Date & location:
Title: Spatial queues with nearest neighbour shifts
Abstract: In this talk, we study queues in a Euclidean space. Consider 𝑁 servers that are distributed uniformly in [0, 1]ᵈ. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide whether to join the queue they arrived at, or shift to one of the nearest neighbours. Such shifting strategies affect the load on the servers, and may cause some of the servers to become overloaded.We derive a law of large numbers and a central limit theorem for the fraction of overloaded servers in the system as the total number of servers 𝑁 → ∞.Additionally, in the one-dimensional case (𝑑 = 1), we evaluate the expected fraction of overloaded servers for any finite 𝑁.Numerical experiments are provided to support our theoretical results.Typical applications of the results include electric vehicles queueing at charging stations, and queues in airports or supermarkets.
Bio: Vinay did his PhD in the Dept. of Electrical Communication Engineering at the Indian Institute of Science, Bangalore, under the guidance of Prof. Navin Kashyap. His thesis was titled “Probabilistic Forwarding of Coded Packets for Broadcasting over Networks”. He was a post-doctoral researcher at Inria Sophia Antipolis working with Konstantin Avrachenkov in the NEO team prior to joining the NETWORKS-COFUND program in 2024 where he works with Nelly Litvak and Remco van der Hofstad.Broadly, his research is in the areas of random graphs and network science. He is interested in problems that involve a graph structure and complex interactions between the network elements. His research goal is to propose and analyse robust mathematical models that capture different physical phenomena observed on practical networks.
