Closed form expression for the probability of collision: Two independent transmitters

In this paper, we derive the closed form expression for the Probability of collision in an independent two transmitter scenario. Our approach to the problem is different starting from the fundamentals. Our analysis involves the discrete as well as the continuous time domain problem formulations. The two transmitter case gives a two dimensional sample space. As the time window is increasing compared with the packet size, a decrease in the probability of collision has to be observed. Our results give a strong mathematical justification for this fact. We also present a 3-D view of the variation in the probability of collision due to the changes in the ratio of packet size and the time window.