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Seminar_20240509

Limits of unpunctual scheduled traffic

09/05/24 | 1:00pm | Business School (MHL 403)

Dr. Koen De Turck, Associate Professor

Ghent University

Abstract: We look at the arrival process resulting from a stream of customers that have been assigned a fixed appointment but whose unpunctuality is large as compared to the appointment durations. We show that in the limit, the process converges to a Poisson process. This can be shown by either classical techniques based on the characteristic function as well as by a Chen-Stein approach. The latter also provides relatively easy-to-compute error bounds on the approximation in the style of Le Cam’s theorem.

We then input this pre-limit arrival process into both an infinite server system as well as a finite server system. The infinite-server case is well-explained by the Poisson limit of the arrival process, but simulation results show that the finite-server system in its entirety does not converge to an equivalent finite-server system with Poisson inputs and consistently shows considerably better performance. We shed light on this surprising result by showing the (negative) correlation structure of the pre-limit arrival process. In particular, we establish that under two different regimes (heavy traffic and large deviations), the finite-server system behaves like a system with deterministic arrivals.

Bio: 

Koen De Turck is an associate professor at the TELIN department of the Faculty of Engineering and Architecture at Ghent University since October 2021. From 2015 to 2021, he was an associate professor (MCF) at the Telecommunications Department of CentraleSupélec and a researcher at the Laboratoire des Signaux et Systèmes, Gif-sur-Yvette.

His research interests include stochastic modelling of telecommunication systems, queueing theory, scaling methods, and asymptotic analysis. These techniques are applied to a number of domains, notably including wireless networks, and in particular, energy efficiency and bandwidth reutilization. He is also interested random graph methods, stochastic learning and designing efficient simulation algorithms

Event Time and Venue: May 9th, 2024, 1:00pm, Business School (MHL 403)

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