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Unformatted text preview: Queueing Systems: Lecture 1 Amedeo R. Odoni October 4, 2006 Announcements • PS #3 out this afternoon • Due: October 19 (graded by 10/23) • Office hours – Odoni: Mon. 2:304:30  Wed. 2:304:30 on Oct. 18 (No office hrs 10/16) _ Or send me a message • Quiz #1: October 25, open book, in class • Old quiz problems and solutions: posted on 10/19 Topics in Queueing Theory • Introduction to Queues • Little’s Law • Markovian BirthandDeath Queues • The M/M/1 and Other Markovian Variations • The M/G/1 Queue and Extensions • Priority Queues • Some Useful Bounds • Congestion Pricing • Queueing Networks; State Representations • Dynamic Behavior of Queues Lecture Outline • Introduction to queueing systems • Conceptual representation of queueing systems • Codes for queueing models • Terminology and notation • Little’s Law and basic relationships • Birthanddeath models • The M/M/1 queueing system Reference: Chapter 4, pp. 182203 Queues • Queueing theory is the branch of operations research concerned with waiting lines (delays/congestion) • A queueing system consists of a user source, a queue and a service facility with one or more identical parallel servers • A queueing network is a set of interconnected queueing systems • Fundamental parameters of a queueing system:  Demand rate  Capacity (service rate)  Demand interarrival times  Service times  Queue capacity and discipline (finite vs. infinite; FIFO/FCFS, SIRO, LIFO, priorities) Myriad details (feedback effects, “balking”, “jockeying”, etc.) A Generic Queueing System Source of users/ customers C C C C C C Queue C C C C C C C Servers Size of user source Arrivals process Queue discipline and Queue capacity Service process Number of servers Arrival point at the system Departure point from the system Queueing network consisting of five queueing systems In Queueing system 1 Queueing system 5 Point where users make a choice Point where users merge + Queueing system 4 Queueing system 2 Queueing system 3 Out Applications of Queueing Theory • Some familiar queues: _ Airport checkin; aircraft in a holding pattern _ Automated Teller Machines (ATMs) _ Fast food restaurants _ Phone center’s lines _ Urban intersection _ Toll booths _ Spatially distributed urban systems and services • Levelofservice (LOS) standards • Economic analyses involving tradeoffs among operating costs, capital investments and LOS • Congestion pricing The Airside as a Queueing Network Strengths and Weaknesses of Queueing Theory • Queueing models necessarily involve approximations and simplification of reality • Results give a sense of order of magnitude, changes relative to a baseline, promising directions in which to...
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.
 Fall '06
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