MAP/G/1 queue with a single server subject to breakdowns and repairs

We study the MAP/G/1 queue with a single server subjected to breakdowns and repairs where occurrences of breakdowns are followed by Markovian Arrival Process (MAP), and successive repair times are independent and identically distributed with a general distribution. Our model generalizes the M/G/1 queue with a single server subjected to Poisson breakdowns and general repairs. This paper describes a unified mathematical treatment and generalization of previous classical works for queue length distribution. Using the notion of Extended Laplace Transforms (ELT) we derive the generating function of queue length to steady state. We present recursive formulae for evaluating the factorial moments of the queue length.