Storage allocation under processor sharing I: exact solutions and asymptotics

摘要

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.