Variability 8/24/04 Paul A. Jensen

Slides:

Advertisements

Similar presentations

Traffic and routing. Network Queueing Model Packets are buffered in egress queues waiting for serialization on line Link capacity is C bps Average packet.

Advertisements

IE 429, Parisay, January 2003 Review of Probability and Statistics: Experiment outcome: constant, random variable Random variable: discrete, continuous.

Lab Assignment 1 COP 4600: Operating Systems Principles Dr. Sumi Helal Professor Computer & Information Science & Engineering Department University of.

Lecture 13 – Continuous-Time Markov Chains

Nur Aini Masruroh Queuing Theory. Outlines IntroductionBirth-death processSingle server modelMulti server model.

Queuing Analysis Based on noted from Appendix A of Stallings Operating System text 6/10/20151.

1 IOE/MFG 543 Chapter 11: Stochastic single machine models with release dates.

Chap. 20, page 1051 Queuing Theory Arrival process Service process Queue Discipline Method to join queue IE 417, Chap 20, Jan 99.

Lecture 11 Queueing Models. 2 Queueing System  Queueing System:  A system in which items (or customers) arrive at a station, wait in a line (or queue),

Simulating Single server queuing models. Consider the following sequence of activities that each customer undergoes: 1.Customer arrives 2.Customer waits.

Queuing Analysis Based on noted from Appendix A of Stallings Operating System text 6/28/20151.

Queuing. Elements of Waiting Lines  Population –Source of customers Infinite or finite.

7/3/2015© 2007 Raymond P. Jefferis III1 Queuing Systems.

To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 14-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 14.

Queuing Theory. Queuing theory is the study of waiting in lines or queues. Server Pool of potential customers Rear of queue Front of queue Line (or queue)

Processor 1 Processor 2 Disk 1 Disk 2 tasks Demo 1: Computer System with 2 Processors Sharing 2 Disks in Parallel.

Introduction to Queuing Theory. 2 Queuing theory definitions  (Kleinrock) “We study the phenomena of standing, waiting, and serving, and we call this.

Internet Queuing Delay Introduction How many packets in the queue? How long a packet takes to go through?

Chapter 9: Queuing Models

Graduate Program in Engineering and Technology Management

___________________________________________________________________________ Operations Research  Jan Fábry Waiting Line Models.

Queuing Networks. Input source Queue Service mechanism arriving customers exiting customers Structure of Single Queuing Systems Note: 1.Customers need.

Spreadsheet Modeling & Decision Analysis

Waiting Line Models ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry.

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Service Processes CHAPTER 5.

Copyright ©: Nahrstedt, Angrave, Abdelzaher, Caccamo1 Queueing Systems.

McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved. 1.

Lecture 14 – Queuing Networks Topics Description of Jackson networks Equations for computing internal arrival rates Examples: computation center, job shop.

Queueing Analysis of Production Systems (Factory Physics)

Structure of a Waiting Line System Queuing theory is the study of waiting lines Four characteristics of a queuing system: –The manner in which customers.

IE 429, Parisay, January 2010 What you need to know from Probability and Statistics: Experiment outcome: constant, random variable Random variable: discrete,

Queueing Theory What is a queue? Examples of queues: Grocery store checkout Fast food (McDonalds – vs- Wendy’s) Hospital Emergency rooms Machines waiting.

Waiting Lines and Queuing Models. Queuing Theory  The study of the behavior of waiting lines Importance to business There is a tradeoff between faster.

1 Queuing Systems (2). Queueing Models (Henry C. Co)2 Queuing Analysis Cost of service capacity Cost of customers waiting Cost Service capacity Total.

1 Chapters 8 Overview of Queuing Analysis. Chapter 8 Overview of Queuing Analysis 2 Projected vs. Actual Response Time.

8/24/04 Paul A. Jensen Operations Research Models and Methods Copyright All rights reserved Material Movement The movement of material through the.

OMSAN LOJİSTİK. Top Management Program in Logistics & Supply Chain Management (TMPLSM) Production and Operations Management 3: Process Analysis.

Waiting Lines and Queuing Theory Models

Structure of a Waiting Line System Queuing theory is the study of waiting lines Four characteristics of a queuing system: –The manner in which customers.

8/24/04 Paul A. Jensen Operations Research Models and Methods Copyright All rights reserved Review Models and Analysis of Manufacturing Systems.

Copyright ©: Nahrstedt, Angrave, Abdelzaher, Caccamo1 Queueing Systems.

Queuing Models.

Simulation of single server queuing systems

Managerial Decision Making Chapter 13 Queuing Models.

McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

Lecture 14 – Queuing Networks

Models of Traffic Flow 1.

McGraw-Hill/Irwin ©2009 The McGraw-Hill Companies, All Rights Reserved

Queuing Models Economic Analyses.

Queueing Theory What is a queue? Examples of queues:

Queuing Theory Jackson Networks

Chapter 9: Queuing Models

Internet Queuing Delay Introduction

Demo on Queuing Concepts

Internet Queuing Delay Introduction

Queuing Systems Don Sutton.

Queuing models Basic definitions, assumptions, and identities

Solutions Queueing Theory 1

IV-2 Manufacturing Systems modeling

System Performance: Queuing

Queuing models Basic definitions, assumptions, and identities

Lecture 13 – Queuing Systems

Solutions Queueing Theory 1

Lecture 14 – Queuing Networks

Queuing Networks Mean Value Analysis

Queueing Theory 2008.

Waiting Line Models Waiting takes place in virtually every productive process or service. Since the time spent by people and things waiting in line is.

Queuing Models J. Mercy Arokia Rani Assistant Professor

Course Description Queuing Analysis This queuing course

Presentation transcript:

Variability 8/24/04 Paul A. Jensen Operations Research Models and Methods Copyright 2004 - All rights reserved

Example A single machine performs an operation for a unit of product. The mean operation time is 30 seconds. Units arrive at the station with an average time between arrivals of 40 seconds. There is room for three waiting units.

Arrival and service processes are constant Arrival rate: 1.5/minute Service rate: 2/minute Percent utilization Average delay Average WIP

Arrival process is random Service process is constant Arrival rate: 1.5/minute Average Service rate: 2/minute Percent utilization Average delay Average WIP

Arrival and service processes are random Average Arrival rate: 1.5/minute Average Service rate: 2/minute Percent utilization Average delay Average WIP

Conclusion:

Analytical Determination of System Characteristics u Unit flow t operation time U = ut Unit time V Production volume s Number of machines

For analytical purposes Assume service and interarrival times have exponential distributions

We want to compute: State Probabilities Average Number and Time in the Queue Average Number and Time in the System Percent Utilization

The State Probabilities The probability that the system is empty The probability of n in the system for n ≤ s The probability of n in the system for n > s

Average Number and Time In the queue In the system Utilization

Queuing Networks

Equivalence Property Assume: All stations have exponential service times and unlimited queues and all inputs to the system are Poisson processes. Then: Each station can be analyzed independently with queuing analysis. Then: System characteristics can be determined by summing station characteristics.

Consider the Job Shop

Queuing Analysis

System Characteristics

Stations Performing More than One Operation

Items Processed in Lots

The effects of producing in lots

Individual vs. lot production (neglecting setup time) The minimum number of stations is the same The traffic intensity is the same The average number in the queue is the same But: For individual production Lq is in units For lot production Lq is in lots For lot production, WIP is Q times greater For lot production, W and Wq is Q times greater

Effects of setup time Setup time increases the minimum number of machines Setup time increases the traffic intensity The effects are reduced by increasing the lot size But, increasing the lot size increases WIP and throughput time by a factor of Q

Example Production of A is 0.417 per minute, and production of B is 0.8333 per minute. Oper. 1 2 3 4 5 6 7 8 9 10 Time A min. 18 Time B 12 15 Unit Flow 1.272 1.111 WIP A 2.65 2.12 8.332 2.315 WIP B 10.6 12.72 9.258 13.89

Analyze Station 3 for flows in individual units

Determining the number of machines

Analyze Station 3 for flows in lots of 10