Solution of Home Work 5


Pg81-10) A disadvantage of a broadcast subnet is the capacity wasted when multiple hosts attempt to access the

         channel at the same time. As a simplistic example, suppose that time is divided into discrete slots, with

             each of the n hosts attempting to use the channel with probability p during each slot. What fraction of the

             slots are wasted due to collisions?




            Distinguish n+2 events. Events 1 through n consist of the corresponding host successfully attempting to use 

            the channel, i.e., without a collision. The probability of these events is p(1-p)n-1. Event n+1 is an idle channel,

            with probability (1-p)n. Event n+2 is a collision. Since these n+2 events are exhaustive, their probabilities must

            sum to unity. The probability of a collision, which is equal to the fraction of slots wasted, is then just

            1 - np(1-p)n-1 - (1-p)n.