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We consider a tandem queue consisting of two stations. We demonstrate that customer numbers and waiting times at both stations are independent of each other in the steady-state. As an optimal design, in the second station, We consider that there is a single channel that has the total service capacity of two parallel channels instead of two identical channels. Then, we indicate that the optimal system works faster than the tandem queue system with parallel channels at the second station. Also, when the total service capacity is limited, the mean waiting time in the system has been minimized in the optimal system obtained the mean waiting time lower limit. We compared it to those found through a numerical example.

Optimization and analysis of a tandem queueing system with parallel channel at second station