He completed his MS degree in electrical engineering in 1977, again from UIUC, and then took his Fellowship to UC Berkeley, where he received his PhD in 1979 under Eugene Wong.

[14] In the 2009-2010 academic year, he was appointed a Rothschild Distinguished Visiting Fellow at the Isaac Newton Institute for Mathematical Sciences at Cambridge.

[25] In relation to these achievements, he was inducted to the National Academy of Engineering in 1999 "for contributions to stochastic systems, communication networks, and control".

[26] In 2003, he received the IEEE Kobayashi Award "for the application of stochastic and probabilistic theory to improved understanding of computer-network behavior, particularly, the modeling and performance optimization of multiple-access channels."

In several contexts he elaborated the consequences of drift towards desireable equlibria in networks, with applications to simulated annealing for discrete optimization problems.

In 2015, Hajek collaborated with Cambridge University Press to publish as a book his course notes for his Random Processes course, ECE 534, at UIUC.

[34] He is also a co-author on the second edition of a more advanced book, Eugene Wong's Stochastic Processes in Engineering Systems (Springer, 1985).