able period is now halved, i.e. is equal to the length of one packet. Assuming that all packets are full during trans- mission, then the throughput is given by Equation 13.16. S = Ge-c (13.16) Figure 13.7 shows the plot of the throughput curve for a slotted ALOHA channel. It has twice the theoretical maximum throughput (0.368) compared to the pure ALOHA channel and this occurs at a value of G equal to one. This however assumes that all the packets are full, since if they are only half full then the actual throughput is the same as for pure ALOHA. So far the discussions have assumed an infinite number of users. If they are finite, and equal to N, then the throughput for the ith user (S) is given by Equation 13.17. Throughput (13.17) Figure 13.9 Delay-throughput characteristics for pure ALOHA and slotted ALOHA For N identical users, this reduces to Equation 13.18. In this equation n equals 2 if, for the colliding packets, one or the (13.18) other gets through; n equals 3 if one gets through a third of the time, = G 1 the other gets a third of the time, and neither gets through at the other times. For n equal to 2 the value of S is about 50% greater than that As N tends towards a very large number of users, S approaches attained with a slotted ALOHA system, as stated earlier. the value given in Equation 13.16. Figure 13.10 compares the performance of ALOHA with capture In a slotted ALOHA channel each time a user has information to with pure ALOHA and slotted ALOHA. transmit it must wait for the start of a slot before doing SO. This Many techniques exist for allocating signal strength to users. For applies also to retransmitted data. There is therefore, on average, an example this could depend on the priority of the user, or could be extra half packet time delay compared to pure ALOHA. At the allocated on a random or pseudo-random basis. theoretical peak transmission point (G = 1 and S = 0.368) there are an average of 2.7 (= G/S) transmissions for every successful trans- mission, resulting in an extra delay td given 