A procedure is given for the computation of the transient state occupancy probabilities of theM/M/1queue. The method makes use of the inverse discrete Fourier transform, computed by means of the fast Fourier transform. It avoids the direct evaluation of modified Bessel functions and sidesteps difficulties due to the computation of very large and very small intermediate quantities.

Skinner's method provides a means of computing; numerically, upper and lower bounds on a cumulative distribution function resulting from the convolution of probability density functions. The method thus provides approximate numerical results whose accuracy is known precisely. This paper provides an exposition of Skinner's method. It shows how the method Can be applied to the computation of numerical solutions of other problems, as well as the waiting time distribution of theM/G/1queue, for which Skinner presented the method.

New teletraffic formulas are derived for the congestion in multicell mobile radio telephone systems. Fixed, dynamic, and hybrid channel asignment are considered and "tromboning," where mobileto-mobile calls go via a base station, is taken into account. The formulas agree with previously published sumulation results.

Formulas are derived for the congestion in single-cell mobile radio systems in which there are both land-to-mobile and mobile-to-mobile calls and in which mobile-to-mobile calls go via the base station. Two approaches are used. The first yields modified forms of the familiar Erlang and Engset formulas. The second gives more complicated but more accurate formulas. The results of computer simulations to establish the accuracy of the formulas are described.

Two methods, based on signal processing techniques, are presented for obtaining numerical solutions for the general single server queue with first-come, first-served discipline. The first method is based on the use of the fast Fourier transform (FFT) for producing iterative solutions to a discrete version of Lindley's integral equation for both nonsteady state and equilibrium conditions. The second method makes use of the complex cepstrum, implemented with the FFT, for providing direct solutions with the queue in equilibrium.

An iterative method is presented by which the distribution of queue lengths in theM/G/1queue may be computed. The method applies to the nonsteady-state case and involves repeatedly performing convolutions. The steady-state solution may be obtained by performing the iterations until convergence occurs. A frequencydomain equivalent of the method is presented which gives much greater computational economy.

A class of real integer Huffman sequences is presented. The zero pattern of thez-transform of these sequences indicates a general method for their synthesis.

A method for increasing the traffic capacity of connecting networks is presented which involves rearrangement of calls while in progress. In contrast to previously studied methods for rearrangement of existing calls, the process involves repacking calls as existing calls terminate, rather than when arriving calls are blocked. The scheme has the advantage that the added control complexity is much less than required for rearrangement in the normal sense.

The question of whether uniform Huffman (impulse equivalent) sequences exist is discussed, and some necessary conditions for a Huffman sequence to be uniform are mentioned. A comprehensive search revealed that no uniform Huffman sequences exist from lengths 4 to 17, inclusive. A procedure is described for synthesizing pairs of Huffman sequences whose cross-correlations are approximately uniform and, incidentally, are also themselves Huffman sequences.

The problem of designing uniform-amplitude codes with good autocorrelation functions can be regarded as a problem of mlnimizing a function of several continuous variables. The application of numerical methods of minimization is shown to yield codes with lower sidelobe levels than other known codes of equal lengths. Codes with no sidelobe exceeding unity have been found for lengths as large as 18.