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On the improvement from scheduling a two-station queueing network in heavy traffic. (English) Zbl 0755.60075

Summary: For a two-station multiclass queueing network in heavy traffic, we assess the improvement from scheduling (job release and priority sequencing) that can occur relative to Poisson input and first-come first-served (FCFS) sequencing. In particular, simple upper bounds are derived on the optimal objective function value [found in the paper of the second author, Math. Oper. Res. 15, No. 2, 215-242 (1990; Zbl 0714.90042)] of a Brownian control problem that approximates (via J. M. Harrison’s model [Stochastic differential systems, stochastic control theory and applications, Proc. Workshop Minneapolis/Minn. 1986, IMA Vol. Math. Appl. 10, 147-186 (1988; Zbl 0658.60123)]) a two-station queueing network scheduling problem in heavy traffic. When the system is perfectly balanced, the Brownian analysis predicts that optimal scheduling will reduce the long run expected average number of customers in the network by at least a factor of four relative to the Poisson input, FCFS sequencing policy that achieves the same throughput rate. When the system is not perfectly balanced, the corresponding factor is slightly smaller than two.

MSC:

60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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References:

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