On the estimation of the throughput for a class of stochastic resources sharing systems

We present in this paper a stochastic model for a class of reservation systems, we define a performance parameter: gamma. This parameter can be seen as the inverse of the asymptotic throughput of the system. We detail some of its elementary properties and show that it can be studied as a function of a graph, from a numerical point of view. We then show how it can be bounded by classical values associated to this graph, as the minimum degree, for instance. Finally, we discuss the interest of the bounds we obtain.