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Overview of Queueing Systems

Explore the fundamentals of queueing systems, including exponential distribution, Poisson process, Little’s Theorem, and steady-state analysis. Learn how to model and analyze queueing systems efficiently.

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Overview of Queueing Systems

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  1. Overview of Queueing Systems Michalis Faloutsos Archana Yordanos The web

  2. Overview of queueing concepts Exponential Distribution Memoryless: The probability of having an arrival(departure) at time x. Poisson Process. with mean arrival rate l: The probability of having k events. Interarrival time in a Poisson process is exponential: tnis the interarrival tn+1-tn

  3. Little’s Theorem N l T l : : customer arrival rate N: average number of customers in system T: average delay per customer in system Little’s Theorem: System in steady-state

  4. Queueing Systems • n : number of customers in the system (including queue + server) • pn : steady state probability of finding n customers in the system • /: Traffic rate (traffic intensity) • M stands for ``Markovian'',

  5. Modeling a queueing system What goes left, must come right: # of transitions  = # of transitions  Pi are probabilities:

  6. Basic formulas Expected number of customers in the system: Expected time a customer spends in the system: Expected time a customer spends in the queue: Expected number of customers in the system:

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