A Monte Carlo Problem in Underground Communications

Abstract

THE problem presented in this paper was a part of a larger survey into the study of the adequacy of underground communications in British collieries. The results of this were summarized in a paper to the International Conference on Operational Research in September 1957. The particular aspect considered here is a method by which the times to warn each man and clear the colliery may be calculated taking into account the various probabilities of obtaining an answer from some of the telephone points. When the Field Investigation Group of the National Coal Board were studying the problem, they devised a method of carrying out repeated warning trials by pencil and paper methods which proved to be laborious. They therefore approached the Mathematics Division of the National Physical Laboratory for advice on how this could be speeded up by the use of machines. It was found that the best method was to use punched card machines in the initial stages, to perform the mathematical calculations in the middle on the ACE pilot model, and to use punched card machines at the end. It is felt that a description of the method of using these machines to solve a particular problem may be of interest to a wider audience and this paper has therefore been prepared. In this paper, the method of approaching the problem is given first. We then derive the mathematical formulation of the problem, illustrating it with a numerical example for a particular simple telephone layout. The method of obtaining the results for repeated trials using the punched card and ACE pilot model equipment is then given. Since the need for the mathematical formulation adopted may not be apparent and since a more detailed worked example may be of interest, the Appendix gives a full statement of the solution for one colliery. The final section of the body of the report quotes the results obtained in this instance and in two others where the method was used.