Repeated flow analysis in infinite-server queueing tandem with MMPP arrivals and feedback at the second stage

Tandem of infinite-server queues with MMPP arrivals feedback at the second stage is considered. Service times at the stages of the tandem have non-exponential distribution. We use the method of Markovian summation to obtain the Kolmogorov differential equations for the probability distribution of the number of arrivals at the second stage (repeated arrivals). An expression for the characteristic probability distribution function of the number of repeated arrivals during given period is derived under the asymptotic condition of high intensity of the MMPP arrivals