19 research outputs found
Spontaneous Resonances and the Coherent States of the Queuing Networks
We present an example of a highly connected closed network of servers, where
the time correlations do not go to zero in the infinite volume limit. This
phenomenon is similar to the continuous symmetry breaking at low temperatures
in statistical mechanics. The role of the inverse temperature is played by the
average load.Comment: 3 figures added, small correction
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.Comment: Final version accepted for publication in Queueing Systems, Theory
and Application