Storage Allocation Under Processor Sharing II: Further Asymptotic Results

Details Storage Allocation Under Processor Sharing II: Further Asymptotic Results Storage Allocation Under Processor Sharing II: Further Asymptotic Results

2009-07-21

arxiv.org/abs/0907.3683v1

Mathematics

Classical Analysis and ODEs

103 pages, five figures, two tables

Scientific paper

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). All of the spaces are numbered and ordered. An arriving customer takes the lowest available space. We define the traffic intensity rho to be lambda/mu where lambda is the customers' arrival rate and mu is the service rate of the processor. We study the joint probability distribution of the numbers of occupied primary and secondary spaces. We study the problem in two asymptotic limits: (1) m -> infinity with a fixed rho <1, and (2) rho -> 1, m -> infinity with m(1-rho)= O(1).

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