## The Annals of Applied Probability

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

Kurt Majewski

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 16, Number 4 (2006), 1893-1924.

Dates
First available in Project Euclid: 17 January 2007

https://projecteuclid.org/euclid.aoap/1169065211

Digital Object Identifier
doi:10.1214/105051606000000439

Mathematical Reviews number (MathSciNet)
MR2288708

Zentralblatt MATH identifier
1160.60314

#### Citation

Majewski, Kurt. Sample path large deviations for multiclass feedforward queueing networks in critical loading. Ann. Appl. Probab. 16 (2006), no. 4, 1893--1924. doi:10.1214/105051606000000439. https://projecteuclid.org/euclid.aoap/1169065211

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