Narahari Umanath (‘Uma’) Prabhu, the founding father of the journal Queueing Systems: Theory and Applications, has passed away a few months ago at the age of 98.

Uma Prabhu was born in 1924 in Kerala, in the southwestern part of India, as the ninth of eleven children in a poor family. He received a B.A. in mathematics from the University of Madras (the current Chennai) in 1946, and then an M.A. in statistics from the University of Bombay (the current Mumbai) in 1950. While lecturing at smaller local Indian universities, he managed to obtain his M.Sc. degree in mathematics from the University of Manchester in 1957. In that time he was already working on queueing-theoretic concepts, albeit using different terminology, as witnessed by the title of his master thesis: ‘Solution to Some Dam Problems’. In 1961 he moved abroad: he first spent three years in Perth, Australia, where he worked at the University of Western Australia, after which he settled in the USA. There he stayed for the rest of his academic career, first a few years at the University of Michigan, and then almost three decades at Cornell University.

Prabhu has been among the most influential queueing theorist, in the first place obviously because of his important work in the area, but in the second place also because of his prominent role in the international research community. Below we comment on two books he authored and elaborate on his efforts in the interest of the queueing and stochastic processes communities.

A major milestone in Prabhu’s work is the book Stochastic Storage Processes — Queues, Insurance Risk, Dams, and Data Communication [4], that was published by Springer in 1998, being a revised and expanded version of an earlier edition. This textbook, intended for an audience of fellow researchers, presents a comprehensive analysis of storage processes using tools from Lévy fluctuation theory and its discrete-time random walk analogue. In a highly transparent manner, the book connects queueing with elements from Wiener-Hopf theory, thus extending results for the class of traditional M/G/1-type queueing systems to the considerably broader class of reflected Lévy processes. Many results in the theory presented focus on systems with Markov modulated input, i.e., queues in which the input (and/or service process) is modulated by an exogenously evolving Markovian background process. The book also nicely highlights the relation between queueing theory and actuarial science. It was a predecessor of this book that caught the attention of Frank Spitzer, the great probabilist and author of the book Principles of Random Walk, which eventually led to the appointment of Prabhu at Cornell.

A second book, Foundations of Queueing Theory [4], published by Kluwer in 1997, is a frequently cited monograph on the basics of queueing theory, intended as a text for an undergraduate course on queueing theory. It covers all the key building blocks, as well as some more advanced concepts, in an accessible manner. The systematic setup very well illustrates the pedagogical talents that Prabhu had.

Prabhu was a co-founder of the journal Stochastic Processes and their Applications (SPA) and a conference series with the same name, but his main service to our community is undoubtedly his role as the founding father, and first editor-in-chief, of the journal Queueing Systems: Theory and Applications (QUESTA). In [1], Onno Boxma describes the process that eventually led to the establishment of QUESTA. Prabhu had decided to consult 18 of his peers, to find out whether there was a need for a journal in this, relatively specialized, area. Until that point queueing theorists mainly published their work in more general applied probability journals (such as Journal of Applied Probability and SPA) and in application-driven journals (such as Operations Research, Mathematics of Operations Research, as well as various of the IEEE journals). With 14 votes in favor and 4 votes against, it was decided that the new journal would be started.

Prabhu remained editor-in-chief until 1995. As described in his paper [2], in the first years after the establishment of the journal, he encouraged the submission of surveys and overviews on specific subareas within queueing theory. Gradually the journal has become the flagship journal in the area, thus solidifying the role of queueing theory. On multiple occasions, Prabhu explicitly expressed his gratitude to the first publisher of QUESTA, J.C. Baltzer, who took a personal interest in his work.

We end this tribute to Prof. Prabhu with a few personal reminiscences by Vidyadhar Kulkarni, a former PhD student of Prabhu’s:

Prof. Prabhu has touched many lives, some as colleagues, some as students, and some as friends and family. Over three decades (from 1964 to 1994) he supervised over 25 PhD students, most of whom went on to establish successful careers of their own, in academia as well as in industry. Interestingly enough, I have had the great fortune of meeting many of them, including his first graduate student (Prof. Narayan Bhat), and his last student (Prof. António Pacheco). He inculcated a love for stochastic processes in general and queueing theory in particular among his students. My personal anecdote that I use till this date is how he told me that we should say “steady state-distribution” and not “steady-state distribution”, since the state evolves randomly all the time, but the state-distribution becomes stationary (or steady). It impressed upon me the need to be precise in one’s writing and thinking. Further personal reminiscences about Prof. Prabhu narrated by his many colleagues can be found in [1]. Further details of his illustrious career can also be found on Wikipedia at [6], and an obituary about his personal life at [5].

After he joined Cornell he established deep scholarly relations with researchers from all over the world: Australia, Russia, Europe, and India. He was truly a world scholar who elicited deep respect from all. However, his interests were not limited to stochastic processes alone. He had wide interests in literature, poetry, old books, history, to name a few. Thus he established a foundation at Cornell in honor of Rabindranath Tagore, a Nobel laureate from India, whose poetry he deeply appreciated. He also co-established (with Prof. Spitzer) an endowed chaired professorship in Stochastic Processes at Cornell.

I had the honor of working with Prof. Prabhu as his graduate student, and this gave me an opportunity to know him as well as his family. His wife Sumi was a very kind and gentle lady. I was treated like a son by Prof. Prabhu as well as Sumi. I briefly met his daughters, Vasundhara and Purnima, who now carry on his memories.