Asymptotics for Distributions of Stationary Characteristics in Queueing Networks with Heavy Tails

Foss, Serguei (Novosibirsk, Russia)
foss@math.nsc.ru

(joint work with François Baccelli and Dima Korshunov)

We consider queueing networks with sub-exponential service times distributions (STD).

1. For a class of stable monotone separable queueing networks, we get upper a low bounds for the tail distribution of a stationary maximal dater. Then we obtain a sharp asymptotic for particular models (including tandem queues, generalized Jackson networks). Finally, a sharp asymptotic for a stationary waiting time in generalized Jackson networks is obtained, too.

2. For a stable ($\rho < 2$) 2-server queue with FCFS policy, a sharp asymptotic for a stationary waiting time distribution is obtained when either
(i) $\rho < 1$ and a second tail of STD is sub-exponential, or
(ii) $1<\rho < 2$ and STD is regularly varying.