An M/G/1 queue with cyclic service times

In this paper we consider a single server queue with Poisson arrivals and general service distributions in which the service distributions are changed cyclically according to customer sequence number. This model extends a previous study that used cyclic exponential service times for the treatment of general service distributions. First, the stationary probability generating function and the average number of customers in the system are found. Then, a single vacation queueing system with an N-limited service policy, in which the server goes on vacation after serving N consecutive customers is analyzed as a particular case of our model. Also, to increase the flexibility of using the M/G/1 model with cyclic service times in optimization problems, an approximation approach is introduced in order to obtain the average number of customers in the system. Finally, using this approximation, the optimal N-limited service policy for a single vacation queueing system is obtained.