Distribution of the interdeparture time in random multi-access protocols

Current telecommunications era includes plenty of services and applications to final users. Specially remarkable are services as Internet, video-on-demand, entertainment, etc, which are expected to grow enormously in a near future. Random Multi-Access protocols (RMAPs) are used as the method of access to networks where there is a large population of bursty users who share the same channel. New RMAPs are being developped for such services, the goal is to share the network in a fair way by all users, improving the performance of the whole network. RMAPs use a Collision Resolution Algorithm (CRA) when two or more packets access me channel simultaneously. The performance of any CRA is measured by the expected values of delay, throughput, stability and number of users waiting in the queue, analyzing the channel in the steady-state. The difficulty of the performance analysis is even greater when we consider a mixture between different protocols: IF, ATM; with different traffics (random or reserved), packet lengths, priorities, and so on, as it will be in HFC (hybrid fiber-coax), or wireless networks. In earlier papers a new method was presented based in the classical queuing theory to analyze the performance of any RMAA. That method needed the computation of the mean length (L-1) of the so called Collision Resolution interval (CRI) of the CRA. This paper advances one step ahead presenting the distribution of the Interdeparture Time of any RMAA. Moreover, the knowledge of this random variable will allow us to analyze new generation CRAs with two or more queues such as DQRAP, DQRUMA or others.