Mathematics – Probability
Scientific paper
2006-02-23
Annals of Applied Probability 2005, Vol. 15, No. 4, 2606-2650
Mathematics
Probability
Published at http://dx.doi.org/10.1214/105051605000000601 in the Annals of Applied Probability (http://www.imstat.org/aap/) by
Scientific paper
10.1214/105051605000000601
A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling 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 customer 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 general, asymptotically equivalent in this regime, with the preemptive version showing an asymptotic behavior that is, in a sense, much simpler. Under appropriate assumptions on the structure of the system we show: (i) The value function for the preemptive problem converges to $V$, the value of a related diffusion control problem. (ii) The two versions of the problem are asymptotically equivalent, and in particular nonpreemptive policies can be constructed that asymptotically achieve the value $V$. The construction of these policies is based on a Hamilton--Jacobi--Bellman equation associated with $V$.
No associations
LandOfFree
Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Scheduling control for queueing systems with many servers: asymptotic optimality in heavy traffic will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-711689