  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).

Classical Analysis and ODEs