In teletraffic applications of retrial queues only the service zone is observable. Another part of a retrial queue, the orbit, which represents the delay before repeated attempts to get service, cannot be observed. Thus, it is very important to get general results about behavior of the orbit. We investigate two characteristics of the orbit, namely, the orbit busy period and the orbit idle period, which seem to be very useful from this point of view. 0 1996 John Wiley &Sons, Inc.
1. Introduction
Retrial queueing systems are characterized by the phenomenon that a customer who finds all servers busy upon arrival is obliged to leave the service area and to repeat his request after some random time. Between trials, a customer is said to be in orbit. Queues in which customers are allowed to conduct retrials have wide practical use in computer and communications networks. A review of the main results, literature, and discussion of situations where retrial queues arise can be found in Yang and Templeton [ 71 and Falin [ 41. In this article we consider the M / G / 1 queue with exponentially distributed retrial times.
The analysis of this system has been the subject matter of many previous articles. However, it is still necessary to carry out a qualitative investigation of problems whose exact solutions look very cumbrous or are unknown. For example, there is extremely poor information on some variants of the classical M / G / 1 retrial queue. This is the case of the model with general retrial times (see Yang et al.
[ 81 and its references). Inference for the retrial rate is an interesting and difficult problem in real telephone systems (see Falin [ 5 I). The point is that in teletraffic applications it is very difficult to observe the retrial group. In addition we cannot distinguish between primary and repeated calls. Thus, it seems interesting to study performance characteristics of retrial systems related directly to the behavior of the orbit. Two such orbit characteristics, the orbit busy period and the orbit idle period, were recently introduced by Artalejo [ 1 , 2 ] . These measures are defined as follows: The orbit idle period L") is the period that starts at an epoch when a customer alone in the orbit produces a repeated call and finds the server idle (thus the orbit becomes empty), and ends when a primary customer finds the server busy and is obliged to join the orbit. Alternatively, the orbit busy period L(b) is the period that starts at an epoch when a primary customer amves and finds the server busy and the orbit idle, and ends at the next epoch at which a repeated attempt finds the server idle and the orbit becomes empty.