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Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

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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.

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Authors and Affiliations

  1. Siemens AG, CT SE 6, 81730, München

    Kurt Majewski

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  1. Kurt Majewski
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Correspondence to Kurt Majewski.

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AMS subject classification: primary 90B15, secondary 60K25, 68M20

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Majewski, K. Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks. Queueing Syst 50, 199–230 (2005). https://doi.org/10.1007/s11134-005-0720-1

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  • DOI: https://doi.org/10.1007/s11134-005-0720-1

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