Storage allocation under processor sharing I: exact solutions and asymptotics

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 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 develop a semi-numerical semi-analytic method for computing the joint distribution. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA. Email: [email protected]. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan (M/C 249), Chicago, IL 60607-7045, USA. Email: [email protected]. Acknowledgement: This work was partly supported by NSF grant DMS 05-03745 and NSA grant H 98230-08-1-0102.