A Queueing System with Auxiliary Servers

We examine a queueing system with multiple primary servers and a fewer number of auxiliary servers. There are two classes of customers---those who require service from a primary server working alone and those who require service from a primary server who is assisted by an auxiliary server. Though the apparent Markovian state space is five-dimensional, we show that an aggregation results in an exact two-dimensional representation which is Markovian. Matrix geometric theory is used to obtain approximations for the mean delay and blocking probability of each customer type.