Congestion and its uncertainty are big factors affecting customers’ decision to join a queue or balk. In a queueing system, congestion itself is resulted from the aggregate joining behavior of other customers. Therefore, the property of the whole group of arriving customers affects the equilibrium behavior of the queue. In this paper, we assume each individual customer has a utility function which includes a basic cost function, common to all customers, and a customer-specific weight measuring sensitivity to delay. We investigate the impacts on the average customer utility and the throughput of the queueing system of different cost functions and weight distributions. Specifically, we compare systems where these parameters are related by various stochastic orders, under different information scenarios. We also explore the relationship between customer characteristics and the value of information.

In this article we study Markov-modulated queues with and without jumps. These queuing models arise naturally in production-inventory systems with and without an external supplier. We show an interesting decomposition property that relates the equilibrium state distributions in these two systems and present an integrated warranty-inventory management model as an application.

We consider order statistics corresponding to X1, …, Xn, where , i = 1, …, n, ℰ1, …, ℰn are independent and identically distributed exponentials with mean 1, and λ1, …, λn are possibly dependent, possibly nonidentically distributed, positive random variables, with . Thus, λ1, …, λn, can be interpreted as random failure rates, and their dependency might be due to common environmental factors.

We introduce and investigate a new type of decision problem related to multiclass fluid networks. Optimization problems arising from fluid networks with known parameters have been studied extensively in the queueing, scheduling, and optimization literature. In this article, we explore the makespan problem in fluid networks, with the assumption that the parameters are known only through a probability distribution. Thus, the decision maker does not have complete knowledge of the parameters in advance. This problem can be formulated as a stochastic nonlinear program. We provide necessary and sufficient feasibility conditions for this class of problems. We also derive a number of other structural results that can be used in developing effective computational procedures for solving stochastic fluid makespan problems.

Expressions for the distribution, density, and percentiles of weighted sums of Rayleigh random variables are given, including the tilted Edgeworth expansion.

In this article we study the joint optimization of finished goods inventory and pricing in a make-to-stock production system with long-run average profit criterion. The production time is random with controllable rate and the demand is Markovian with rate depending on the sale price. The objective is to dynamically adjust the production rate and the sale price to maximize the long-run average profit. We obtain the optimal dynamic pricing and production control policy and present an efficient bisection algorithm for computing the policy parameters.

We study the value of multistage advance demand information (MADI) in a production system in which customers place an order in advance of their actual need, and each order goes through multiple stages before it becomes due. Any order that is not immediately filled at its due date will be backordered. The producer must decide whether or not to produce based on real-time information regarding current and future orders. We formulate the problem as a Markov decision process and analyze the impact of the demand information on the production policy and the cost. We show that the optimal production policy is a state-dependent base-stock policy, and we show that it has certain monotonicity properties. We also introduce a simple heuristic policy that is significantly easier to compute and that inherits the structural properties of the optimal policy. In addition, we show that its base-stock levels bound those of the socially optimal policy. Numerical study identifies the conditions under which MADI is most beneficial and shows that the heuristic performs almost as well as the optimal policy when MADI is most beneficial.