We study a single-router Network-on-Chip modelled as a tandem queuing system. The first node is a geoK/D/1 queue (K fixed) representing a network interface, and the second node is a ./G/1 queue representing the packet switch. If K>1 we have train arrivals at the second node. If K=1 the arrival process of the second node reduces to a Bernoulli process. In the latter case, routers have been studied extensively as part of ATM and LAN networks under the assumption that the number of input ports N tends to infinity. In Networks-on-Chips N is usually 4 or 5 and results for ATM and LAN routers lead to inaccurate results. We introduce a new approximation scheme that yields accurate results for small switches. In addition to this we analyse the tandem network, both for K=1 and K>1, and we approximate the mean sojoum time in the switch and the mean end-to-end delay. If N=4 our approximation has a relative error of only 4.5% if K=6 and 1% if K=1.
