Exact queueing analysis of discrete time tandems with arbitrary arrival processes

We consider a discrete time tandem of queues serving fixed length packets, where each queue can serve a single packet during a timeslot. Arrivals and departures take place at each stage according to arbitrary stochastic processes. Using the sample path techniques and stochastic coupling methods, we present an exact analysis of the queue occupancy distribution at each stage when all queues operate according to the furthest-to-go service discipline. Explicit expressions for average queue occupancies are provided in terms of the average occupancy in a single queue with a superposition of the original inputs. To our knowledge, this is the first analysis of a multi-input multi-output queueing network yielding exact solutions for general arrival processes.