Consider Nu = 10 wireless nodes, all within the transmission range of one another, which all broadcast data on a shared channel in the following manner: for any given node a single broadcast packet of length L = 1000 bits is sent at any one time, any given node sends packets over the channel according to a Poisson process with rate λ packet/s, which includes new transmissions as well as retransmissions (i.e., λ models the offered traffic from the user). Whenever a packet is ready for transmission, it is sent over the channel at a rate of Rb = 1 Mbit/s, irrespective of the channel status. Whenever two or more packets overlap in time, they result in a collision, while packets sent in disjoint time intervals are successfully received by all nodes.
a) Find the value of λ that maximizes the normalized throughput of this system – the rate at which the Nu users successfully send packets over the shared channel.
b) Now, consider τ˜p = 0.01 and solve the above problem considering non-persistent CSMA as the channel access policy. Compare the results with respect to those obtained with the previous access method.