Hd28 .m414 No . Working Paper Alfred P. Sloan School of Management a Unified Method to Analyze Overtake Free Queueing Systems a Unified Method to Analyze Overtake Free Queueing Systems a Unified Method to Analyze Overtake Free Queueing Systems

In this paper we demonstrate that the distributional laws that relate the number of customers in the system (queue), L (<?) and the time a customer spends in the system (queue), S (W) under the first-in-first-out (FIFO) discipline lead to a complete solution for the distributions of L, Q, S, W for queueing systems which satisfy distributional laws for both L and Q {overtake free systems). Moreover, in such systems the derivation of the distributions of L, Q, S, W can be done in a unified way. Our results include a generalization of PASTA to queueing systems with arbitrary renewal arrivals under heavy traffic conditions, a generalization of the Pollaczek-Khinchin formula to the GI/G/1 queue, an extension of the Fuhrmann and Cooper decomposition for queues with generalized vacations under mixed generalized Erlang renewal arrivals, new approximate results for the distributions of L, S in a GI/G/oo queue, and new exact results for the distributions of L, Q, S, W in priority queues with mixed generalized Erlang renewal arrivals. 'Dimitris Bertsimas, Sloan School of Management and Operations Research Center, MIT, Cambridge. Ma 02139. 'Georgia Mourtzinou, Operations Research Center, MIT, Cambridge, Ma 02139. 'The research of D. Bertsimas was partially supported by a Presidential Young Investigator Award DDM-9158118 with matching funds from Draper Laboratory. The research of both authors was partially supported by the National Science Foundation under grant DDM-9014751.