Moments in Tandem Queues

Alan Scheller-Wolf and Karl Sigman
Additional contact information
Alan Scheller-Wolf: Carnegie Mellon University, Pittsburgh, Pennsylvania
Karl Sigman: Columbia University, New York, New York

Operations Research, 1998, vol. 46, issue 3, 378-380

Abstract: We settle a conjecture concerning necessary conditions for finite mean steady-state customer delay at the second node of a tandem queue, using as an example a stable tandem queue with mutually independent i.i.d. interarrival and service times. We assume that the service times have infinite variance at the first node, finite variance at the second node, and smaller mean at the first node than at the second node. We show that this causes infinite mean stationary delay at the second node. Thus, in general, when the mean service time is smaller at the first node than at the second, finite variance of service times at node 1 is necessary for finite mean delay at node 2. This confirms a conjecture made by Wolff. Our result complements sufficiency conditions previously published by Wolfson; together these necessary and sufficient conditions are presented as a theorem at the conclusion of the paper. Our proof uses a known duality between risk processes and queues.

Keywords: Sample path properties; Queuing theory; finite moments of steady-state distribution; Applications; customer delay (search for similar items in EconPapers)
Date: 1998
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.46.3.378 (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:46:y:1998:i:3:p:378-380

Access Statistics for this article

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