Date of Original Version
Abstract or Description
We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in  and , we obtain fluid and diffusion limits for the sojourn time of the Mt/Mt/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.
Queueing Systems: Theory and Applications journal (QUESTA) , 53, 1-2, 19-30.