A model for rational abandonments from invisible queues

We propose a model for abandonments from a queue, due to excessive wait, as suming that waiting customers act rationally but without being able to obse rve the queue length. Customers are allowed to be heterogeneous in their pr eferences and consequent behavior. Our goal is to characterize customers' p atience via more basic primitives, specifically waiting costs and service b enefits: these two are optimally balanced by waiting customers, based on th eir individual cost parameters and anticipated waiting time. The waiting ti me distribution and patience profile then emerge as an equilibrium point of the system. The problem formulation is motivated by teleservices, prevalen tly telephone- and Internet-based. In such services, customers and servers are remote and queues are typically associated with the servers, hence queu es are invisible to waiting customers. Our base model is the M/M/m queue, w here it is shown that a unique equilibrium exists, in which rational abando nments can occur only upon arrival (zero or infinite patience for each cust omer). As such a behavior fails to capture the essence of abandonments, the base model is modified to account for unusual congestion or failure condit ions. This indeed facilitates abandonments in finite time, leading to a non trivial, customer dependent patience profile. Our analysis shows, quite sur prisingly, that the equilibrium is unique in this case as well, and amenabl e to explicit calculation.