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Partitioning of Servers in Queueing Systems During Rush Hour

Department of Operations and Management Science, Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109
Division of Industrial and Systems Engineering, Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455
hub{at}umich.edu
saif{at}umn.edu

This paper is motivated by two phenomena observed in many queueing systems in practice. The first is the partitioning of server capacity among different customers based on their service time requirements. The second is rush hour demand where a large number of customers arrive over a short period of time followed by few or no arrivals for an extended period thereafter. We study a system with multiple parallel servers and multiple customer classes. The servers can be partitioned into server groups, each dedicated to a single customer class. The system operates under a rush hour regime with a large number of customers arriving at the beginning of the rush hour period. We show that this allows us to reduce the problem to one that is deterministic and for which closed-form solutions can be obtained. We compare the performance of the system with and without server partitioning during rush hour and address three basic questions. (1) Is partitioning beneficial to the system? (2) Is it equally beneficial to all customer classes? (3) If it is implemented, what is an optimal partition? We evaluate the applicability of our results to systems where customers arrive over time using (1) deterministic fluid models and (2) simulation models for systems with stochastic interarrival times.

Key Words: server partitioning; multiserver queueing systems; multiple demand classes; rush hour demand
History: Received: October 26, 2006; accepted: April 11, 2008.