On Rational Behavior in a Loss System with One Observable Queue and One Unobservable Queue

摘要

We examine a system with two heterogeneous servers. An arriving customer first observes the queue length at the slower server and decides whether to join it or join the unobservable queue of the faster server. Customers arrive to the system and decide which queue to join according to the reward, waiting cost, and service rates. Once a customer chooses a queue, she cannot change her decision. We analyze a special case of this model where there is no waiting space except for the customer in service. The probability for entering the observable queue (if the server idle) is denoted by p, and this is the strategy of the customers. We analyze and characterize the Nash equilibria and the socially-optimal probabilities of the system, and the relation between the two as function of the model's parameters. We also examine throughput maximization.