Operations & Supply Chain Management

For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation.

We examine the relative effects of several service order disciplines on important operating characteristics of queues in which customers request a random number of servers. This class of queues is characterized by customers who cannot begin service until all required servers are available. We show that for many systems in this class, it is possible to define a new service order disciplien which is more efficient than FIFO with respect to one or more measures such as expected waiting time, probability of delay, etc.

We consider the Policy Iteration Algorithm for undiscounted Markov Renewal Programs. Previous specifications of the policy evaluation part of this algorithm all required the analysis of the chain structure for each policy generated. The purpose of this paper is to provide a unique specification of the value sectors as well as an anticycling rule which avoids parsing the transition probability matrices into their subchains.

This paper considers two-person zero-sum sequential games with finite state and action spaces. We consider the pair of functional equations (f.e.) that arises in the undiscounted infinite stage model, and show that a certain class of successive approximation schemes is guaranteed to converge to a solution pair whenever an equilibrium policy with respect to the average return per unit time criterion (AEP) exists. Existence of the latter thus implies the existence of a solution to this pair of f.e. whereas the converse implication is shown only to hold under special circumstances.

This paper presents a simple and computationally tractable method which recursively computes the stationary probabilities of the queue size in an M/G/1 queueing system with variable service rate. For each service two possible service types are available and the service rule is characterized by two switch-over levels. The computational approach discussed in this paper can be applied to a variety of queueing problems.

This paper considers undiscounted two-person, zero-sum sequential games with finite state and action spaces. Under conditions that guarantee the existence of stationary optimal strategies, we present two successive approximation methods for finding the optimal gain rate, a solution to the optimality equation, and for any ϵ > 0, ϵ-optimal policies for both players.

We consider a multiserver queueing system in which customers request service from a random number of identical servers. In contrast to batch arrival queues, customers cannot begin service until all required servers are available. Servers assigned to the same customer may free separately. For this model, we derive the steady-state distribution for waiting time, the distribution of busy servers, and other important measures. Sufficient conditions for the existence of a steady-state distribution are also obtained.

This paper establishes a rather complete optimality theory for the average cost semi-Markov decision model with a denumerable state space, compact metric action sets and unbounded one-step costs for the case where the underlying Markov chains have a single ergotic set.

This paper considers undiscounted Markov decision problems. With no restriction (on either the periodicity or chain structure of the problem) we show that the value iteration method for finding maximal gain policies exhibits a geometric rate of convergence, whenever convergence occurs. In addition, we study the behaviour of the value-iteration operator; we give bounds for the number of steps needed for contraction, describe the ultimate behaviour of the convergence factor and give conditions for the existence of a uniform convergence rate.