Abstract
We study the many-server queue shown in Figure 1(a). Customers from class j ∈ {1, 2} arrive according to renewal processes having rate λj > 0 and request processing. There are N ∈ {1, 2,…} servers, each working at rate one. All servers are fully flexible; that is, every server can serve customers from both classes. Each customer has a randomly distributed patience time that may depend on the class and reneges (abandons the system without receiving service) if service does not begin before the patience time expires. The system incurs the penalty p1 > 0 when a class 1 customer reneges and the penalty p2 > 0 when a class 2 customer reneges. Upon arrival, each class j customer independently samples from the distribution determined by cumulative distribution function (cdf) [Formula: see text] having mean 1/θj < ∞ to find its patience time and from the distribution determined by cdf [Formula: see text] having mean 1/μj < ∞ to determine its service time (that is, the required processing time).
Highlights
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History: This paper was accepted for the Stochastic Systems Special Section on Open Problems in Applied Probability, presented at the 2018 INFORMS Annual Meeting in Phoenix, Arizona, November 4–7, 2018
Each customer has a randomly distributed patience time that may depend on the class and reneges if service does not begin before the patience time expires
Summary
Publication details, including instructions for authors and subscription information: http://pubsonline.informs.org. Open Problem—Regarding Static Priority Scheduling for Many-Server Queues with Reneging. Ward (2019) Open Problem—Regarding Static Priority Scheduling for Many-Server Queues with Reneging. Full terms and conditions of use: https://pubsonline.informs.org/Publications/Librarians-Portal/PubsOnLine-Terms-andConditions. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. INFORMS provides unique networking and learning opportunities for individual professionals, and organizations of all types and sizes, to better understand and use O.R. and analytics tools and methods to transform strategic visions and achieve better outcomes. For more information on INFORMS, its publications, membership, or meetings visit http://www.informs.org http://pubsonline.informs.org/journal/stsy
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