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$%J. Artalejo and G. Falin, Standard and retrial queueing systems: a comparative analysis, Rev. Mat. Complut. 15 (2002), no. 1, 101129.%$

Standard and Retrial Queueing Systems: a Comparative Analysis
Jesús ARTALEJO and Gennadi FALIN
Departamento de Estadística e I.O.
Facultad de CC. Matemáticas
Universidad Complutense de Madrid
Madrid 28040 — Spain
Department of Probability Theory
Moscow State University
Moscow 119899 Russia

Received: June 21, 2001
Revised: November 27, 2001


We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get 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. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server M/G/1  type and multiserver M/M/c  type retrial queues and discuss similarities and differences between the retrial queues and their standard counterparts. We demonstrate that although retrial queues are closely connected with these standard queueing models they, however, possess unique distinguished features. We also mention some open problems.

2000 Mathematics Subject Classification: 60K25.