Some Inequalities in the Theory of Telephone Traffic

Determining the grade of service of a telephone connecting network, as measured, for example, by the probability of blocking, continues to be a major outstanding problem of telephone traffic theory. Two principal methods are available for solving this problem. The first, simulation of a mathematical model of the operating system, has, with the advent of large high-speed computers, become very much less arduous than it used to be. The second, calculation of desired probabilities and expectations from [the] statistical equilibrium equations [of a mathematical model for network operation], is still hampered by the astronomical order of the equations, and in spite of its apparent promise, and its success with trunking problems early in the century, cannot be said to have reached fruition as far as connecting networks are concerned. Indeed, it is taking so long for the strictly analytical approach to develop beyond its trunking and delay applications that in practical 1941 1942 THE BELL SYSTEM