Abstract
Solving a Riccati equation a collection of service times distributions, very general, is determined. For it the ∞ / / G M queue busy period and busy cycle probabilistic study, very comfortable, is performed. In addition the properties of that distributions collection are deduced and also presented. / G M queue system, such as in any other queue system, there is a sequence of idle periods and busy periods. An idle period followed by a busy period is called a busy cycle. When applying this queue system to real problems, the busy period and the busy cycle length probabilistic study is very important. Along this work it is shown that the solution of the problem may be obtained solving a Riccati equation. The solution is a collection of service distributions for which both the busy period and the busy cycle have lengths with quite simple distributions, generally related with exponential distributions and the degenerated at the origin one. Some results for that collection of service distributions are also presented.
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