Capacity Rationing in Multiserver, Nonpreemptive Priority Queues

Opher Baron (), Tianshu Lu () and Jianfu Wang ()
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Opher Baron: Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Tianshu Lu: Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Jianfu Wang: College of Business, City University of Hong Kong, Hong Kong

Manufacturing & Service Operations Management, 2025, vol. 27, issue 4, 1107-1125

Abstract: Problem definition : Many service and manufacturing systems use both capacity rationing (CR) and priority to differentiate among their customers. We model these as a two-class nonpreemptive priority M / M / c queueing model and the practice of CR; an arriving low-priority customer can directly enter service only when the number of idle servers is higher than the CR level, k . For these systems, we separately discuss two important features that are common in practice but ignored in the literature; supply is narrowly matched with demand, and service rates are heterogeneous, reflecting different customer types. Methodology and results : When the service times of both classes are identical, our asymptotic results indicate that for a system with a large number of servers, the nondegenerative CR level does not exceed O ( c ) . When the service times of classes differ, we derive exact solutions for different performance measures of interest using queueing and Markov chain decomposition. We numerically demonstrate the impact of system parameters on these performance measures and provide insights on the CR level. Management implications : We show that as predicted by the asymptotic analysis, an O ( c ) CR level can significantly reduce the waits of high-priority customers with little effect on low-priority customers’ waiting. We establish that this insight is robust to heterogeneous service times across classes and other system parameters, such as the number of servers and the arrival rates of the classes.

Keywords: nonpreemptive priority queue; capacity rationing; heavy traffic; numerical algorithm (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormsom:v:27:y:2025:i:4:p:1107-1125

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