aluated by considering the queue as an M/G/1 queue for which the Pollaczek-Khintchine formulas [32] hold. Switching Systems: Architecture and Performances In particular, the average time a packet remains in the queue, excluding the service time, is given by (7.27) where o2 is the service time variance p N/U is the ratio between the average service time 1/u and the average arrival time 1/2 Naturally, it is assumed that p< 1. The average service time and the service time variance can be deduced from Equation 7.26. In particular the following is derived (7.28) To write the final expression of the latency, it is useful to assume as independent vari- able the overall traffic offered to the switch fabric, coinciding with the average number of offered packets in the considered slot, whatever the incoming port, that is, 0 = Nnts. Moreover, it is also useful to refer to the average delay in terms of number of bus time slots, that is, St = T/ts. Adopting these variables and substituting (7.28) in (7.27) we have (7.29) This is a simple expression that presents a vertical asymptote, as expected. As a matter of fact, when the traffic goes near Np, it means that almost every slot a packet is offered to the switch fabric from some input port. However, the bus cannot manage more than one packet in each slot; thus, it is clear that the average delay gets higher and higher going nearer to the maximum bus load. We have seen in Equation 7.13 that in conditions of heavy traffic =RT/ER that approxi- mate the value 1/N corresponding to the optimum throughput for the frame efficiency approximating to 100%. Thus, in condition of heavy traffic, Equation 7.29 can be further approximated as follows: (7.30) The average normalized latency is plotted in Figure 7.23 for different values of the nor- malized total offered traffic and in conditions of high traffic. Different dimensions of the switch fabric are also considered. As expected, the average delay remains quite low up to a sort of threshold value of the offered traffic, above threshold i