Individual equilibrium dynamic routing in a multiple server retrial queue

Customers arrive sequentially to a service system where the arrival times f orm a Poisson process of rate lambda. The system offers a choice between a private channel and a public set of channels. The transmission rate at each of the public channels is faster than that of the private one; however, if all of the public channels are occupied, then a customer who commits itsel f to using one of them attempts to connect after exponential periods of tim e with mean mu(-1). Once connection to a public channel has been made, serv ice is completed after an exponential period of time, with mean nu(-1). Eac h customer chooses one of the two service options, basing its decision on t he number of busy channels and reapplying customers, with the aim of minimi zing its own expected sojourn time. The best action for an individual custo mer depends on the actions taken by subsequent arriving customers. We estab lish the existence of a unique symmetric Nash equilibrium policy and show t hat its structure is characterized by a set of threshold-type strategies; w e discuss the relevance of this concept in the context of a dynamic learnin g scenario.