A Program to Study the Effect of Random Delays on the Ability of Trains to Run to a Schedule

This paper gives an example of a somewhat unusual application of a computer to a combinatorial problem. The problem which is being dealt with is of a typical Operational Research type and concerns the cumulative effect of delays which trains suffer between stations, if some rules are operative which make departures of some trains dependent on the arrivals of others. The paper describes the structure of the program and the manner in which the results are exhibited, viz. by comparing the time table according to which trains should run with time tables according to which they might in fact run, and/or by constructing statistical histograms of delays at certain selected stations, showing the effect of random delays between stations. Use has been made of a subroutine generating random numbers, which has been used in other A.R.L. projects as well. The fundamental combinatorial ideas can, of course, be applied to other problems of similar structure, even though they might be expressed in dissimilar terms.