A stochastic network with mobile users in heavy traffic

We consider a stochastic network with mobile users in a heavy-traffic regime. We derive the scaling limit of the multi-dimensional queue length process and prove a form of spatial state space collapse. The proof exploits a recent result by Lambert and Simatos 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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