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The distribution of wasted spaces in the M/M/∞ queue with ranked servers
Published online by Cambridge University Press: 01 July 2016
Abstract
We consider the M/M/∞ queue with m primary servers and infinitely many secondary servers. All the servers are numbered and ordered. An arriving customer takes the lowest available server. We define the wasted spaces as the difference between the highest numbered occupied server and the total number of occupied servers. Letting ρ = λ0/μ be the ratio of arrival to service rates, we study the probability distribution of the wasted spaces asymptotically for ρ → ∞. We also give some numerical results and the tail behavior for ρ = O(1).
MSC classification
- Type
- General Applied Probability
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- Copyright
- Copyright © Applied Probability Trust 2008
Footnotes
This work was partly supported by NSF grant DMS 05-03745.
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