Open Access
Translator Disclaimer
August 2001 Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy
S. L. Bell, R. J. Williams
Ann. Appl. Probab. 11(3): 608-649 (August 2001). DOI: 10.1214/aoap/1015345343

Abstract

This paper concerns a dynamic scheduling problem for a queueing system that has two streams of arrivals to infinite capacity buffers and two (nonidentical) servers working in parallel. One server can only process jobs from one buffer. The service time distribution may depend on the buffer being served and the server providing the service. The system manager dynamically schedules waiting jobs onto available servers. We consider a parameter regime in which the system satisfies both a heavy traffic condition and a resource pooling condition. Our cost function is a mean cumulative discounted cost of holding jobs in the system, where the (undiscounted) cost per unit time is a linear function of normalized (with heavy traffic scaling) queue length. We first review the analytic solution of the Brownian control problem (formal heavy traffic approximation) for this system. We "interpret" this solution by proposing a threshold control policy for use in the original parallel server system. We show that this policy is asymptotically optimal in the heavy traffic limit and the limiting cost is the same as the optimal cost in the Brownian control problem. The techniques developed here are expected to be useful for analyzing the performance of threshold-type policies in more complex multiserver systems.

Citation

Download Citation

S. L. Bell. R. J. Williams. "Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy." Ann. Appl. Probab. 11 (3) 608 - 649, August 2001. https://doi.org/10.1214/aoap/1015345343

Information

Published: August 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1015.60080
MathSciNet: MR1865018
Digital Object Identifier: 10.1214/aoap/1015345343

Subjects:
Primary: 60K25 , 68M20 , 90B22 , 90B35
Secondary: 60J70

Keywords: dynamic control , heavy traffic , Queueing networks , resource pooling

Rights: Copyright © 2001 Institute of Mathematical Statistics

JOURNAL ARTICLE
42 PAGES


SHARE
Vol.11 • No. 3 • August 2001
Back to Top