How Networks of Queues Came About

Abstract

queues. To summarize, interest in jobshop manufacturing led me to a good mathematical subject area. I tried the only technique I knew that seemed applicable to one of the more obvious problems in this area; surprisingly, this technique worked, so the first findings on networks of queues were uncovered. Since then, original context of the results has been broadened to include a large range of systems of potential interest to workers in operations research. Now I will expand the paragraph above, filling in details, which may be interesting to some readers and which perhaps belong in the recorded history of operations research. I received my UCLA Ph.D. in very pure mathematics in 1952. The job market then pulled (or pushed) me into the early days of operations research-simply because the only interesting job I could find was with the Naval Logistics Research Project at UCLA (later renamed the Management Science Research Project). The idea of OR immediately appealed to me, and in accordance with the stated mission of the project, I was soon attracted to the problems of jobshop scheduling, epitomized by many small machine shops in the Los Angeles area. First, I carried out some primitive simulations-by hand, and later, with Bill Marlowe's help, using the primitive wireboard-programmed logistics computer at George Washington University, and still later, with Yoshiro Kuratani's help, using UCLA's pioneering Bureau of Standards Western Automatic Computer (SWAC). In spite of impressively skillful programming by Marlowe and Kuratani, these machines simply were not adequate for such simulations. In retrospect, I doubt if my early ideas would have led to anything worthwhile even on the most powerful machines of today. An audited course given by Alex Mood, using William Feller's classic 1950 textbook, Probability Theory and Its Applications, got me into elementary queueing theory and the classical models of simple Markovian waiting-line models.