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Introduction to Queueing and Simulation

Introduction to Queueing and Simulation. Kingshuk Roy Choudhury Statistics Department UCC. Examples of queues. `That's the way the whole thing started, Silly but it's true, Thinking of a sweet romance Beginning in a queue." --G. Gouldman, ``Bus Stop," The Hollies.

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Introduction to Queueing and Simulation

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  1. Introduction to Queueing and Simulation Kingshuk Roy Choudhury Statistics Department UCC

  2. Examples of queues `That's the way the whole thing started, Silly but it's true, Thinking of a sweet romance Beginning in a queue." --G. Gouldman, ``Bus Stop," The Hollies

  3. Introductory Examples • people waiting • for tickets at a box office each gets his own ticket one person gets tickets for a group • in a bank for a teller with one line and several tellers • at a grocery store in several check out lines, and jockeying • for Star Tours at Disneyland, then reneging • for medical treatment in a hospital emergency room • machines waitingfor repair • office copiers under maintenance contract • factory equipment • telephone calls waiting for • switching and available lines • service at the other end hanging up if busy waiting on hold • factory jobs waiting at several stages of production • cars waiting to get on the freeway • cases working their way through the court system

  4. Local Area Networksor Media Access Systems

  5. Subdividing an Ethernet with switches

  6. Frequency Division Multiple Access (FDMA)

  7. Time Division Multiplex Access (TDMA)

  8. Basic queueing system components

  9. Performance evaluation

  10. Arrival processes Memoryless Deterministic General

  11. Poisson Process The random process used most frequently to model the arrival pattern. Characteristics of the Poisson process : 1. P[instant occurrence in (t, t+Dt)] = lDt+o(Dt); l is mean arrival rate; o(Dt) approaches 0 faster than Dt. 2. P[no instance occurrence in (t, t+Dt)] = 1- lDt+o(Dt); 3. Arrivals are memoryless. Arrival in one time interval is independent of arrivals in previous or future intervals. 4. P[2 or more arrivals in (t, t+Dt)] = o(Dt). Note that the probability is independent of t.

  12. Queueing disciplines • FIFO • LIFO • Round Robin • SJF • SRPT • FBn • Priority

  13. Number of servers

  14. Birth and death processes Steady-state probabilities (p10) pn = pn+1 (1) …………………………..  pn+1 = n+1 p0 (2) …………………………..  pn = n ( 1 -  ) (3) …………………………..  N =  / ( 1 -  ) (4)

  15. Administrivia • Lectures : Mon. 10-11, Boole LL3, Tue 5-6 CE110 • Contacting Kingshuk: • ph. 4902546 • e-mail: kingshuk@stat.ucc.ie • Office: Room 258 Aras Na Laoi • Hours: 3-4 pm Tue. and Thu. • Notes/practicals later • 20% of grade final will be exercises.

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