Software based desktop videoconferencing tools are developed to demonstrate techniques necessary for video delivery in heterogeneous packet networks. Pyramidal compression, congestion avoidance, end-to-end delivery, and predictive rate control results are presented.

Fairness in multiple-path optimal routing algorithms in virtual circuit data networks is investigated. Fairness measures are developed to evaluate optimal routings. Several objective functions are considered to be possible replacements of the average packet delay objective function that is widely used in optimal routing algorithms, and evaluated for various network and traffic configurations. A numerical study using the fairness measures developed shows that the objective function which is in the integral form of the average packet delay achieves perfect fairness while sacrificing only a nominal increase in the average packet delay. The numerical study also confirms the conjecture by D.P. Bertsekas and R.G. Gallager (1987) that the form of objective function does not affect the average packet delay in any significant way.>

A generalized Q function representation for the transient M/M/1 queue variance is developed. The expression is highly accurate and computationally efficient, and an upper bound on the error is easily calculated. For a Q function relative error of 2*10-/sup 12/ using Parl's method, the relative error of the variance is generally less than 10/sup -9/. Average execution time is of the order of 70 ms per point on a VAX 11/750, but faster execution times can be obtained by using larger Q function relative errors.>

Several methods have been proposed for calculating the generalizedQ-functionQ_{m}(\alpha, \beta), but only isolated comparisons of the various techniques have been reported. The accuracy, range, and execution time of prominent methods for computing theQ-function are compared, and limitations of the algorithms are identified.

GeneralizedQ-function expressions are developed for the transient state occupancy cumulative distribution function (cdf), probability density function (pdf), and expected value for anM/M/1queue. The pdf equation is an extension of a previous result. When Parl's method is used to calculate the generalizedQ-function, the equations are computationally efficient and accurate. For aQ-function relative error of2\cdot10^{-12}, 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 theQfunction 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.

Parl has previously given error bounds suitable for calculating Marcum'sQ-function. However, it is shown that additional terms in the error bound are necessary for accurate calculations of the generalizedQ-functionQ_{m}(\alpha, \beta). The values ofm, \alpha, and\betathat result in successful algorithm completion are examined. Numerical results are presented for calculations of the noncentral chi-square distribution and the probability of detection for a classical multiobservation detection problem.