Scheduling Networks of Queues: Heavy Traffic Analysis of a Multistation Network with Controllable Inputs

• Published in: Operations research Vol. 40; no. 3-supplement-2; pp. S312 - S334
• Main Author: Wein, Lawrence M.
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.05.1992; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; Approximation; Brownian motion; Control theory; Exact sciences and technology; Heuristic; Heuristics; Job shops; Linear programming; Markov chains; Mathematical models; Network servers; Operational research and scientific management; Operational research. Management science; Operations research; Production scheduling; production/scheduling: priority sequencing in a stochastic job shop; Queueing networks; queues: Brownian models of network scheduling problems; Queuing theory. Traffic theory; Scheduling; Sequencing; Workloads; Markov chain; Singular control; Brownian motion; Approximation; Priority; Traffic; Linear programming; Scheduling; Queueing network; Queue; Finite difference method
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.40.3.S312

Motivated by a factory scheduling problem, we consider the problem of input control (subject to a specified input mix) and priority sequencing in a multistation, multiclass queueing network with general service time distributions and a general routing structure. The objective is to minimize the long-run expected average number of customers in the system subject to a constraint on the long-run expected average output rate. Under balanced heavy loading conditions, this scheduling problem can be approximated by a control problem involving Brownian motion. Linear programming is used to reduce the workload formulation of this control problem to a constrained singular control problem for a multidimensional Brownian motion. The finite difference approximation method is then used to find a linear programming solution to the latter problem. The solution is interpreted in terms of the original queueing system to obtain an effective scheduling policy. The priority sequencing policy is based on dynamic reduced costs from a linear program, and the workload regulating input policy releases a customer into the system whenever the workload process enters a particular region. An example is provided that illustrates the procedure and demonstrates its effectiveness.