Source: J. Appl. Probab. Volume 44, Number 2
(2007), 306-320.
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of
the epochs of the arrival process. This framework contains several classical queueing network models, including
generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of
stochastic Petri nets. We use comparison relationships between networks of this class with independent and
identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the
stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given
as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for
the case of queues in tandem under various stochastic assumptions.
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription.
Read more about accessing full-text
References
Anantharam, V. (1989). How large delays build up in a GI/G/1 queue. Queueing Systems Theory Appl. 5, 345--367.
Baccelli, F. and Brémaud, P. (2003). Elements of Queueing Theory, 2nd edn. Springer, Berlin.
Baccelli, F. and Foss, S. (1995). On the saturation rule for the stability of queues. J. Appl. Prob. 32, 494--507.
Baccelli, F. and Foss, S. (2004). Moments and tails in monotone-separable stochastic networks. Ann. Appl. Prob. 14, 612--650.
Baccelli, F., Foss, S. and Lelarge, M. (2005). Tails in generalized Jackson networks with subexponential service-time distributions. J. Appl. Prob. 42, 513--530.
Baccelli, F., Lelarge, M. and Foss, S. (2004). Asymptotics of subexponential max plus networks: the stochastic event graph case. Queueing Systems 46, 75--96.
Dembo, A. and Zeitouni, O. (1998). Large Deviations Techniques and Applications, 2nd edn. Springer, New York.
Duffy, K., Lewis, J. T. and Sullivan, W. G. (2003). Logarithmic asymptotics for the supremum of a stochastic process. Ann. Appl. Prob. 13, 430--445.
Ganesh, A. (1998). Large deviations of the sojourn time for queues in series. Ann. Operat. Res. 79, 3--26.
Iglehart, D. L. (1972). Extreme values in the GI/G/1 queue. Ann. Math. Statist. 43, 627--635.
Mathematical Reviews (MathSciNet):
MR305498
Lelarge, M. (2006). Tail asymptotics for discrete event systems. In Proc. 1st Internat. Conf. Performance Eval. Methodol. Tools, ACM Press, New York.
Pakes, A. G. (1975). On the tails of waiting-time distributions. J. Appl. Prob. 12, 555--564.
Mathematical Reviews (MathSciNet):
MR386056
