Probability distributions of interdeparture time and response time in multipacket CSMA/CD systems

An exact analysis is presented of an asynchronous (unslotted) multipacket CSMA/CD-DFT (carrier-sense multiple-access/collision detection with delayed first transmission) model and used to derive (1) the Laplace-Stieltjes transform of the probability distribution function (PDF) of the packet interdeparture time, (2) the LST of the PDF of the message interdeparture time, (3) the moment generating function (MGF) of the message response time, and (4) the MGF of the message response time conditioned on the number of packets necessary for transmission of a message. Higher moments as well as averages of these performance measures are important for performance evaluation of interconnected networks or integrated networks of voice and data. As the performance model allows each message to consist of a geometrically distributed number of constant-length packets, the result is also useful in examining the performance of error-prone CSMA/CD systems as well as the impact of random message sizes on the system performance. Numerical examples include comparisons between the DFT model and the IFT (immediate-first-transmission) model