The stochastic machine minimization problem with hard deadlines and arrivals

Stochastic machine minimization problems are motivated by resource allocation issues in communication networks and in image formation systems. We consider the following stochastic machine minimization problem: Initially (at time t=0) there are N projects (jobs, messages) available for processing. New projects arrive according to a Poisson process with fate μ. All the projects´ processing times are independent samples of an exponentially distributed random variable T. There is an unlimited number of identical machines to process the projects. A timer is associated with each project. The objective is to determine a machine allocation policy that minimizes, over an infinite horizon and within the class of nonpreemptive allocation policies, the expected number of machines used throughout the schedule. We determine qualitative properties of optimal machine allocation policies for the above problem