Computation of the Transient M/M/1 Queue cdf, pdf, and Mean with Generalized Q-Functions

Generalized -function expressions are developed for the transient state occupancy cumulative distribution function (cdf), probability density function (pdf), and expected value for an queue. The pdf equation is an extension of a previous result. When Parl\´s method is used to calculate the generalized -function, the equations are computationally efficient and accurate. For a -function relative error of , the relative error of the result is typically 10^-10or better. Relative error will increase, however, for cdf and pdf values on the order of the 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.