Theory of Queues with Particular Reference to Traffic Problems

The original intention of this paper was to investigate queuing problems related exclusively to automobile traffic. However the author was confronted by these two difficulties: the theory of queues is fragmentary and scattered among many journal articles; and most of the work in the field has been limited to Poissonian input and first serve queue discipline. So the author has elected to concern himself with alleviating these difficulties by gathering the formulated theory into a single integrated discussion, in which whenever the calculations are too long-winded merely the results have been stated; and by emphasizing the priority and random choice queue disciplines and the regular input. Most of the theory concerning the latter is not available in the literature. The application to automobile traffic has been retained in the discussion of the fitting of the distribution of traffic to the Poissonian distribution and to some of the queues having Possonian input