Control and scheduling in a two-station queueing network: Optimal policies and heuristics

Control and scheduling in a two-station queueing network: Optimal policies and heuristics

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Article ID: iaor19952307
Country: United States
Volume: 18
Issue: 3/4
Start Page Number: 301
End Page Number: 332
Publication Date: Nov 1994
Journal: Queueing Systems
Authors: , ,
Keywords: heuristics
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, the authors establish the optimality of a specific stationary policy, and show that its value function satisfies certain properties, which lead to a switching-curve structure. They further classify the problem into six parametric cases. Based on the structural properties of the stationary policy, the authors 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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