| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Industrial Engineering and Management, Technion, Haifa 32000, Israel
We consider a queueing system with multitype customers and flexible (multiskilled) servers that work in parallel. If Qi is the queue length of type i customers, this queue incurs cost at the rate of Ci(Qi), where Ci(·) is increasing and convex. We analyze the system in heavy traffic (Harrison and Lopez 1999) and show that a very simple generalized cµ-rule (Van Mieghem 1995) minimizes both instantaneous and cumulative queueing costs, asymptotically, over essentially all scheduling disciplines, preemptive or non-preemptive. This rule aims at myopically maximizing the rate of decrease of the instantaneous cost at all times, which translates into the following: when becoming free, server j chooses for service a type i customer such that i
An analogous version of the generalized cµ-rule asymptotically minimizes delay costs. To this end, let the cost incurred by a type i customer be an increasing convex function Ci(D) of its sojourn time D. Then, server j always chooses for service a customer for which the value of C'i(D) µij is maximal, where D and i are the customer's sojourn time and type, respectively.
Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974
avim{at}tx.technion.ac.il
stolyar{at}research.bell-labs.com
arg maxi Cµi(Qi)µij, where µij is the average service rate of type i customers by server j.
Subject classifications: queues; diffusion models, networks, optimization; production/scheduling; sequencing/stochastic; networks; stochastic.
History: Received January 2002;
revision received February 2003; revision received June 2003;
accepted July 2003.
This article has been cited by other articles:
|
|
 |
|
  R. Atar, A. Mandelbaum, and G. Shaikhet Simplified Control Problems for Multiclass Many-Server Queueing Systems Mathematics of Operations Research, November 1, 2009; 34(4): 795 - 812. [Abstract] [PDF]
|
|
|
|
|
|
I. Gurvich and W. Whitt Queue-and-Idleness-Ratio Controls in Many-Server Service Systems Mathematics of Operations Research, May 1, 2009; 34(2): 363 - 396. [Abstract] [PDF]
|
|
|
|
 |
|
 I. Gurvich and W. Whitt Scheduling Flexible Servers with Convex Delay Costs in Many-Server Service Systems MSOM, April 1, 2009; 11(2): 237 - 253. [Abstract] [PDF]
|
|
|
|
 |
|
 E. L. Plambeck Asymptotically Optimal Control for an Assemble-to-Order System with Capacitated Component Production and Fixed Transport Costs Operations Research, September 1, 2008; 56(5): 1158 - 1171. [Abstract] [PDF]
|
|
|
|
|
|
H.-Q. Ye and D. D. Yao Heavy-Traffic Optimality of a Stochastic Network Under Utility-Maximizing Resource Allocation Operations Research, March 1, 2008; 56(2): 453 - 470. [Abstract] [PDF]
|
|
|
|
|
|
T. Tezcan Optimal Control of Distributed Parallel Server Systems Under the Halfin and Whitt Regime Mathematics of Operations Research, February 1, 2008; 33(1): 51 - 90. [Abstract] [PDF]
|
|
|
|
 |
|
 J. M. Milner and T. L. Olsen Service-Level Agreements in Call Centers: Perils and Prescriptions Management Science, February 1, 2008; 54(2): 238 - 252. [Abstract] [PDF]
|
|
|
|
|
|
S. Andradottir, H. Ayhan, and D. G. Down Compensating for Failures with Flexible Servers Operations Research, July 1, 2007; 55(4): 753 - 768. [Abstract] [PDF]
|
|
|
|
|
|
S. M. R. Iravani and V. Krishnamurthy Workforce Agility in Repair and Maintenance Environments MSOM, January 1, 2007; 9(2): 168 - 184. [Abstract] [PDF]
|
|
|
|
|
|
A. Bassamboo, J. M. Harrison, and A. Zeevi Design and Control of a Large Call Center: Asymptotic Analysis of an LP-Based Method Operations Research, May 1, 2006; 54(3): 419 - 435. [Abstract] [PDF]
|
|
|
|
|
|
S. Andradottir and H. Ayhan Throughput Maximization for Tandem Lines with Two Stations and Flexible Servers Operations Research, May 1, 2005; 53(3): 516 - 531. [Abstract] [PDF]
|
|
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
