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

J.W.C.H. Visschers, I.J.B.F. Adan, G. Weiss

Research output: Contribution to journalArticleAcademicpeer-review

33 Citations (Scopus)

Abstract

We consider a memoryless single station service system with servers S={m_1, ..., m_K}, and with job types C={a, b, ...}. Service is skill-based, so that server m_i can serve a subset of job types C(m_i). 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. Keywords: Service system – First-come-first-served policy – Multi-type jobs – Multi-type servers – Partial balance – Product form solution
Original languageEnglish
Pages (from-to)269-298
JournalQueueing Systems: Theory and Applications
Volume70
Issue number3
DOIs
Publication statusPublished - 2012

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