Breaking the Symmetry in Queues with Delayed Information

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system.

Queues with Choice via Delay Differential Equations

Delay or queue length information has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information. In the first fluid model, customers join each queue according to a Multinomial Logit Model, however, the queue length information the customer receives is delayed by a constant [Formula: see text]. We show that the delay can cause oscillations or asynchronous behavior in the model based on the value of [Formula: see text]. In the second model, customers receive information about the queue length through a moving average of the queue length. Although it has been shown empirically that giving patients moving average information causes oscillations and asynchronous behavior to occur in U.S. hospitals, we analytically and mathematically show for the first time that the moving average fluid model can exhibit oscillations and determine their dependence on the moving average window. Thus, our analysis provides new insight on how operators of service systems should report queue length information to customers and how delayed information can produce unwanted system dynamics.

Product Design Strategy with Commonality by Considering Customer-Choice Behavior in Supply Chain

Product design decisions have significant impact on a firm's competitive edge. This paper investigates the condition under which component commonality is a profitable product design strategy for a firm by considering customer-choice behavior in the supply chain environment. The design configuration with commonality can lower manufacturing cost, but it also reduces product differentiation and revenue. While the customer-choice behavior with utility maximization will impact the retailer's product pricing, we analyze a stylized model of the manufacturer who designs a product family consisting of two products for two market segments with different valuations of quality. By explicitly considering the interrelationship between customer's utility and retail price, we find that commonality strategy is conditionally profitable. Theoretical research reveals that the optimal product design strategy depends on the marginal valuations of customer-choice behavior and the cost-coefficient of the common component determined by the supplier. An example is used to illustrate how some supply chain parameters impact the optimal product design strategy.