The "model of the repairman" is an archetype in queuing theory. It provides a useful tool for exemplifying and testing either theoretical statements or simulation tools, especially when rare events are a matter of concern. But an oversimplified example can be more confusing than enlightening, and it will be shown that the M/M repairman model ... is a model for nothing since it cannot be generalized in any way.
This fact is correlated to the more general fact that the exponential law induces simplifications when it applies and ... false generalizations otherwise. This is especially true in telecommunication networks, where real services can seldom be modeled as exponential ones and slight modifications of the pdf's may result in a complete change of the rare events properties.
The present work was undertaken in the framework of a Ph.D. thesis [3] and has been intensively checked by simulations. Conversely, it served to check the results of intensive simulations by providing the variances of involved estimators. The pursued aim is to show that the less straightforward M/G repairman model is more useful, but still remains tractable thanks to the explosive development of formal computing tools such as Maple, Axiom, etc. [4]