Sample path large deviations for multiclass feedforward queueing networks in critical loading

Details Sample path large deviations for multiclass feedforward queueing networks in critical loading Sample path large deviations for multiclass feedforward queueing networks in critical loading

2007-02-09

arxiv.org/abs/math/0702256v1

Annals of Applied Probability 2006, Vol. 16, No. 4, 1893-1924

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051606000000439 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051606000000439

We consider multiclass feedforward queueing networks with first in first out and priority service disciplines at the nodes, and class dependent deterministic routing between nodes. The random behavior of the network is constructed from cumulative arrival and service time processes which are assumed to satisfy an appropriate sample path large deviation principle. We establish logarithmic asymptotics of large deviations for waiting time, idle time, queue length, departure and sojourn-time processes in critical loading. This transfers similar results from Puhalskii about single class queueing networks with feedback to multiclass feedforward queueing networks, and complements diffusion approximation results from Peterson. An example with renewal inter arrival and service time processes yields the rate function of a reflected Brownian motion. The model directly captures stationary situations.

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