An N Server Cutoff Priority Queue Where Arriving Customers Request a Random Number of Servers

Christian Schaack and Richard C. Larson
Additional contact information
Christian Schaack: Harvard Business School, Boston, Massachusetts 02163
Richard C. Larson: Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Management Science, 1989, vol. 35, issue 5, 614-634

Abstract: We consider a multi-priority, N-server, Poisson arrival, nonpreemptive queue, motivated by police applications. The number of servers requested by an arrival has a known priority dependent probability distribution. All servers requested by a customer must start service simultaneously; the servers' service times are independent and exponentially distributed with parameter \mu , independent of priority, server identity or system state. In order to save available servers for higher priority customers, arriving customers of each lower priority are deliberately queued whenever the number of servers busy equals or exceeds a given priority-dependent cutoff number. Whenever all higher priority queues are empty, the longest waiting priority i customer will enter service the instant there is a service completion from a state having precisely N i - k + 1 servers busy, where k is the number of servers requested by the customer and N i is the server cutoff number for priority i. The queueing discipline is in a sense HOL by priorities. We derive the priority i waiting time distribution (in transform domain) and other system statistics. Illustrative computational results are given.

Keywords: priority queue; random number of servers; cutoff queue; police; server management (search for similar items in EconPapers)
Date: 1989
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://dx.doi.org/10.1287/mnsc.35.5.614 (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:ormnsc:v:35:y:1989:i:5:p:614-634

Access Statistics for this article

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