Summary: The Annals of Applied Probability
2005, Vol. 15, No. 4, 2606­2650
DOI: 10.1214/105051605000000601
© Institute of Mathematical Statistics, 2005
SCHEDULING CONTROL FOR QUEUEING SYSTEMS WITH
MANY SERVERS: ASYMPTOTIC OPTIMALITY
IN HEAVY TRAFFIC1
BY RAMI ATAR
Technion­Israel Institute of Technology
A multiclass queueing system is considered, with heterogeneous service
stations, each consisting of many servers with identical capabilities. An opti-
mal control problem is formulated, where the control corresponds to schedul-
ing and routing, and the cost is a cumulative discounted functional of the
system's state. We examine two versions of the problem: "nonpreemptive,"
where service is uninterruptible, and "preemptive," where service to a cus-
tomer can be interrupted and then resumed, possibly at a different station.
We study the problem in the asymptotic heavy traffic regime proposed by
Halfin and Whitt, in which the arrival rates and the number of servers at each
station grow without bound. The two versions of the problem are not, in gen-
eral, asymptotically equivalent in this regime, with the preemptive version

Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology

Collections: Engineering