Abstract
We consider a processor-sharing storage allocation model, which has m primary holding spaces and infinitely many secondary ones, and a single processor servicing the stored items (customers). An arriving customer takes a primary space, if one is available. We define the traffic intensity ρ to be λ/μ where λ is the customers’ arrival rate and μ is the service rate of the processor. We study the joint probability distribution of the numbers of occupied primary and secondary spaces. For 0<ρ<1, we obtain the exact solutions for m=1 and m=2. For arbitrary m we study the problem in the asymptotic limit ρ↑1 with m fixed. We also give the tail of the distribution for a fixed ρ<1 and any m.
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This work was partly supported by NSF grant DMS 05-03745 and NSA grant H 98230-08-1-0102.
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Sohn, E., Knessl, C. Storage allocation under processor sharing I: exact solutions and asymptotics. Queueing Syst 65, 1–18 (2010). https://doi.org/10.1007/s11134-010-9164-3
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DOI: https://doi.org/10.1007/s11134-010-9164-3
Keywords
- Storage allocation
- Ranked server models
- Processor sharing
- Asymptotics
- Heavy traffic
- Joint probability distribution of occupied spaces