The cμ/θ Rule for Many-Server Queues with Abandonment
Authors:
- 1 October 2010
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Operations Research
- Vol. 58 (5) , 1427-1439
Abstract
We consider a multiclass queueing system with multiple homogeneous servers and customer abandonment. For each customer class i, the holding cost per unit time, the service rate, and the abandonment rate are denoted by ci, μi, and θi, respectively. We prove that under a many-server fluid scaling and overload conditions, a server-scheduling policy that assigns priority to classes according to their index ciμi/θi is asymptotically optimal for minimizing the overall long-run average holding cost. An additional penalty on customer abandonment is easily incorporated into this model and leads to a similar index rule.Keywords
This publication has 21 references indexed in Scilit:
- Fluid limits of many-server queues with renegingThe Annals of Applied Probability, 2010
- The Modern Call Center: A Multi‐Disciplinary Perspective on Operations Management ResearchProduction and Operations Management, 2007
- Scheduling a multi class queue with many exponential servers: asymptotic optimality in heavy trafficThe Annals of Applied Probability, 2004
- Dynamic Scheduling with Convex Delay Costs: The Generalized $c|mu$ RuleThe Annals of Applied Probability, 1995
- Optimal scheduling in a machine with stochastic varying processing rateIEEE Transactions on Automatic Control, 1994
- Further results for dynamic scheduling of multiclassG/G/1 queuesJournal of Applied Probability, 1989
- K competing queues with geometric service requirements and linear costs: The μc-rule is always optimalSystems & Control Letters, 1985
- The cμ rule revisitedAdvances in Applied Probability, 1985
- Time-Sharing Service Systems. ITheory of Probability & Its Applications, 1975
- Various optimizers for single‐stage productionNaval Research Logistics Quarterly, 1956