Large deviations for many server networks with long range dependent and batch arrivals

A sample path large deviations principle is established for the (scaled) vector of number of customers in a Jackson network of many-server queues, in the asymptotic regime where the arrival rate at each queue and the number of servers increase to infinity in a specified fashion. This result is obtained under the assumption of (possibly time-inhomogeneous) Markovian service and routing, and a condition on the scaled sequence of cumulative arrival processes, which holds for a wide class of long-range dependent and batch arrival processes. Moreover, the explicit form of the rate function is obtained in the single-queue setting, and the most likely way in which a large number of customers build up in the system is identified by solving a variational problem.