This paper considers a processor-sharing GI/M/1 queue that can hold at most K customers. Assuming that K is large, asymptotic expansions are constructed for the first two moments of a tagged customer’s remaining sojourn time, given the present value of (i) the number of other customers in the system, (ii) the remaining service time the customer must receive, and (iii) the clock on the renewal process that governs the arrivals. From this, formulas are obtained for the moments of the total sojourn time. The mean sojourn time is also computed, given only the total required service. The results are obtained using singular perturbation methods.
