On the approximation of the output process of multiuser random-access communication networks

Bernoulli and first-order Markov processes are used to approximate the output process of a class of slotted multiuser random-access communication networks. The output process is defined as the process of the successfully transmitted packets within the network. The parameters of the approximating processes are analytically calculated for a network operating under a specific random access algorithm. The applied methods are general and can be used to calculate these parameters in the case of any random access algorithm within a class. To evaluate the accuracy of the approximations, a star topology of interconnected multiuser random-access communication networks is considered. The mean time that a packet spends in the central node of the star topology is calculated under the proposed approximations of the output processes of the interconnected networks. The results are compared to simulation results of the actual system. It turns out that the memoryless approximation gives satisfactory results up to a certain per network traffic load. Beyond that per network traffic load, the first-order Markov process performs better