Optimal incentive-compatible priority pricing for the M/M/1 queue
Operations Research
User delay costs and internal pricing for a service facility
Management Science
A model for rational abandonments from invisible queues
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
How Multiserver Queues Scale with Growing Congestion-Dependent Demand
Operations Research
Equilibrium strategies for queues with impatient customers
Operations Research Letters
Call Centers with Impatient Customers: Many-Server Asymptotics of the M/M/n + G Queue
Queueing Systems: Theory and Applications
The Impact of Delay Announcements in Many-Server Queues with Abandonment
Operations Research
The impacts of customers’ delay-risk sensitivities on a queue with balking
Probability in the Engineering and Informational Sciences
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We consider the modelling of abandonment from a queueing system by impatient customers. Within the proposed model, customers act rationally to maximise a utility function that weights service utility against expected waiting cost. Customers are heterogeneous, in the sense that their utility function parameters may vary across the customer population. The queue is assumed invisible to waiting customers, who do not obtain any information regarding their standing in the queue during their waiting period. Such circumstances apply, for example, in telephone centers or other remote service facilities, to which we refer as tele-queues. We analyse this decision model within a multi-server queue with impatient customers, and seek to characterise the Nash equilibria of this system. These equilibria may be viewed as stable operating points of the system, and determine the customer abandonment profile along with other system-wide performance measures. We provide conditions for the existence and uniqueness of the equilibrium, and suggest procedures for its computation. We also suggest a notion of an equilibrium based on sub-optimal decisions, the myopic equilibrium, which enjoys favourable analytical properties. Some concrete examples are provided to illustrate the modelling approach and analysis. The present paper supplements previous ones which were restricted to linear waiting costs or homogeneous customer population.