CONVERGENCE-RATES FOR M G/1 QUEUES AND RUIN PROBLEMS WITH HEAVY TAILS/

The time-dependent virtual waiting time in a M/G/1 queue converges to a proper limit when the traffic intensity is less than one. In this pa per we give precise rates on the speed of this convergence when the se rvice time distribution has a heavy regularly varying tail. The result also applies to the classical ruin problem. We obtain the exact rate of convergence for the ruin probability after time t for the case wher e claims arrive according to a Poisson process and claim sizes are hea vy tailed. Our result supplements similar theorems on exponential conv ergence rates for relaxation times in queueing theory and ruin probabi lities in risk theory.