On Single Server Queue with Batch Arrivals

This paper deals with a queuing system with general renewal arrivals, exponential service times, single service channel and infinite number of waiting positions, customers are serviced in the order of their arrival. In the stationary case a new form of the probability generating functions of the number of clients in the system is derived. This new form is written in terms of the probability generating functions of the tail distribution function of the number of customers per group and of the probability generating functions of a embedded discrete time homogeneous Markov chain.