A state diagram analysis of the multi-queueM/M/1 model with finite lengths

The M/M/1 model is the most frequently used model in queueing problems. The research on the M/M/1 model with single queue and finite/infinite buffer length is already well developed. However, combinations of multiple queues with limited buffer capacity are rarely discussed. The reason for this deficiency is the lack of queue selection probability with the involved polling strategies. In this article, we propose to apply the multi-dimensional state diagram in analyzing the queueing behaviors of the q-M/M/1/Ki /FCFS/QSR model, where q is the number of queues, Ki the limited length of the ith queue, and QSR the dedicated queue selection rule. The considered QSRs can be either first-come-first-served polling or priority polling in this study. The state probabilities are solved by a set of linear equations, based on steady-state distributions. In order to verify the accuracy and performance of the proposed approach, we conducted several experiments to estimate the state probabilities, queue lengths, and waitin...