PDF, AND MEAN WITH GENERALIZED Q-FUNCTIONS. COMPUTATION OF THE TRANSIENT M/M/1 QUEUE CDF

Generalized Q-function expressions are developed for the transient-state-occupancy cumulative distribution function (cdf), probability density function (pdf), and the expected value for an M/M/1 queque. The pdf equation is a more compact form of a previous result. When Parl's method is used to calculate the generalized Q-function, the equations are computationally efficient and accurate. For a Q-function relative error of 2 multiplied by 10-**1 **2 , the relative error of the result is typically 10-**1 **0 or better. The relative error will increase, however, for cdf and pdf values on the order of the Q-function relative error. Execution time per point on a VAX 11/750 is on the order of tens of milliseconds for the range of parameters considered.

COMPUTATION OF THE TRANSIENT M/M/1 QUEUE CDF, PDF, AND MEAN WITH GENERALIZED Q-FUNCTIONS. Academic Article