arXiv subjects

Alexandre Rybko

Publications and source records attributed to Alexandre Rybko.

3 recordsLinked to original sources

arXiv2014

Poisson Hypothesis for Open Networks at Low Load

We study large communication networks of the mean-field type. The input flows to the nodes of the network are supposed to be stationary and with low rate. We show that such a network is ergodic, i.e. it goes to the stationary state, which does not depend on the initial state of the network. This is in contrast with the high load regime, when the large time behavior of the network might depend on its initial state. Our technique is based on the coupling construction, which couples two Non-Linear Markov Processes.

math.PR↗

arXiv2013

Queuing Networks with Varying Topology -- A Mean-Field Approach

We consider the queuing networks, which are made from servers, exchanging their positions. The customers, using the network, try to reach their destinations, which is complicated by the movements of the servers, taking their customers with them, while they wait for the service. We develop the general theory of such networks, and we establish the convergence of the symmetrized version of the network to the Non-Linear Markov Process.

math.PR↗

arXiv2005

Self-averaging property of queuing systems

We establish the averaging property for a queuing process with one server, M(t)/GI/1. It is a new relation between the output flow rate and the input flow rate, crucial in the study of the Poisson Hypothesis. Its implications include the statement that the output flow always possesses more regularity than the input flow.

math.PR↗