Transform Methods for Queuing Asymptotics

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Resource allocation problems that arise in various engineering systems such as data centers, wireless networks, cloud computing, ride hailing etc are modeled using queues. However, except in simple examples, it is not possible to obtain closed form expressions on delay, queue lengths, and their distributions, and so various asymptotic views are adopted. In this talk, I will focus on the heavy-traffic limit where the system is loaded close to its maximum capacity. Over the last few years, our group developed transform methods to study heavy-traffic limits of queues, and applied them to study a variety of systems: a single server queue, load balancing system, input-queued switches that arise in data center networks, queues with abandonments, two-sided queues that arise in online platforms such as ride-hailing, and stationary behavior of SGD based machine learning algorithms. In some of these cases, our approach presents a simpler alternative proofs to known results. However, others such as the switch were not amenable to other methods, and so our approach obtains the first known results. The key ingredient in the method is to work with drift arguments of exponential test functions, and this naturally enables us to exploit results from Laplace and Fourier transforms. The talk will give a tutorial style overview of the method while presenting some of the aforementioned results in more detail. No background on queueing or heavy-traffic is expected.

Siva Theja Maguluri, Georgia Institute of Technology

Siva Theja Maguluri is Fouts Family Early Career Professor and Assistant Professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Tech. He obtained his Ph.D. and MS in ECE as well as MS in Applied Math from UIUC, and B.Tech in Electrical Engineering from IIT Madras. His research interests span the areas of Control, Optimization, Algorithms and Applied Probability. In particular, he works on Reinforcement Learning theory, scheduling, resource allocation and revenue optimization problems that arise in a variety of systems including Data Centers, Cloud Computing, Wireless Networks, Block Chains, Ride hailing systems, etc. His research and teaching are recognized through several awards including the “Best Publication in Applied Probability” award, NSF CAREER award, second place award at INFORMS JFIG best paper competition, Student best paper award at IFIP Performance, “CTL/BP Junior Faculty Teaching Excellence Award,” and “Student Recognition of Excellence in Teaching: Class of 1934 CIOS Award.”