System-theoretical algorithmic solution to waiting times in semi-Markov queues
In this paper, we consider correlated queues where the service time of a packet is strongly correlated with its inter-arrival time due to the finite transmission capacity of input and output links. We present an analytical method to derive the LST (Laplace Stieltjes Transform) of the (actual) waiting time distribution and the system time distribution. To investigate the impact of such correlation between service and inter-arrival times on the system performance, we consider a counterpart GI/G/1 queue where the service time and inter-arrival time distributions are the same as in our correlated system, but they are independent. Some numerical examples are provided to show that such correlation gives significant impact on the system performance.