Patterns of Buffer Overflow in a Class of Queues with Long Memory in the Input Stream

We study the time it takes until a a uid queue with a nite, but large, holding capacity reaches the overrow point. The queue is fed by an on/oo process, with a heavy tailed on distribution, which is known to have long memory. It turns out that the expected time until overrow, as a function of capacity L, increases only polynomially fast, and so overrows happen much more often than in the \classical" light tailed case, where the expected overrow time increases as an exponential function of L. Moreover, we show that in the heavy tailed case, overrows are basically caused by single huge jobs. An implication is that the usual GI=G=1 queue with nite but large holding capacity and heavy tailed service times, will overrow about equally often no matter how much we increase the service rate. We also study the time until overrow for queues fed by a superposition of k iid. on/oo processes with a heavy tailed on distribution, and show the beneet of pooling the system resources as far as time until overrow is concerned.