Heavy-Traffic Limits for Queues with Many Exponential Servers

Shlomo Halfin and Ward Whitt
Additional contact information
Shlomo Halfin: Bell Laboratories, Holmdel, New Jersey
Ward Whitt: Bell Laboratories, Holmdel, New Jersey

Operations Research, 1981, vol. 29, issue 3, 567-588

Abstract: Two different kinds of heavy-traffic limit theorems have been proved for s -server queues. The first kind involves a sequence of queueing systems having a fixed number of servers with an associated sequence of traffic intensities that converges to the critical value of one from below. The second kind, which is often not thought of as heavy traffic, involves a sequence of queueing systems in which the associated sequences of arrival rates and numbers of servers go to infinity while the service time distributions and the traffic intensities remain fixed, with the traffic intensities being less than the critical value of one. In each case the sequence of random variables depicting the steady-state number of customers waiting or being served diverges to infinity but converges to a nondegenerate limit after appropriate normalization. However, in an important respect neither procedure adequately represents a typical queueing system in practice because in the (heavy-traffic) limit an arriving customer is either almost certain to be delayed (first procedure) or almost certain not to be delayed (second procedure). Hence, we consider a sequence of ( GI / M / S ) systems in which the traffic intensities converge to one from below, the arrival rates and the numbers of servers go to infinity, but the steady-state probabilities that all servers are busy are held fixed. The limits in this case are hybrids of the limits in the other two cases. Numerical comparisons indicate that the resulting approximation is better than the earlier ones for many-server systems operating at typically encountered loads.

Date: 1981
References: Add references at CitEc
Citations: View citations in EconPapers (170)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.29.3.567 (application/pdf)

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:inm:oropre:v:29:y:1981:i:3:p:567-588

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().