Working Curves for Delayed Exponential Calls Served in Random Order

Working curves of delays for waiting calls served at random are given for a considerable range of loads and group sizes. Exponential holding time calls are assumed originating at random, and served by a simple group of paths. Results of a number of throwdown tests are given to illustrate the effect on call delays of several modes of service, and particularly of service on a random basis. For random service, these results verify the theory recently developed by J. Riordan; perhaps more interestingly they show the effects on delays of certain blends of queued and random service which approximate methods of handling delayed calls in practical use (such as gating and limited storage circuits). The use of random and. queued delay theory is illustrated by a number of examples. To remind the reader that these results are not limited to telephony, department store and vehicular traffic problems are included. A theory for predicting the delays which telephone calls (or other corresponding types of traffic such as vehicular, aircraft, people waiting in line, etc.) having exponentially distributed holding times would encounter when the delayed calls are served in a random order was published in a recent issue of this J O U R N A L * by John Riordan. Mr Riordan's mathematical analysis involved a determination of the first several moments of the delay distributions. He then devised a method of combining elementary exponential curves in such a way as to satisfy the moments previously calculated.