x an arbitrary time window of duration equal to ts that is equal to the packet duration at the bus bit rate, and let us call p the probability that a generic access point will start to transmit a packet within the interval. If two or more access points will start to transmit within the interval, the packets will overlap generating collision, SO that the probability of a successful transmission coincides with the probability that, starting one access point the transmission at a certain instant, no other access point will start to transmit in a time interval of duration ts. Summarizing, three conditions are needed to have a successful transmission [30]: 1. An access point starts to transmit in the instant t. 2. No access point is transmitting at the instant and no access point started transmis- sion within the interval (t - ts, t). 3. No access point will start a transmission in the interval ts). The three conditions are independent; thus, the overall transmission success probability is the product of the three probabilities, that we will call Pi, 1, 2, 3. Telecommunication Networks The individual probabilities are easily evaluated using a model similar to that used in the previous section, since the bus access points are assumed independent. At the end, we obtain (7.16) In this case, the probability p cannot be evaluated as in the slotted case, since no synchro- nization occurs. Optimization with respect to p can be done however in the same way, deriving (7.16) and finding the value of p that corresponds to the maximum value of n. It is obtained that the maximum efficiency is attained for p=0.5/N and it is (7.17) SO that, for large values of N the throughput tends to may=1/2e=18%. 7.3.2.3 Switch Fabric Based on a Carrier Sense Multiple Access Bus Random access busses are very simple to implement and their performances are inde- pendent of the packet duration and the propagation delay; however, other possible bus protocols exist that are nearly as simple to implement and can significantly improve the throughput per