Abstract : The paper deals with age of information (AoI) in a networkof multiple sources and parallel queues with buffering capabilities,preemption in service and losses in served packets. Thequeues do not communicate between each other and the packetsare dispatched through the queues according to a predefined probabilisticrouting. By making use of the stochastic hybrid system(SHS) method, we provide a derivation of the average AoI of a systemof two parallel queues (with and without buffer capabilities)and compare the results with those of a single queue. We showthat known results of packets delay in Queuing Theory do not holdfor the AoI. Unfortunately, the complexity of computing the averageAoI using the SHS method increases highly with the numberof queues. We therefore provide an upper bound of the averageAoI in a system of an arbitrary number of M/M/1/(N+1)* queuesand show its tightness in various regimes. This upper bound allowsproviding a tight approximation of the average AoI with a very lowcomplexity. We then provide a game framework that allows eachsource to determine its best probabilistic routing decision. By usingMean Field Games, we provide an analysis of the routing gameframework, propose an efficient iterative method to find the routingdecision of each source and prove its convergence to the desiredequilibrium.
Index terms : Age of Information, probabilistic routing, stochastic hybrid system.