On Mmpp (2) To Reach The Two Queuing System Analysis

Two queueing systems are studied in this article , one is MMPP(2)/E₂/1 queueing system with pure limited and single vacation , the other is MMPP(2)/G/1 queueing system with feedback times having geometric distribution. Both systems are about MMPP(2) arrival processes. MMPP(2) arrival is a kind of more widely used Markovian arrival processes than that of Erlang- and PH-distributions. The queueing system with pure limited and single vacation, besides the queueing systems with feedback times having geometric distribution have been studied by many researchers and a lot of results have been obtained. However both systems with MMPP(2) arrival processes have not been studied in open literatures.For this reason, the generator matrix of Markov process is given in recurrence formulation, the traffic density , the busy period, the probability for the system to be idle at any time and the waiting time of MMPP(2)/E₂/1(PL,SV) queueing system are obtained by means of matrix analysis theory and probability theory. At the same time, the steady condition, the mean queue length, the mean busy period lengths and the average amount of customers being served in the busy period of MMPP(2)/G/1 system with feedback times having geometric distribution are obtained.