An Overview of Retrial Queues

The talk deals with a branch of queuing theory, retrial queuing systems, which is characterized by a basic assumption: a customer who cannot receive service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again to request service. As a result, repeated attempts for service from the pool of unsatisfied customers, called the orbit, are superimposed on the ordinary stream of arrivals of first attempts.<br /> <br /> The talk is divided into three parts. Part I introduces the audience to the broad range of applications of retrial queues and compares retrial queues to standard queues with waiting line and queues with losses. We show that, though retrial queues are closely connected with standard queuing models, they possess unique and distinguishing characteristics. In Part II, we give a survey of main results for the main M/G/1 and M/M/c retrial queues. We also present the analysis of descriptors arising from the idiosyncrasies of the retrial feature. Part III uses the matrix-analytic formalism to analyze a selected number of retrial queues with underlying structured Markov chains.