The two-dimensional Output Process of Retrial Queue with Two-Way Communication and MMPP input

Ivan Lapatin, Alexey Blaginin
In this paper, we review a retrial queue with MMPP input and two-way communication. Incoming applications, arriving at the server and finding it busy, join orbit and try to enter the server again after some exponentially distributed time. While idle, the server makes outgoing calls and serves them for exponentially distributed time with another intensity. MMPP (Markov Modulated Poisson Process) is an input process, in which control is driven by a continuous Markov chain, can change its state, which entails a change of the intensity of the arrival of applications. For this model we present an asymptotic approximation of the two-dimensional characteristic function under the condition of a large delay of applications in the orbit. For this approximation we carried out a numerical experiment, where asymptotic results were compared to computations, which were obtained via simulation.