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Unformatted text preview: Lecture 8 Lecture 8 Delays in Probabilistic Models: Delays in Probabilistic Models: Elements from Elements from Queueing Queueing Theory Theory Profs. Profs. Ismail Chabini Ismail Chabini and and Amedeo Odoni Amedeo Odoni 1.225 1.225 J (ESD 225) Transportation Flow Systems J (ESD 225) Transportation Flow Systems 1.225, 11/26/02 Lecture 8, Page 2 Lecture 8 Outline Lecture 8 Outline Introduction to Queueing Conceptual Representation of Queueing Systems Codes for Queueing Models Terminology and Notation Littles Law and Basic Relationships Exponential Distribution for Interarrival and Service times Modeling State Transition Diagram Derivation of waiting characteristics for M/M/1 Summary 1 Applications of Applications of Queueing Queueing Theory Theory Some familiar queues: Airport checkin Automated Teller Machines (ATMs) Fast food restaurants On hold on an 800 phone line Urban intersection Toll booths Aircraft in a holding pattern Calls to the police or to utility companies Levelofservice (LOS) standards Economic analyses involving tradeoffs among operating costs, capital investments and LOS Queueing theory predicts various characteristics of waiting lines (or queues) such as average waiting time 1.225, 11/26/02 Lecture 8, Page 3 1.225, 11/26/02 Lecture 8, Page 4 Queueing Queueing Models Can Be Essential in Analysis of Capital Models Can Be Essential in Analysis of Capital Investments Investments Cost Capacity Cost of building the capacity Total cost Cost of losses due to waiting Optimal capacity Optimal cost 2 1.225, 11/26/02 Lecture 8, Page 5 Strengths and Weaknesses of Strengths and Weaknesses of Queueing Queueing Theory Theory Queueing models necessarily involve approximations and simplification of reality Results give a sense of order of magnitude, of changes relative to a baseline, of promising directions in which to move Closedform results are essentially limited to steady state conditions and derived primarily (but not solely) for birthand death systems and phase systems Some useful bounds for more general systems at steady state...
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 Fall '02
 IsmailChabini

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