Stat Colloquium: Dr. Jyotirmoy Sarkar
Indiana University Indianapolis
Location
Mathematics/Psychology : 104
Date & Time
November 7, 2025, 11:00 am – 12:00 pm
Description
Title: Limiting Behavior of Two M/M/1 Queues Sharing a Common Waiting Room
Abstract: Customers arrive independently to receive service at one of two businesses, each managed by a single server, according to Poisson processes with different rates. The customers' service times are independent and exponentially distributed with server-specific rates. The customers wait in a limited-capacity common facility. During regular business hours, if a new arrival to either business finds the facility full, they leave; otherwise, they enter and wait until served, even after closing time. We study the limiting behavior of these two M/M/1 queuing systems sharing a common facility with a capacity constraint N to answer these questions relevant to the servers: (Q1) What percentage of customers does each server lose? (Q2) What percentage of time does each server remain idle during regular business hours? (Q3) At closing time, how many customers are waiting to be served by each server?
Joint work with three students: William Boler, William Henby, and Gregory Vaugh