Steady-State Queue-Length Distribution for Mx/G/1 Queue under N-policy

This paper develops a new method for calculating the steady-state queue-length distribution on M
^x
/G/1 queueing system under N-policy. By the Leibniz formula of derivation and the stochastic decomposition property, we get the additional queue-length distribution and the recursion expressions of queue-length distribution. An example is given for illustrating the application of the recursion expression and the sensitivity analysis is also investigated.