On the Average Parallelism in Trace Monoids
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Approximability and non-approximability results in computing the mean speedup of trace monoids
DLT'07 Proceedings of the 11th international conference on Developments in language theory
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We present in this paper a stochastic model for a class of reservation systems, we define a performance parameter: γ. 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.