The repairable queueing system (RQS) in which the server has an exponential lifetime distribution has been studied in several articles. Here, the paper deals with the new RQS M/G(Ek/H)/1 in which the lifetime distribution of the server is Erlangian. By forming a vector Markov process, i.e. by using the method of supplementary variables, it obtained some system characters, the reliability indices of the server, and the time distribution of a customer spent on the server. For this RQS, the generalized service time distribution of each customer will depend on the remainder life of the server. Based on this, a new kind of queues, for which the service time distributions are chosen by the customers in some stochastic manner, appears in queueing theory.
