Rate of convergence of the fluid approximation for generalized Jackson networks
- 1 September 1996
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 33 (3) , 804-814
- https://doi.org/10.2307/3215360
Abstract
It is known that a generalized open Jackson queueing network after appropriate scaling (in both time and space) converges almost surely to a fluid network under the uniform topology. Under the same topology, we show that the distance between the scaled queue length process of the queueing network and the fluid level process of the corresponding fluid network converges to zero in probability at an exponential rate.Keywords
This publication has 5 references indexed in Scilit:
- Hierarchical Modeling of Stochastic Networks, Part II: Strong ApproximationsPublished by Springer Nature ,1994
- Discrete Flow Networks: Bottleneck Analysis and Fluid ApproximationsMathematics of Operations Research, 1991
- Open Queueing Networks in Heavy TrafficMathematics of Operations Research, 1984
- Reflected Brownian Motion on an OrthantThe Annals of Probability, 1981
- Preservation of rates of convergence under mappingsProbability Theory and Related Fields, 1974