Optimal Simulation of Buffer Overflows in - Queueing Systems with Application to ATM Switches*

works is M/M/l queues and Jackson networks, and it is shown how one can find an asymptotically opSimply because of their rarity, the estimation of timal simulation system for simulating buffer overthe statistics of buffer overflows in queueing s y s flows in these systems. H ~ ~ ~ ~ ~ ~ , in con. terns via direct simulation is often very expensive figurations, it is more usual to have systems whose in computer time. Past work on fast simulation usservice tirne is both deterministic and constant. ing importance sampling has concentrated on sYsthis paper, we concentrate on queues with deterterns with Poisson arrival processes and exponenrninistic service times. tially distributed service times. The main reason section 2 describes the problem, and summa for this has been the analytic tractability of these ,iZes a that can be used for generating an distributions. However, in practical systems, such optimal system for arbi. as ATM switches, service times are often determintrary arrival and distributions, but with spe. istic and constant. This Paper demonstrates bow cific reference to queues with deterministic service one can generate an asymptotically optimal simutimes, In Section 3, this technique is applied to lation system (in the sense of variance) for queues the simple example of an M / M / ~ queue. specific with deterministic service times and a variety of arfor queues with deterministic service times rival processes. are presented in Sections 4 and 5. The arrival processes analysed are Poisson and Markov-modulated