A stochastic network with mobile users in heavy traffic |
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Authors: | Sem Borst Florian Simatos |
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Affiliation: | 1. Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands 2. Alcatel–Lucent Bell Labs, P.O. Box 636, Murray Hill, NJ, 07974-0636, USA 3. Eurandom, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
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Abstract: | We consider a stochastic network with mobile users in a heavy traffic regime. We derive the scaling limit of the multidimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by Lambert and Simatos (preprint, 2012), which provides a general principle to establish scaling limits of regenerative processes based on the convergence of their excursions. We also prove weak convergence of the sequences of stationary joint queue length distributions and stationary sojourn times. |
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