2007/01/15 by Marc Lelarge, Lelarge, Marc
Business, Management and Accounting · Computer Science · Decision Sciences · #60F10 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Petri Nets in System Modeling #Probability (math.PR) #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.math/0701420
openalex publication_date 2007/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of communication networks, the framework of stochastic event graphs allows a modeling of control mechanisms induced by the communication protocol and an analysis of its performances. We concentrate on the logarithmic tail asymptotics of the stationary response time for a class of networks that admit a representation as (max,plus)-linear systems in a random medium. We are able to derive analytic results when the distribution of the holding times are light-tailed. We show that the lack of independence may lead in dimension bigger than one to non-trivial effects in the asymptotics of the sojourn time. We also study in detail a simple queueing network with multipath routing.