Hostname: page-component-6766d58669-bp2c4 Total loading time: 0 Render date: 2026-05-23T11:40:07.019Z Has data issue: false hasContentIssue false
  • English
  • Français

The slow server problem

Published online by Cambridge University Press:  14 July 2016

Michael Rubinovitch
Michael Rubinovitch*
Affiliation:
Technion — Israel Institute of Technology
*
∗ Postal address: Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

The problem is what to do with a slow server in a service facility which has fast and slow servers. Should the slow server be used to render service, or is it better not to use it at all? Simple models for answering this question are formulated and studied.

Keywords

QUEUESMULTISERVER QUEUESHETEROGENEOUS SERVERS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 1 , March 1985 , pp. 205 - 213
Copyright
Copyright © Applied Probability Trust 1985 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

Research partly carried out while the author was visiting Northwestern University.

References

[1] Bell, C. E. and Stidham, S. (1983) Individual versus social optimization in the allocation of customers to alternative servers. Management Sci. 29, 831–839.Google Scholar
[2] Cohen, J. W. and Boxma, O. J. (1983) Boundary Value Problems in Queueing System Analysis. North-Holland, Amsterdam.Google Scholar
[3] Hirshleifer, J. (1971) The private and social value of information and the reward of inventive activities. American Econom. Rev. 61, 561–574.Google Scholar
[4] Moder, J. J. and Phillips, C. R. (1962) Queuing with fixed and variable channels. Operat. Res. 10, 218–231.Google Scholar
[5] Neuts, M. F. and Takahashi, Y. (1981) Asymptotic behavior of the stationary distribution in the GI/PH/c queue with heterogeneous servers. Z. Wahrscheinlichkeitsth. 57, 441–452.Google Scholar
[6] Rubinovitch, M. (1985) Queues with stalling. J. Appl. Prob. 22.Google Scholar
[7] Saaty, L. S. (1961) Elements of Queuing Theory. McGraw-Hill, New York.Google Scholar
[8] Singh, V. P. (1973) Queue-dependent servers. J. Engineering Math. 7, 123–126.CrossRefGoogle Scholar
[9] Stidham, S. (1974) A last word on L = ?W. Operat. Res. 22, 417–421.Google Scholar
[10] Walrand, J. (1983) A note on 'Optimal control of queuing systems with two heterogeneous servers. Technical Report, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley.Google Scholar
[11] Yu, O. S. (1977) The steady state solution of a heterogeneous-server queue with Erlang service times. TIMS Studies in Management Sciences 7, 199–213.Google Scholar