QUEUING THEORY 1.  - means the number of arrivals per second   - service rate of a device  T - mean service time for each arrival   = ( ) Utilization,

Slides:

Advertisements

Similar presentations

Introduction to Queuing Theory

Advertisements

Queueing Model 박희경.

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.

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

System Performance & Scalability i206 Fall 2010 John Chuang.

1 Performance Evaluation of Computer Networks Objectives  Introduction to Queuing Theory  Little’s Theorem  Standard Notation of Queuing Systems  Poisson.

Queuing and Transportation

1 Queuing Theory 2 Queuing theory is the study of waiting in lines or queues. Server Pool of potential customers Rear of queue Front of queue Line (or.

Data Communication and Networks Lecture 13 Performance December 9, 2004 Joseph Conron Computer Science Department New York University

1 Queueing Theory H Plan: –Introduce basics of Queueing Theory –Define notation and terminology used –Discuss properties of queuing models –Show examples.

Queueing Network Model. Single Class Model Open - Infinite stream of arriving customers Closed - Finite population eg Intranet users Indistinguishable.

Little’s Theorem Examples Courtesy of: Dr. Abdul Waheed (previous instructor at COE)

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.

Module 2.0: Modeling of Network Components. Queueing theory  Basics : average number of packets 1/  : mean service time per packet [s] arriving per.

Queueing Theory.

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)

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?

Group members  Hamid Ullah Mian  Mirajuddin  Safi Ullah.

Introduction to Queuing Theory

Queueing Theory I. Summary Little’s Law Queueing System Notation Stationary Analysis of Elementary Queueing Systems  M/M/1  M/M/m  M/M/1/K  …

M EAN -V ALUE A NALYSIS Manijeh Keshtgary O VERVIEW Analysis of Open Queueing Networks Mean-Value Analysis 2.

Network Analysis A brief introduction on queues, delays, and tokens Lin Gu, Computer Networking: A Top Down Approach 6 th edition. Jim Kurose.

Introduction to Queuing Theory

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

Queuing models Basic definitions, assumptions, and identities Operational laws Little’s law Queuing networks and Jackson’s theorem The importance of think.

CS433 Modeling and Simulation Lecture 13 Queueing Theory Dr. Anis Koubâa 03 May 2009 Al-Imam Mohammad Ibn Saud University.

Introduction to Operations Research

Chapter 20 Queuing Theory to accompany Operations Research: Applications and Algorithms 4th edition by Wayne L. Winston Copyright (c) 2004 Brooks/Cole,

NETE4631:Capacity Planning (2)- Lecture 10 Suronapee Phoomvuthisarn, Ph.D. /

Introduction to Queueing Theory

Queuing Theory Basic properties, Markovian models, Networks of queues, General service time distributions, Finite source models, Multiserver queues Chapter.

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

1 Queuing Models Dr. Mahmoud Alrefaei 2 Introduction Each one of us has spent a great deal of time waiting in lines. One example in the Cafeteria. Other.

TexPoint fonts used in EMF.

1 Elements of Queuing Theory The queuing model –Core components; –Notation; –Parameters and performance measures –Characteristics; Markov Process –Discrete-time.

CS433 Modeling and Simulation Lecture 12 Queueing Theory Dr. Anis Koubâa 03 May 2008 Al-Imam Mohammad Ibn Saud University.

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

Queuing Theory and Traffic Analysis Based on Slides by Richard Martin.

CS352 - Introduction to Queuing Theory Rutgers University.

Chapter 1 Introduction. “Wait-in-line” is a common phenomenon in everywhere. Reason: Demand is more than service. “How long must a customer wait?” or.

Internet Applications: Performance Metrics and performance-related concepts E0397 – Lecture 2 10/8/2010.

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

Queuing Theory.  Queuing Theory deals with systems of the following type:  Typically we are interested in how much queuing occurs or in the delays at.

CS 4594 Broadband Intro to Queuing Theory. Kendall Notation Kendall notation: [Kendal 1951] A/B/c/k/m/Z A = arrival probability distribution (most often.

COMT 4291 Queuing Analysis COMT Call/Packet Arrival Arrival Rate, Inter-arrival Time, 1/ Arrival Rate measures the number of customer arrivals.

Queueing Theory. The study of queues – why they form, how they can be evaluated, and how they can be optimized. Building blocks – arrival process and.

Mohammad Khalily Islamic Azad University.  Usually buffer size is finite  Interarrival time and service times are independent  State of the system.

Simple Queueing Theory: Page 5.1 CPE Systems Modelling & Simulation Techniques Topic 5: Simple Queueing Theory  Queueing Models  Kendall notation.

Queuing Theory Simulation & Modeling.

Chapter 1 Introduction.

Al-Imam Mohammad Ibn Saud University

Queueing Theory What is a queue? Examples of queues:

Internet Queuing Delay Introduction

CPSC 531: System Modeling and Simulation

Queueing Theory Carey Williamson Department of Computer Science

Introduction Notation Little’s Law aka Little’s Result

Queuing models Basic definitions, assumptions, and identities

Waiting Lines Queues.

Chapter 20 Queuing Theory

Queuing models Basic definitions, assumptions, and identities

Queueing theory Birth-death Analysis

Queuing Theory By: Brian Murphy.

Mitchell Jareo MAT4340 – Operations Research Dr. Bauldry

Queueing Theory 2008.

Carey Williamson Department of Computer Science University of Calgary

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.

Presentation transcript:

QUEUING THEORY 1

 - means the number of arrivals per second   - service rate of a device  T - mean service time for each arrival   = ( ) Utilization, percentage of time a device is in use  q – mean number of customers in the system (either waiting or in service)  Q – number of customers in the system waiting or being served  N – number of servers  Response time – time from when a process is entered, until it completes  Throughput – Work / Time  Bottlenecks – resource that is in limiting the use of the system because it can’t get it’s work done.  Saturated System – the bottleneck device has reached 100 utilization. 2 NOTATION/DEFINITIONS USED IN QUEUING THEORY

A/B/c/K/m/z  A – interarrival distribution  B – service time distribution  c – number of servers  K – the capacity of the queue  m – number of customers in the system  z – queuing discipline 3 KENDALL NOTATION

 A/B/c is used when -There is no limit on the length of the queue -The source is infinite -The queue discipline is FCFS  A and B may be any of the following: -GI for general independent interarrival time -G for general service time -E for Erlang-k interarrival or service time distribution -M for exponential interarrival or service time distribution -D for deterministic interarrival or service time distribution -H or hyperexponential (with k stages) interarrival or service time distribution. 4 EXAMPLES OF KENDALL NOTATION

5 M/D/3/4/12/FCFS

6 LITTLE’S LAW (A.K.A. LITTLE’S RESULT)

7 M/M/1 QUEUE EXAMPLE

8 M/D/3

9 DISK DRIVE EXAMPLE

Questions: What is the expected number of visits to the disk.  E = (0.5) ( 1 + E)  E = ½ + E/2  ½ E = ½  E = 1 Question: What is the expected number of visits to the cpu?  E = 1 + (0.5) E  ½ E = 1  E = 2 10 QUESTIONS ABOUT CPU DISK EXAMPLE

11 MULTI USER MULTI RESOURCES

12 MULTI PROCESS MULTI DISKS EXAMPLE

13 MEMORY HIT RATIO EXAMPLE

14 BIRTH DEATH PROCESSES

 The rate of moving from state 2 into state 3 should be the same as the rate from moving from state 3 into state 2. Over the course of a day if the queuing system moved from state 2 to /day then the rate that the system goes from state 3 to state 2 must also be 5000/day(or maybe 4999/day).  The probability of being in one state i is P. The probability of being in state i and going to state i+1 is equal to the probability of doing from state i+1 and going to state i. 15 THOUGHTS ON BIRTH DEATH PROCESSES

16 BIRTH DEATH CONTINUED

17 STATE PROBABILITIES

18 EXPECTED NUMBER IN STATE

19 M/M/1 EXAMPLE

20 TIME IN SYSTEM EXAMPLE

21 TIME IN SYSTEM EXAMPLE CONT.