|This is an introductory course in queueing theory and performance modeling, with applications including but not limited to service operations (healthcare, call centers) and computer system resource management (from datacenter to kernel level). The aim of the course is two-fold:
(i) Build insights into best practices for designing service systems (How many service stations should I provision? What speed? How should I separate/prioritize customers based on their service requirements?)
(ii) Build a basic toolbox for analyzing queueing systems in particular and stochastic processes in general.
Tentative list of topics: Open/closed queueing networks; Operational laws; M/M/1 queue; Burke’s theorem and reversibility; M/M/k queue; M/G/1 queue; G/M/1queue; Ph/Ph/k queues and their solution using matrix-analytic methods; Arrival theorem and Mean Value Analysis; Analysis of scheduling policies (e.g., Last-Come-First Served; Processor Sharing); Jackson network and the BCMP theorem (product form networks); Asymptotic analysis (M/M/k queue in heavy/light traffic, Supermarket model in mean-field regime)
Background: Exposure to undergraduate probability (random variables, discrete and continuous probability distributions) and calculus is required. Basics of stochastic processes (continuous/discrete time Markov processes, renewal processes, modes of convergence) will be covered as needed depending on background of enrolled students.