Unreliable queueing system with Markovian arrival process and backup server as a model of hybrid communication system

Valentina Klimenok, Alexander Dudin, Vladimir Vishnevsky
In this paper, we analyze a queueing system with two main unreliable servers and backup reliable server. The input flow is a defined by the BMAP (Batch Markovian Arrival Process). Heterogeneous breakdowns arrive to the main servers according to a MMAP (Marked Markovian Arrival Process). Service times and repair times have PH (Phase type) distribution. The queueing system under consideration is an adequate model of operation of hybrid communication systems which combine the use of Free Space Optics and radio technologies. We derive a condition for the stable operation of the system, compute its stationary distribution and the key performance measures. Illustrative numerical examples give some insight into the behavior of the system.