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Dynamic Scheduling of a System with Two Parallel Servers in Heavy Traffic with Resource Pooling: Asymptotic Optimality of a Threshold Policy (1999)
| Venue: | Annals of Applied Probability |
| Citations: | 114 - 6 self |
BibTeX
@ARTICLE{Bell99dynamicscheduling,
author = {S. L. Bell and R. J. Williams},
title = {Dynamic Scheduling of a System with Two Parallel Servers in Heavy Traffic with Resource Pooling: Asymptotic Optimality of a Threshold Policy},
journal = {Annals of Applied Probability},
year = {1999},
volume = {11},
pages = {608--649}
}
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Abstract
This paper concerns a dynamic scheduling problem for a queueing system that has two streams of arrivals to infinite capacity buffers and two (non-identical) servers working in parallel. One server can only process jobs from one buffer, whereas the other server can process jobs from either 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 contro...
Keyphrases
heavy traffic dynamic scheduling asymptotic optimality threshold policy parallel server dynamic scheduling problem heavy traffic condition linear function parameter regime formal heavy traffic approximation service time distribution unit time available server brownian control problem cost function queueing system analytic solution system manager capacity buffer threshold contro queue length
