Scheduling parallel servers in the nondegenerate slowdown diffusion regime: Asymptotic optimality results

Rami Atar, Itai Gurvich

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the wellstudied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (many-server) Halfin-Whitt regime. It has the distinguishing property that waiting times and service times are of comparable magnitudes. We establish an asymptotic lower bound on the cost and devise a sequence of policies that asymptotically attain this bound. As in the conventional regime, the asymptotics can be described by means of a Brownian control problem, the solution of which exhibits a state space collapse.

Original languageEnglish (US)
Pages (from-to)760-810
Number of pages51
JournalAnnals of Applied Probability
Volume24
Issue number2
DOIs
StatePublished - Apr 2014

Keywords

  • Asymptotically optimal control
  • Diffusion limits
  • Heavy traffic
  • Many-server queues
  • Nondegenerate slowdown regime
  • The parallel server model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Scheduling parallel servers in the nondegenerate slowdown diffusion regime: Asymptotic optimality results'. Together they form a unique fingerprint.

Cite this