An empirical study of the multi-queue finite capacity M/G/1 model

The M/G/1 model with multiple queues and finite capacity is very common and can be found very often in our daily life. Interesting measures of this model can be the waiting times of messages, mean queue lengths, etc. Usually, these problems are solved by the transformed approach to determine model parameters. Instead of the transformed approach, we present a state-space approach to decide the state probability directly, by solving a set of state transition equations. To justify the accuracy and reliability of the proposed method, our simulation results illustrate the root-mean-squared-error values between the derived state probabilities and the measured quantities from runtime. The small error confirms the applicability of the state-space approach.