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We focus on correlated queues where service and inter-arrival times are strongly correlated, and the input and output link speeds are the same. We present an analytical method to derive the LST (Laplace Stieltjes transform) of the (actual) waiting time distribution. To investigate the effect of correlation between service and inter-arrival times on the system performance, we consider a counterpart GI/G/1 queue where inter-arrival time and service time distributions are the same as in our correlated system, but they are independent. Some numerical examples are provided to show that such correlations have significant impact on the system performance.