CREATING A MATHEMATICAL THEORY OF COMPUTER NETWORKS LEONARD KLEINROCK University of California at Los Angeles, Computer Science Department, 405 Hilgard Avenue, Los Angeles, California 90095-1361, [email protected] 1. ORIGINS of data networks. I chose this area because I was sur- It all began with a comic book! At the age of 6, I was rounded by computers at MIT, and it was clear to me that reading a Superman comic at my apartment in Manhattan some technological breakthroughs were necessary to allow when, in the centerfold, I found plans for building a crys- them to communicate with each other efficiently. In 1961, tal radio. To do so, I needed my father’s used razor blade, I submitted a Ph.D. proposal (Kleinrock 1961a) to study a piece of pencil lead, an empty toilet paper roll, and some data networks, thus launching the technology that eventu- wire, all of which I had no trouble obtaining. In addition, I ally led to the Internet. In the middle of 1961 I published the basic paper (Kleinrock 1961b) laying out the begin- needed an earphone, which I promptly appropriated from a nings of the mathematical theory of data networking, intro- public telephone booth. The one remaining part was some- duced the ideas of segmenting messages into smaller pieces thing called a “variable capacitor.” For this, I convinced my (later called “packets”) in early 1962 (Kleinrock 1962a), mother to take me on the subway down to Canal Street, and completed my Ph.D. work in 1962 (Kleinrock 1962b), the center for radio electronics. Upon arrival to one of the which was later published in 1964 by McGraw-Hill as an shops, I boldly walked up to the clerk and proudly asked to MIT book entitled Communication Nets (Kleinrock 1964). purchase a variable capacitor, whereupon the clerk replied In these works, I developed the theory of stochastic flow of with, “what size do you want?” This blew my cover, and I message traffic in connected networks of communication confessed that I not only had no idea what size, but I also centers and developed the basic principles of packet switch- had no idea what the part was for in the first place. After ing, thus providing the fundamental underpinnings for the explaining why I wanted one, the clerk sold me just what Internet technology. When I use the phrase “Internet tech- I needed. I built the crystal radio and was totally hooked nology,” I intend it to refer to the fundamental analytic and when “free” music came through the earphones—no bat- design principles and algorithms, and not to a wider use teries, no power, all free! An engineer was born, and the of the term which might include, for example, the World seeds for the Internet technology were sown. Wide Web, HTML, Java, etc. I spent the next few years cannibalizing discarded radios I set up the mathematical model using queueing the- as I sharpened my electronics skills. I went to the leg- ory, introduced the critical Independence Assumption, eval- endary Bronx High School of Science and appended my uated network performance, and developed optimal design studies with courses in radio engineering. When the time procedures for determining the capacity assignment, the came to go to college, I found I could not afford to attend, topology, the routing procedure, and the message size. I even at the tuition-free City College of New York (CCNY), introduced and evaluated distributed adaptive routing con- so I enrolled in their evening session program in electri- trol procedures, evaluated different queueing disciplines for cal engineering while working full time as an electronics handling traffic in the nodes (specifically, chopping mes- technician/engineer and bringing a solid paycheck home to sages into smaller segments, now known as packets), and my parents. My work and college training were invaluable tested the theory against extensive simulations. The princi- and led to my winning a full graduate fellowship to attend ples I uncovered (along with my subsequent research) con- the Massachusetts Institute of Technology in the Electrical tinue to provide a basis for today’s Internet technology. For Engineering Department. this work, I am considered to be the inventor of the Internet technology and one of the fathers of the Internet. 2. THE MIT ENVIRONMENT At MIT, I found that the vast majority of my classmates 3. THE NATURE OF DATA COMMUNICATIONS were doing their Ph.D. research in the overpopulated area Back in the late 1950s, it was not clear to most engineers of information theory. This was not for me, and instead I and practitioners that data communications were fundamen- chose to break new ground in the virtually unknown area tally different from voice communications. Not only were Subject classification: Professional: comments on. Area of review: Anniversary Issue (Special). 0030-364X/02/5001-0125 $05.00 Operations Research © 2002 INFORMS 1526-5463 electronic ISSN 125 Vol. 50, No. 1, January–February 2002, pp. 125–131 126 / Kleinrock these differences unrecognized by most, but also in those access. The basic structure I chose was that of a queue cases where they were recognized, the conclusion was that (Kleinrock 1975). A queue is a perfect resource shar- it did not matter because data transmission was of no inter- ing mechanism. It is dynamic, adaptive, and efficient. The est relative to voice transmission. Today, the differences are server does not wait around for a customer who is not understood, important, and of such significance that cur- there, but rather provides service to whoever is there need- rent packet switching networks are seriously threatening the ing service. In the case of data communications, the server business viability of the 100-year-old voice communication consists of the resources of the data network (e.g., the com- telephone networks. munication channels and the switches or routers), the user Voice communication uses a technology called “circuit is the data message or packet stream, and the service ren- switching,” which requires that a dedicated path of network dered is transmission of the message across the data net- resources be set up and allocated between the two com- work. Moreover, the quantities that one considers in queue- municating parties. These resources are dedicated to this ing theory are throughput, response time, efficiency, loss, voice communication during the entire “call,” even if noth- priorities, etc., and these are just the quantities of interest in ing is being spoken by either party. With speech, there is data networks. Indeed, it was clear to me that a queue was silence on the line approximately 1/3 of the time, and this just the right structure for implementing demand access and inefficiency has always been tolerable. However, the nature that queueing theory was perfect for describing and analyz- of data communications is considerably different. Data is ing data networks. inherently “bursty” in that it occurs in short bursts of com- A. K. Erlang, the father of queueing theory (Brockmeyer munications followed by long periods of silence; the ratio et al. 1948), used that theory for representing the behavior of silence to communication can be as high as 1000 1 of telephone traffic and telephone exchanges (Syski 1960). or even 10000 1, and this inefficiency in the use of net- When operations research appeared and then grew in World working resources is totally intolerable. Indeed, one can War II, queueing theory began to be used in other appli- characterize data communication users who wish network cations; but telephony was still the dominant application, resources to send their data as follows: and most of that work utilized models that consisted of a a. they don’t warn you exactly when they will demand single queue. What I needed was to consider networks of access queues. In the late 1950s, the published literature contained b. you cannot predict how much they will demand almost no work on networks of queues. Tandem queues c. most of the time they do not need access (Hunt 1957) had been studied to some extent, as had par- d. when they ask for it, they want immediate access. allel queues (Morse 1958), but these were not rich enough It is not surprising that bursty traffic is nasty to deal with. It topologies for data networks. However, a singular excep- was clear to me back in the late 1950s that the inefficiencies tion to this was the work by James Jackson who published of circuit switching in handling bursty data traffic could not a classic paper (Jackson 1957) on open networks of queues. be tolerated. A new technology had to be invented. Jackson modeled a “job shop” where the nodes were work- stations and the customers were the jobs. He assumed Pois- 4. THE NEED FOR DEMAND ACCESS son job input traffic, independent exponential job service The technology I set out to develop had at its founda- times at each of the stations, and paths through the network tion the principle that a user should be assigned a resource that were governed by independent transition probabilities (e.g., a communications channel) only when he needs it among the workstations. He solved for the equilibrium joint (i.e., when he actually has data to send). I referred to distribution of the number of jobs in each of the stations this as “dynamic resource sharing” or “demand access.” and showed some remarkable properties of the solution. As Examples of demand access schemes that have been devel- we see below, I was able to take exquisite advantage of oped are polling, message switching, packet switching, Jackson’s result for modeling data networks, but not with- asynchronous TDMA, and CSMA/CD (Kleinrock 1976a).