A discrete-time queueing system with many servers

A discrete-time queueing system with multiple servers is studied. It is assumed that the arrival process of customers is a discrete Markovian arrival process, and there are c different servers in the system and the service times of each server follow phase type distributions. By using matrix-geometric theory, the stationary queue length distributions are obtained. The stationary distribution of queue length seen by an arriving customer and the mean waiting time are given.