Distributed algorithms for the computation of noncooperative equilibria
Automatica (Journal of IFAC)
Optimal incentive-compatible priority pricing for the M/M/1 queue
Operations Research
Improving Service by Informing Customers About Anticipated Delays
Management Science
Individual Equilibrium and Learning in Processor Sharing Systems
Operations Research
Equilibrium strategies for queues with impatient customers
Operations Research Letters
Dynamic service sharing with heterogeneous preferences
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Customer Loyalty and Supplier Quality Competition
Management Science
Rational Abandonment from Tele-Queues: Nonlinear Waiting Costs with Heterogeneous Preferences
Queueing Systems: Theory and Applications
Call center simulations: call center simulation modeling: methods, challenges, and opportunities
Proceedings of the 35th conference on Winter simulation: driving innovation
Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue
Queueing Systems: Theory and Applications
Manufacturing & Service Operations Management
Managing Service Systems with an Offline Waiting Option and Customer Abandonment
Manufacturing & Service Operations Management
Fluid models of many-server queues with abandonment
Queueing Systems: Theory and Applications
Data-stories about (im)patient customers in tele-queues
Queueing Systems: Theory and Applications
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We propose a model for abandonments from a queue, due to excessive wait, assuming that waiting customers act rationally but without being able to observe the queue length. Customers are allowed to be heterogeneous in their preferences and consequent behavior. Our goal is to characterize customers' patience via more basic primitives, specifically waiting costs and service benefits: these two are optimally balanced by waiting customers, based on their individual cost parameters and anticipated waiting time. The waiting time distribution and patience profile then emerge as an equilibrium point of the system. The problem formulation is motivated by teleservices, prevalently telephone- and Internet-based. In such services, customers and servers are remote and queues are typically associated with the servers, hence queues are invisible to waiting customers. Our base model is the M/M/m queue, where it is shown that a unique equilibrium exists, in which rational abandonments can occur only upon arrival (zero or infinite patience for each customer). As such a behavior fails to capture the essence of abandonments, the base model is modified to account for unusual congestion or failure conditions. This indeed facilitates abandonments in finite time, leading to a nontrivial, customer dependent patience profile. Our analysis shows, quite surprisingly, that the equilibrium is unique in this case as well, and amenable to explicit calculation.