Queues with impolite customers

An interesting behavior of customers arriving to a queue for service concerns the manner in which they join the queue. The arrival discipline of the customers may be impolite, in the sense that an arriving customer who finds all servers busy may pick a position which is not necessarily at the end of the line. The authors introduce and discuss in detail such an arrival discipline of sufficient generality which has interesting applications. In particular, they show that the more impolite an arrival discipline is, the bigger is the variance of the waiting time. The authors also study a special model in more depth to provide simple computational formulas for several performance measures.