Showing papers by "J. Michael Harrison published in 1975"

Dynamic Scheduling of a Multiclass Queue: Discount Optimality

Abstract: We consider a single-server queuing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and we assume a linear cost structure. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (nonpreemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy that is optimal, and a simple algorithm for its computation is presented.

A Priority Queue with Discounted Linear Costs

Abstract: We consider a nonpreemptive priority queue with a finite number of priority classes, Poisson arrival processes, and general service time distributions. It is not required that the system be stable or even that the mean service times be finite. The economic framework is linear, consisting of a holding cost per unit time and fixed service reward for each customer class. Future costs and rewards are continuously discounted with a positive interest rate. Allowing general initial queue sizes, we develop an expression for the expected present value of rewards received minus costs incurred over an infinite horizon. From this we obtain the Laplace transform of the time-dependent expected queue length for each customer class.

A diffusion approximation for the ruin function of a risk process with compounding assets

Abstract: The traditional theory of collective risk is concerned with fluctuations in the capital reserve {Y(t): t ⩾O} of an insurance company. The classical model represents {Y(t)} as a positive constant x (initial capital) plus a deterministic linear function (cumulative income) minus a compound Poisson process (cumulative claims). The central problem is to determine the ruin probability ψ(x) that capital ever falls to zero. It is known that, under reasonable assumptions, one can approximate {Y(t)} by an appropriate Wiener process and hence ψ(.) by the corresponding exponential function of (Brownian) first passage probabilities. This paper considers the classical model modified by the assumption that interest is earned continuously on current capital at rate β > O. It is argued that Y(t) can in this case be approximated by a diffusion process Y*(t) which is closely related to the classical Ornstein-Uhlenbeck process. The diffusion {Y*(t)}, which we call compounding Brownian motion, reduces to the ordinar...