Analysis and Comparison of Queues with Different Levels of Delay Information

 

 

Paul Zipkin and Pengfei Guo

Duke University

 

 

Abstract

 

Information about delays can enhance service quality in many industries. Delay information can take many forms, with different degrees of precision. Different levels of information have different effects on customers and so on the overall system. To explore these effects, we consider a queue with balking under three levels of delay information: no information, partial information (the system occupancy) and full information (the exact waiting time). We posit that customers decide to balk or stay based on their expected costs of waiting, given the information available, and on the values they obtain from service. Customers are heterogeneous; they weight service and waiting differently. We show how to compute the key performance measures in the three systems, obtaining closed-form solutions for special cases.

 

In general, the customers and the service provider have different, perhaps conflicting, objectives. Under certain conditions, however, those objectives are perfectly aligned; they are proportional to a single measure, the throughput. This measure improves with more accurate information. In other cases, such harmony need not prevail. We show that, even then, more information helps someone, but not necessarily both parties.