Many Sources Asymptotics for Networks with Small Buffers

In this paper, we obtain the overflow asymptotics in a network with small buffers when the resources are accessed by a large number of stationary independent sources. Under the assumption that the network is loop-free with respect to source–destination routes, we identify the precise large deviations rate functions for the buffer overflow at each node in terms of the external input characteristics. It is assumed that each type of source requires a Quality of Service (QoS) defined by bounds on the fraction of offered work lost. We then obtain the admissible region for sources which access the network based on these QoS requirements. When all the sources require the same QoS, we show that the admissible region asymptotically corresponds to that which is obtained by assuming that flows pass through each node unchanged.