Abstract
We consider a memoryless single station service system with servers \(\mathcal{S}=\{m_{1},\ldots,m_{K}\}\), and with job types \(\mathcal{C}=\{a,b,\ldots\}\). Service is skill-based, so that server m i can serve a subset of job types \(\mathcal{C}(m_{i})\). 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.
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Dedicated to Jaap Wessels (1939–2009).
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Visschers, J., Adan, I. & Weiss, G. A product form solution to a system with multi-type jobs and multi-type servers. Queueing Syst 70, 269–298 (2012). https://doi.org/10.1007/s11134-011-9274-6
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DOI: https://doi.org/10.1007/s11134-011-9274-6
Keywords
- Service system
- First-come-first-served policy
- Multi-type jobs
- Multi-type servers
- Partial balance
- Product form solution