A product form solution to a system with multi-type jobs and multi-type servers

Jeremy Visschers, Ivo Adan, Gideon Weiss

Research output: Contribution to journalArticlepeer-review


We consider a memoryless single station service system with servers S = {m1,...,mK}and with job types C = {a,b...}. Service is skill-based, so that server mi can serve a subset of job types C(mi). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignment probabilities under which the system has a product-form stationary distribution, and obtain explicit expressions for it. We also derive waiting time distributions in steady state.

Original languageEnglish
Pages (from-to)269-298
Number of pages30
JournalQueueing Systems
Issue number3
StatePublished - Mar 2012

Bibliographical note

Funding Information:
Research of I. Adan was supported in part by the Netherlands Organization for Scientific Research (NWO). Research of G. Weiss was supported in part by Israel Science Foundation Grants 454/05 and 711/09, hospitality of the Newton Institute of Mathematics is gratefully acknowledged.


  • First-come-first-served policy
  • Multi-type jobs
  • Multi-type servers
  • Partial balance
  • Product form solution
  • Service system

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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