Los Angeles Math Circle

11/1 -- High School II: Queueing Theory, part 1

Queueing theory applies mathematical models for waiting lines, with applications in the design of telephone systems, computer networks, hospital emergency departments, and more. In a queueing system, customers arrive and are served by servers, and the arrival times of customers and the service times for customers may be random. We study one model of queues (the "M/M/1/K" model) and how customer arrival rate, service rate, and system capacity affect properties of the queue.