ABSTRACT

Necessary conditions for ergodicity of retrial queues can be obtained quite easily from the fact that the mean number of busy channels (which in the steady state equals the intensity of carried traffic and can usually be expressed in terms of the system parameters and performance characteristics) must be less than the total number of channels which are available to calls. Often the conditions obtained in this manner are sufficient for ergodicity, but a proof of this is much more difficult. A direct approach which is based on explicit solution of the Kolmogorov equations for the stationary distribution leads to very cumbersome arguments and does not seem to be useful. Batch arrival retrial queues were considered for the first time by Falin, who used the embedded Markov chain technique to derive the joint distribution of the channel state and the queue length. Another approach to the problem was proposed by Yang and Templeton.