The Unobservable Queue: The Effect of Incomplete Information on Queueing Systems

Abstract

The majority of queueing theory surrounds systems that are “observable,” in which a physical line exists. In many of these systems, customers can abandon the line prior to receiving service if they deem their wait time unreasonable. In these physical queues, both the servers and customers observe these abandonments as they happen. In “unobservable” queues however, customers are given a ticket number or virtual place in line upon arrival, and are relinquished of the requirement of standing in a physical queue. In these systems, if customers choose to abandon the line, neither servers nor other customers observe their abandonment immediately; instead, an abandonment is only recognized when the abandoned place reaches the front of the line, or the corresponding ticket number is called and the customer does not present himself for service. Due to this disparity in the time of recognition of abandonments, the two types of systems behave differently. In this work, we model and extensively simulate the single and multi-server standard and unobservable queues, utilizing the analysis of call center data to inform the simulations. We find that in unobservable systems, the queue length is perceived as longer, yielding a higher proportion of balking upon arrival and, as a result, fewer service completions. Furthermore, we find that these differences in performance of the unobservable and standard queueing systems hold across a variety of different dimensions, and are magnified in the heavily overloaded case. We also explore the addition of “clearing times” in unobservable systems - in which the server takes time to look for abandoned customers - finding that this addition results in even fewer service completions. Through both these empirical and, in some cases theoretical, comparisons, this work deeply explores the differences between standard and unobservable systems. Finally, this work discusses the potential commercial implications of the unobservable queue.