Show simple item record

dc.contributor.authorGranville, Kevin
dc.contributor.authorDrekic, Steve 17:59:34 (GMT) 17:59:34 (GMT)
dc.descriptionThis is a post-peer-review, pre-copyedit version of an article published in TOP. The final authenticated version is available online at:
dc.description.abstractWe analyze a 2-class maintenance system within a single-server polling model framework. There are C+f machines in the system, where C is the cap on the number of machines that can be turned on simultaneously (and hence, be at risk of failure), and the excess f machines comprise a maintenance float which can be used to replace machines that are taken down for repair. The server’s behavior is dynamic, capable of switching queues upon a machine failure or service completion depending on both queue lengths. This generalized server behavior permits the analysis of several classic service policies, including preemptive resume priority, non-preemptive priority, and exhaustive. More complicated polices can also be considered, such as threshold-based ones and a version of the Bernoulli service rule. The system is modeled as a level-dependent quasi-birth-and-death process and matrix analytic methods are used to find the steady-state joint queue length distribution, as well as the distribution for the sojourn time of a broken machine. An upper bound on the expected number of working machines as a function of C is derived, and Little’s Law is used to find the relationship between the expected number of working machines and the expected sojourn time of a failed machine when f=0 or f≥1. Several numerical examples are presented, including how one might optimize an objective function depending on the mean number of working machines, with penalty costs attributed to increasing C or f.en
dc.description.sponsorshipSteve Drekic and Kevin Granville acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada through its Discovery Grants program (RGPIN-2016-03685) and Postgraduate Scholarship-Doctoral program, respectively.en
dc.subjectmaintenance modelen
dc.subjectpolling modelen
dc.subjectdynamic serveren
dc.subjectthreshold policyen
dc.subjectswitch-in timesen
dc.subjectquasi-birth-and-death processen
dc.titleA 2-class maintenance model with dynamic server behavioren
dcterms.bibliographicCitationGranville, Kevin, and Steve Drekic. ‘A 2-Class Maintenance Model with Dynamic Server Behavior’. TOP, 29 April 2019.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Statistics and Actuarial Scienceen

Files in this item


This item appears in the following Collection(s)

Show simple item record


University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages