The performance analysis of leaky bucket algorithm with Markov-modulated Bernoulli process

In ATM networks, the time axis is divided into equal intervals called time slots, so most references assume that the Markov chain makes a transition from state i to state j in the boundary of time slots in view of Markov-modulated Bernoulli process (MMBP). This paper considers a more general situation, i.e., the Markov chain makes a transition from state i to state j in the boundary of frames whose length are an integral multiple of length of one time slot. Under this MMBP model, the paper develops a four-dimensional discrete-time Markov chain, and obtains results of the performance analysis of leaky bucket algorithms