A new Markovian description of the M/G/1 retrial queue

This article deals with a new Markovian description of the M/G/1 retrial queue. We consider the process (M(t), N(t)), where M(t) is the total number of arrivals from the last departure until time t and N(t) is the number of customers in orbit at time t. We obtain the generating function together with a recurrent formula for factorial moments in the steady state. We use this process to get an estimator of the parameter of retrial and its variance by solving some linear differential equations. We also give some numerical examples.