Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks |
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Authors: | Kurt Majewski |
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Institution: | (1) Siemens AG, CT SE 6, 81730, München |
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Abstract: | We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20 |
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Keywords: | weak convergence critical loading first in first out priority service discipline sojourn time self similar long range dependence stationary behavior |
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