I . ADVANCED RESEARCH PROJECTS AGENCY SEMIANNUAL TECHNICAL REPORT G . Estrin

A queuing model with limited waiting room (buffer), batch (burst)Poisson arrivals, and a synchronous single server (transmittion channel)with constant service time (constant transmission rate) is studied. Usingaverage burst length and traffic intensity as parameters, the relationshipsamong buffer size, overflow probabilities, and an approximation to theexpected queuing delay of each burst due to buffering are obtained. Theserelationships are represented in graphs which provided a guide to thebuffer design problem. A simple example is given which applies thestsresults to the design of a buffer system in a time-sharing computer system.Although the problem discussed this paper arose in studies of design ofstatistical multiplexers, the queuing model developed is quite general,and may be useful for other industrial applications. The author was with Bell Telephone Laboratories, Holmdel, N.J. He isnow at the University of California, Los Angeles, California. This researchii, in part supported by Advanced Research Pfojecis Agency of the Depart-ment of Defense (DAHC 15-69-0285) and the Office of Naval Research,N00014-69-A-02000-4027.