The output of a switch, or, effective bandwidths for networks

Consider a switch which queues traffic from many independent input flows. We show that in the large deviations limiting regime in which the number of inputs increases and the service rate and buffer size are increased in proportion, the statistical characteristics of a flow are essentially unchanged by passage through the switch. This significantly simplifies the analysis of networks of switches. It means that each traffic flow in a network can be assigned an effective bandwidth, independent of the other flows, and the behaviour of any switch in the network depends only on the effective bandwidths of the flows using it.