these writers in relation to far more general problems, and their solutions are accordingly less simple than is possible in the special case: This special case has recently been investigated by Bailey (1954) by means of a generating function technique. In view of its importance I propose to obtain the result directly: it will be found in terms of Bessel Functions in the form obtained by Dr. A. B. Clarke. He has pointed out there that this solution is easily adapted to the case where the ratio of the exponential parameters for the two waiting times is constant but where each parameter is not necessarily constant.This publication has 2 references indexed in Scilit:
- A Continuous Time Treatment of a Simple Queue using Generating FunctionsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1954
- Spectral theory for the differential equations of simple birth and death processesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1954