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Overview of Queueing Systems. Michalis Faloutsos Archana Yordanos The web. 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.
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Overview of Queueing Systems Michalis Faloutsos Archana Yordanos The web
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
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
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'',
Modeling a queueing system What goes left, must come right: # of transitions = # of transitions Pi are probabilities:
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: