An error in calculating the first and second moments of the "exponential-Rayleigh" distribution appears in a recent paper; this correspondence presents the correct calculations.

Cellular mobile radio systems have been proposed that use many base stations to provide radio service over a large geographical area. In such systems, a stored-program processor assigns radio channels to base stations in real time, under certain interference constraints. The capacity and the queueing characteristics of the overall system are strongly dependent on the processor algorithms that are used. This paper presents three algorithms which are in a certain minimax sense statistically optimum. The procedures are quite general, and may be applied to any system that employs many servers, the use of some combinations of which is not allowed. The first algorithm provides for the preferential assignment of a "standard" channel. If all standard channels are busy, a "nonstandard" channel is selected in such a manner that the probability of blocking is minimized in that interferable facility most likely to suffer blocking. The second algorithm provides for the transfer of service from nonstandard to standard channels whenever standard channels become free. The choice of the particular nonstandard channel to be freed is again made in a manner which minimizes the maximum probability of future blockage. The third algorithm provides for the rearrangement of channel assignments in those instances when all assignable channels, both standard and nonstandard, are busy. Such rearrangement can cause channels to become available under certain circumstances. If more than one rearrangement is possible, again the choice of what particular action should be taken is governed by the goal of minimizing the maximum probability of future blockage. All three algorithms attain short-term optimality by enumeration; that is, each candidate for assignment is considered in turn. Under the condition that the given candidate is selected, the conditional probability of future blocking in each of the server groups is calculated, and the maximum of these probabilities is associated with the candidate. After all candidates have been considered, that candidate which has the minimum associated probability is assigned. These algorithms produce, by definition, an instantaneous system state which is always optimum in the above minimax sense. In systems with large numbers of servers, the system changes state rapidly; thus, occasional short-term errors disappear rapidly, and short-term optimization tends to lead to peak performance in the long term as well.

A commonly used model for signal fading in many types of communication channels is that the amplitude of the received signal at a given time is a Rayleigh-distributed random variable. In this paper we show how classical statistical techniques may be applied to the problem of estimating the Rayleigh distribution parameter (i.e., the mean), given samples from the distribution. In particular, we first consider the problem of estimating the population mean, given a sequence of independent samples. We derive an unbiased maximum-likelihood estimator. We show that this estimator is unique, and since it is based on a sufficient statistic, it is therefore "best" in the Blackwell-Rao sense of minimizing expected loss. Using this estimator, we then develop confidence intervals whose length can be used as a guide in selecting the required sample size. We then consider the same estimation problem when the signal samples are obtained from the output of a logarithmic receiver. We derive an interval estimator which does not require taking the antilogs of the log samples, and which is not appreciably worse than the "best" estimator.

If a server group carrying short-holding-time queued traffic at high blocking probability is combined with another server group carrying normal blocked-calls-cleared traffic at low blocking probability, the resulting mixed group will in many cases operate at an intermediate blocking probability. Thus the mixed group provides better service to the queued traffic, while degrading the service of the cleared traffic. If the random arrival characteristics of the short-holding-time traffic are suitably modified by delaying calls an appropriate time before service, then the grades of service for both types of traffic may be engineered independently. An example of a possible use of this technique of induced delay, the combining of dispatch and mobile-telephone traffic on the same set of radio channels in the High-Capacity Mobile Telecommunications System, is discussed.