Abstract

Introduction. Start with the following elegant interval packing (IP) problem. Let random subintervals arrive at a service facility in a rate- Poisson stream; a random subinterval is simply the interval between two independent uniform random draws from [0; 1]. Place an arrival at time t immediately into service if it is disjoint from each of the subintervals, if any, being served at time t; otherwise, place it into a queue. When a subinterval completes service, at time t say, scan the queue in arrival order, placing into service each subinterval encountered that is disjoint from all subintervals already accepted for service at time t. Determine the stability condition under the assumption that service times are independent unit-mean exponentials. A little reflection shows that, since the midpoint 1=2 is the most "congested" point of [0;

Citations