Storage allocation under processor sharing I: exact solutions and asymptotics.
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| Title: | Storage allocation under processor sharing I: exact solutions and asymptotics. |
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| Authors: | Sohn, Eunju1 esohn3@math.uic.edu, Knessl, Charles1 knessl@uic.edu |
| Source: | Queueing Systems. May2010, Vol. 65 Issue 1, p1-18. 18p. 1 Diagram, 2 Charts. |
| Subjects: | Dynamic storage allocation (Computer science), Client/server computing, Asymptotic expansions, Distribution (Probability theory), Poisson processes |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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