Delay-Minimizing Capacity Allocation in an Infinite Server-Queueing System

Refael Hassin, Liron Ravner

Research output: Contribution to journalArticlepeer-review


We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered by their speed, and arriving customers join the fastest idle server. A capacity allocation is an infinite sequence of service rates. We study the probabilistic properties of this system by considering overflows from sub-systems with a finite number of servers. Several stability measures are suggested and ana-lyzed. The tail of the series of service rates that minimizes the average expected delay (service time) is shown to be approximately geometrically decreasing. We use this property to ap-proximate the optimal allocation of service rates by constructing an appropriate dynamic program.

Original languageEnglish
Pages (from-to)27-46
Number of pages20
JournalStochastic Systems
Issue number1
StatePublished - Mar 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 The Author(s).


  • capacity allocation
  • heterogeneous servers
  • infinite state dynamic programming
  • queues

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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