Control and scheduling in a two-station queueing network: Optimal policies and heuristics |
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Authors: | Hong Chen Ping Yang David D. Yao |
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Affiliation: | (1) Faculty of Commerce and Business Administration, University of British Columbia, V6T 1Y8 Vancouver, BC, Canada;(2) School of Management, University of Texas at Dallas, 75083-0688 Richardson, TX, USA;(3) Department of Industrial Engineering and Operations Research, Columbia University, 10027-6699 New York, NY, USA |
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Abstract: | Consider a two-station queueing network with two types of jobs: type 1 jobs visit station 1 only, while type 2 jobs visit both stations in sequence. Each station has a single server. Arrival and service processes are modeled as counting processes with controllable stochastic intensities. The problem is to control the arrival and service processes, and in particular to schedule the server in station 1 among the two job types, in order to minimize a discounted cost function over an infinite time horizon. Using a stochastic intensity control approach, we establish the optimality of a specific stationary policy, and show that its value function satisfies certain properties, which lead to a switching-curve structure. We further classify the problem into six parametric cases. Based on the structural properties of the stationary policy, we establish the optimality of some simple priority rules for three of the six cases, and develop heuristic policies for the other three cases. |
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Keywords: | Dynamic scheduling stochastic control multiclass queueing networks |
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