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Introduction to Queueing Theory

Introduction to Queueing Theory Raj Jain Washington University in Saint Louis or A Mini-Course offered at UC Berkeley, Sept-Oct 2012. These slides and audio/video recordings are available on-line at: and ~jain/queue UC Berkeley, Fall 2012 2012 Raj Jain 30-1. Overview Queueing Notation Rules for All Queues Little's Law Types of stochastic Processes UC Berkeley, Fall 2012 2012 Raj Jain 30-2. Basic Components of a Queue 1. Arrival 6. Service 2. Service time process discipline distribution 5. Population Size 4. Waiting positions 3. Number of servers UC Berkeley, Fall 2012 2012 Raj Jain 30-3. Kendall Notation A/S/m/B/K/SD. A: Arrival process S: Service time distribution m: Number of servers B: Number of buffers (system capacity). K: Population size, and SD: Service discipline UC Berkeley, Fall 2012 2012 Raj Jain 30-4.

Stochastic Processes Process: Function of time Stochastic Process: Random variables, which are functions of time Example 1: n(t) = number of jobs at the CPU of a computer system Take several identical systems and observe n(t) The number n(t) is a random variable. Can find the probability distribution functions for n(t) at

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