Consider the following access scheme that combines TDMA and

Consider the following access scheme that combines TDMA and

Consider the following access scheme that combines TDMA and a specialized version of slotted ALOHA. There are 30 users, separated into two groups of n1 = 10 (group 1) and n2 = 20 users (group 2). Even access slots (slot numbers 0, 2, 4,… ) are reserved for users of group 1. Odd access slots (1, 3, 5,… ) are reserved for users of group 2. Contention within each group is resolved by the following specialized slotted ALOHA protocol: whenever a user has a packet to transmit it waits for the first available access slot – an even time slot if the user belongs to group 1 and an odd time slot if the user belongs to group 2, and with probability pi (i is 1 or 2 according to the corresponding group label) transmits the packet, otherwise it defers its transmission to a later slot. Users always have a packet to send whenever there is a transmission opportunity (whenever a slot is selected for transmission). Furthermore, when more than one packet is transmitted in a slot, a collision occurs and all packets transmitted in that slot are lost. A successful transmission event occurs when a single packet is transmitted in the slot. We define pi as optimal if it maximizes the probability of a successful transmission in the slots alloted to group i ∈ {1, 2}. Determine the normalized throughput (in packet/slot) of the system, assuming that every user has always something to send and that all users use the corresponding optimal access probability p i , where i ∈ {1, 2} is their group label.
 

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