Duopoly pricing and waiting lines

The paper deals with a model of duopoly pricing in the context of firms providing services to consumers. Each of the firms has a waiting line of customers arriving randomly. The service provided by both firms is identical and the service time of both firms is assumed to obey the same distribution. Different consumers have different time costs and have to decide whether or not to join one of the lines. It is shown that the Cournot-Nash equilibrium is such that the two firms charge in general different prices. One of the firms specializes in servicing individuals with high cost of time (and the other the rest). Moreover, some examples of non-existence of Cournot-Nash equilibrium and permanent oscillations of prices are shown.