A practical guide to heavy tails
Asymptotics of stochastic networks with subexponential service times
Queueing Systems: Theory and Applications
Tail asymptotics for discrete event systems
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Tail Asymptotics for Discrete Event Systems
Discrete Event Dynamic Systems
Asymptotic behavior of generalized processor sharing queues under subexponential assumptions
Queueing Systems: Theory and Applications
Non-asymptotic delay bounds for networks with heavy-tailed traffic
INFOCOM'10 Proceedings of the 29th conference on Information communications
Tandem queues with subexponential service times and finite buffers
Queueing Systems: Theory and Applications
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We calculate the exact tail asymptotics of stationary response times for open stochastic event graphs, in the irreducible and reducible cases. These networks admit a representation as (max, plus)-linear systems in a random medium. We study the case of renewal input and i.i.d. service times with subexponential distributions. We show that the stationary response times have tail asymptotics of the same order as the integrated tail of service times. The mutiplicative constants only involve the intensity of the arrival process and the (max, plus)-Lyapunov exponents of the sequence of (max, plus)-matrices.