Volume 1284 of the series Lecture Notes in Computer Science pp 232245
Scheduling multiclass queueing networks on parallel servers: Approximate and heavytraffic optimality of Klimov's priority rule
 Kevin D. GlazebrookAffiliated withDepartment of Statistics, Newcastle University
 , José NiñoMoraAffiliated withCORE, Université catholique de Louvain
Abstract
We address the problem of scheduling a multiclass queueing network on M parallel servers to minimize timeaverage linear holding costs. We analyze a heuristic priorityindex rule, based on Klimov's solution to the singleserver model: Compute the indices given by Klimov's adaptive greedy algorithm and, when a server becomes free, select a customer with largest index. We present closedform performance guarantees for this heuristic, with respect to (1) the optimal cost in the original parallelservers network, and (2) the optimal cost in a “corresponding” singleserver network, attended by a server working M times faster. Simpler expressions are derived for the special case that there is no customer feedback, where the heuristic becomes the cµrule. Our analysis is based on a primaldual approach: We compare the cost of the heuristic to the value of (the dual of) a strong linear programming (LP) relaxation, which represents the optimal cost for the “corresponding” singleserver network. This relaxation follows from a set of approximate conservation laws (ACLs) satisfied by the network. Our proof of these laws relies on the first set of work decomposition laws known for this model, which we obtain from a classical flow conservation law.
 Title
 Scheduling multiclass queueing networks on parallel servers: Approximate and heavytraffic optimality of Klimov's priority rule
 Book Title
 Algorithms — ESA '97
 Book Subtitle
 5th Annual European Symposium Graz, Austria, September 15–17, 1997 Proceedings
 Pages
 pp 232245
 Copyright
 1997
 DOI
 10.1007/3540633979_18
 Print ISBN
 9783540633976
 Online ISBN
 9783540695363
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1284
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Kevin D. Glazebrook ^{(1)}
 José NiñoMora ^{(2)}
 Author Affiliations

 1. Department of Statistics, Newcastle University, NE1 7RU, Newcastle upon Tyne, UK
 2. CORE, Université catholique de Louvain, 34 voie du Roman Pays, 1348, LouvainlaNeuve, Belgium
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