Performance analysis of a star topology of interconnected networks under 2nd-order Markov network output processes

The concept of approximating the output process of slotted multiuser random-access communication networks (i.e. the process of the successfully transmitted packets within the networks) by a second-order Markov process is introduced. A method is developed for analytically calculating the parameters of the approximating process for a class of random-access algorithms. The method is illustrated by considering a specific random-access algorithm from that class. The mean time that a packet spends in the central node of a star topology of interconnected networks is incorporated in the evaluation of the accuracy of the proposed approximation. This quantity is calculated under the proposed approximation on the output processes of the interconnected networks and is compared to simulation results from the actual system. Results showing the accuracy of the proposed approximation for networks operating under a specific random-access algorithm are presented