Data-stories about (im)patient customers in tele-queues

Credible queueing models of human services acknowledge human characteristics. A prevalent one is the ability of humans to abandon their wait, for example while waiting to be answered by a telephone agent, waiting for a physician’s checkup at an emergency department, or waiting for the completion of an Internet transaction. Abandonments can be very costly, to either the service provider (a forgone profit) or the customer (deteriorating health after leaving without being seen by a doctor), and often to both. Practically, models that ignore abandonment can lead to either overor under-staffing; and in well-balanced systems (e.g. well-managed telephone call centers), the “fittest (needy) who survive” and reach service are rewarded with surprisingly short delays. Theoretically, the phenomenon of abandonment is interesting and challenging, in the context of Queueing Theory and Science as well as beyond (e.g. Psychology). Last, but not least, queueing models with abandonment are more robust and numerically stable, when compared against their abandonment-ignorant analogues. For our relatively narrow purpose here, abandonment of customers, while queueing for service, is the operational manifestation of customer patience, perhaps impatience, or (im)patience for short. This (im)patience is the focus of the present paper. It is characterized via the distribution of the time that a customer is willing to wait, and its dynamics are characterized by the hazard-rate of that distribution. We start with a framework for comprehending impatience, distinguishing the times that a customer expects to wait, is required to wait (offered wait), is willing to wait (patience time), actually waits and felt waiting. We describe statistical methods that are used to infer the (im)patience time and offered wait distributions. Then some useful queueing models, as well as their asymptotic approximations, are discussed. In the main part of the paper, we discuss several “data-based pictures” of impatience. Each “picture” is associated with an important phenomenon. Some theoretical and practical problems that arise from these phenomena, and existing models and methodologies that address these problems, are outlined. The problems discussed cover statistical estimation of impatience, behavior of overloaded systems, dependence between patience and service time, and validation of queueing models. We also illustrate how impatience changes across customers (e.g. VIP vs. regular customers), during waiting (e.g. in response to announcements) and through phases of service (e.g. after experiencing the answering machine over the phone). Our empirical analysis draws data from repositories at the Technion SEELab, and it utilizes SEEStat its online EDA (Exploratory Data Analysis) environment. SEEStat and most of our data are internet-accessible, which enables reproducibility of our research.