Abstract
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 language | English |
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Pages (from-to) | 269-298 |
Number of pages | 30 |
Journal | Queueing Systems |
Volume | 70 |
Issue number | 3 |
DOIs | |
State | Published - 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.
Keywords
- 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