Storage allocation under processor sharing I: exact solutions and asymptotics

Authors:
Eunju Sohn;Charles Knessl
Affiliations:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA 60607-7045;Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, USA 60607-7045
Venue:
Queueing Systems: Theory and Applications
Year:
2010

Citing 2
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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 驴 to be 驴/μ where 驴 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驴m=1 and m=2. For arbitrary m we study the problem in the asymptotic limit 驴驴1 with m fixed. We also give the tail of the distribution for a fixed 驴m.