Computation of the transient M/M/1 queue cdf, pdf, and mean with generalized Qfunctions
Abstract
Generalized Qfunction expressions are developed for the transient state occupancy cumulative distribution function (cdf), probability density function (pdf), and expected value for an M/M/1 queue. The pdf equation is an extension of a previous result. When Parl's method is used to calculate the generalized Qfunction, the equations are computationally efficient and accurate. For a Qfunction relative error of 2 x 10 to the 12th, the relative error of the result is typically 10 to the 10th or better. Relative error will increase, however, for cdf and pdf values on the order of Qfunction 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.
 Publication:

IEEE Transactions on Communications
 Pub Date:
 August 1986
 Bibcode:
 1986ITCom..34..814C
 Keywords:

 Distribution Functions;
 Probability Density Functions;
 Pulse Communication;
 Queueing Theory;
 Error Analysis;
 Mean;
 Run Time (Computers);
 Series Expansion;
 Transient Response;
 Communications and Radar