A Queueing Problem in Which Customers Have Different Service Distributions

T. W. R. Collings

Journal of the Royal Statistical Society Series C, 1974, vol. 23, issue 1, 75-82

Abstract: A single‐server queue is examined whose customers can be categorized into k groups. For the ith group : (1) Arrivals follow a Poisson distribution, the average arrival rate per unit time being λi. (2) The service time follows the exponential distribution with average service time equal to 1/μi. Using a method of “cuts”, the recurrence relations between states of the queueing system are examined. The equilibrium probabilities of queue size are found and it is shown that the approximation of a group of exponential service distributions by a single exponential distribution, having a mean equal to that of the group, always underestimates the mean queue size.

Date: 1974
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.2307/2347057

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssc:v:23:y:1974:i:1:p:75-82

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9876

Access Statistics for this article

Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith

More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().