The paper deals with Age of Information  in a network of multiple sources and parallel servers/ queues with buffering capabilities, preemption in service and losses in served packets. The servers do not communicate between each other and the packets are dispatched through the servers according to a predefined probabilistic routing. By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average Age of Information of a system of two parallel servers (with and without buffer capabilities) and compare the result with that of a single queue. We show  known results of packets delay in Queuing Theory do not hold for Age of Information . Unfortunately, the complexity of computing the Age of Information using the SHS method increases highly with the number of queues. We therefore provide an upper bound of the average Age of Information in a parallel server system of an arbitrary number of M/M/1/(N+1) queues and  its tightness in various regimes. This upper bound allows providing a tight approximation of the Age of Information with a very low complexity  .
The paper deals with Age of Information (AoI) in a network of multiple sources and parallel queues with buffering capabilities, preemption in service and losses in served packets. The queues do not communicate between each other and the packets are dispatched through the queues according to a predefined probabilistic routing. By making use of the Stochastic Hybrid System (SHS) method, we provide a derivation of the average AoI of a system of two parallel queues (with and without buffer capabilities) and compare the results with those of a single queue. We show that known results of packets delay in Queuing Theory do not hold for the AoI . Unfortunately, the complexity of computing the average AoI using the SHS method increases highly with the number of queues. We therefore provide an upper bound of the average AoI in a system of an arbitrary number of M/M/1/(N+1) queues and show its tightness in various regimes. This upper bound allows providing a tight approximation of the average AoI with a very low complexity . We then provide a game framework that allows each source to determine its best probabilistic routing decision. By using Mean Field Games, we provide an analysis of the routing game framework, propose an efficient iterative method to find the routing decision of each source and prove its convergence to the desired equilibrium .
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. We then provide a game framework that allows each source to determine its best probabilistic routing decision. By using Mean Field Games, we provide an analysis of the routing game framework, propose an efficient iterative method to find the routing decision of each source and prove its convergence to the desired equilibrium