nd that exit from the output ports and the number Tin in of packets per second offered at the input ports. The dependence of n(Tin) on Tin depends on the bus implementation, but from a qualitative point of view has always the shape represented in Figure 7.19 [29]. The shape of this curve can be justified easily. As a matter of fact, at small values of offered traffic, the probability that a collision occurs on the bus is negligible and almost all the incoming packets go out of the bus without the need of retransmission. Increasing the offered traffic, collisions are more frequent and the throughput is no more linear with the traffic, up to a point where a maximum throughput is reached, that is called saturation throughput. For higher values of the traffic the throughput cannot increase and generally decreases, increasing the offered load due to the fast increase of the collision probability bringing the bus in a congestion state. In order to present some examples that can give an idea of the effectiveness of the bus- based switch fabric, we will carry out a specific analysis of a few representative examples of bus-based switches. FIGURE 7.18 Dynamic time division switch fabric based on a bus Input Input Output Output architecture. queues terminals terminals queues Switching Systems: Architecture and Performances FIGURE 7.19 Qualitative behavior of the throughput of a generic bus Offered traffic (Tin) versus the offered traffic. In any case, we will do the approximation that the input queue overflow can be neglected, SO that the entire traffic offered to the switch fabric is offered to the bus. 7.3.2.1 Switch Fabric Based on a Slotted Random Access Bus In this case, we imagine that all the packets have the same duration, that is, all the packets are composed by ND bytes and travel at a bit rate RT. All the packets in the switch fabric input queues are synchronized by inserting suitable delays and the TDM frame in the bus is divided into slots of suitable length SO as to contain exactly a packet at the bus transmis