Statistically-Optimum Dynamic Server Assignment in Systems with Interfering Servers

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.