A note on varying the number of states in the arrival process of MR/GI/1 queue

A single server queue with an autocorrelated arrival process is considered. A specific way of changing the number of states in the arrival process is introduced which enables us to extract the pure effect of the number of different types of arrivals on the queueing performance measures. We see that increasing the number of arrival types makes the arrival stream more correlated and causes longer waiting times in the system. This impact is much stronger when the successive arrival types tend to be the same under heavy traffic.