| PhD Viva

Name of the Speaker: Ms. Sushmitha Shree (EE18D702)
Guide: Dr. Avhishek Chatterjee
Co-Guide: Prof. Krishna Jagannathan
Online meeting link: https://meet.google.com/vqo-gxdy-fhs
Date/Time: 3rd October 2024 (Thursday), 12:00 PM
Title: A Study of Resource Allocation and Opinion Dynamics in Social Systems

Abstract :

The rapid growth of e-commerce platforms has prompted research in multiple dimensions, including efficient resource allocation for improved customer experience and managing public opinion for enhanced performance. In this talk, we delve into these two essential aspects. Firstly, we aim to identify optimal strategies for minimizing delays and maximizing customer satisfaction, thereby enhancing system performance. Secondly, we employ mathematical frameworks to model the evolution of public opinion and study its behavior, providing insights into managing online perception effectively.

The first part of this talk is motivated by the delay-sensitivity of recent applications, including e-commerce services, quantum communication, and multimedia streaming. The effective system performance in these applications is known to exhibit nonlinear dependencies on the delay. In this part, we address the problem of maximizing the long-term average reward in a single-server queuing system, where the reward obtained for a job is a non-increasing, possibly nonlinear function of its sojourn time (delay). Although the goal of optimizing the total sojourn time is well-studied in the literature, optimizing a nonlinear function of the sojourn times remains unexplored to the best of our knowledge. We consider two arrival models --- the first is a `burst arrival' model, wherein all jobs arrive at the server simultaneously. We show that shortest job first (SJF) maximizes the average reward for any monotonic function of the sojourn times. In the second setting, jobs arrive according to some stochastic process with i.i.d. service requirements. This setting is significantly more challenging to analyze, and identifying an optimal discipline remains elusive. We introduce a new service discipline, shortest predicted sojourn time (SPST), and provide analytical guarantees under specific settings. Numerically, we demonstrate that SPST outperforms well-known disciplines across multiple settings.

In the next part of this talk, we explore a recently proposed framework in opinion dynamics, stochastic bounded confidence (SBC) dynamics, to model the evolution of opinions in social networks. SBC dynamics generalize the classical opinion update models, linear graph-based dynamics and bounded confidence dynamics, capturing the inherent stochasticity and noise in real-life interactions. The asymptotic analysis of SBC dynamics in prior work is a significant analytical contribution. However, such analyses do not shed light on the finite-time behavior of the dynamics, which is often crucial, e.g., in marketing campaigns, election canvassing, etc. In this part of the talk, we present the first finite-time analysis of the existing SBC dynamics. The finite-time analysis of SBC presents some technical challenges mainly due to inherent nonlinearity and stochasticity. We first characterize the finite-time behavior of SBC dynamics of two agents and then extend our analysis to a bistar social graph representing bipartisan democracies and commercial duopolies. Moreover, finite-time analysis of SBC requires us to develop concentration bounds for asymptotically zero-drift unbounded jump Markov processes, which, to our knowledge, have not been studied before. We derive high probability bounds for the opinion difference between any two agents and demonstrate a strong concentration of opinion difference around zero under the exact conditions that ensure the asymptotic stability of the dynamics. We also provide numerical experiments to compare with our analytical results.