ECEN4533 Data Communications Lecture #1818 February 2013 Dr. George Scheets n Problems: 2011 Exam #1 n Corrected Design #1 u Due 18 February (Live) u 1.

Slides:

Advertisements

Similar presentations

Technische universiteit eindhoven 1 Problem 16: Design-space Exploration Jeroen Voeten, Bart Theelen Eindhoven University of Technology Embedded Systems.

Advertisements

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

1 Chapter 8 Queueing models. 2 Delay and Queueing Main source of delay Transmission (e.g., n/R) Propagation (e.g., d/c) Retransmission (e.g., in ARQ)

CS 408 Computer Networks Congestion Control (from Chapter 05)

Multiaccess Problem How to let distributed users (efficiently) share a single broadcast channel? ⇒ How to form a queue for distributed users? The protocols.

1 CNPA B Nasser S. Abouzakhar Resource Allocation 2 Week 6 – Lecture 2 2 nd November, 2009.

1 ELEN 602 Lecture 8 Review of Last lecture –HDLC, PPP –TDM, FDM Today’s lecture –Wavelength Division Multiplexing –Statistical Multiplexing –Preliminary.

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

Queuing Models Basic Concepts

Previously Optimization Probability Review Inventory Models Markov Decision Processes.

ECS 152A Acknowledgement: slides from S. Kalyanaraman & B.Sikdar

Performance analysis for high speed switches Lecture 6.

Crossbar Switches Crossbar switches are an important general architecture for fast switches. 2 x 2 Crossbar Switches A general N x N crossbar switch.

CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Simple queuing models (Sec )

ELEN 602 Lecture 9 Review of last lecture Little’s Formula M/M/1 Queue

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

UCB Review for M2 Jean Walrand U.C. Berkeley

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

Rensselaer Polytechnic Institute © Shivkumar Kalvanaraman & © Biplab Sikdar1 ECSE-4730: Computer Communication Networks (CCN) Network Layer Performance.

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

QUEUING MODELS Queuing theory is the analysis of waiting lines It can be used to: –Determine the # checkout stands to have open at a store –Determine the.

Analysis of Input Queueing More complex system to analyze than output queueing case. In order to analyze it, we make a simplifying assumption of "heavy.

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

Lesson 11: Solved M/G/1 Exercises

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

N Read: 2.4 n Problems: 2.1, 2.3, Web 4.2 n Design #1 due 8 February (Async DL) u Late = -1 per working day n Quiz #1 u < 11 February (Async Distance Learning)

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

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

 Birth Death Processes  M/M/1 Queue  M/M/m Queue  M/M/m/B Queue with Finite Buffers  Results for other Queueing systems 2.

ECEN4533 Data Communications Lecture #2125 February 2013 Dr. George Scheets n Read 11.4 n Problems: Chapter 11.2, 4, & 5 n Quiz #2, 25 March (Live) < 1.

Introduction to Operations Research

Performance Analysis of Computer Systems and Networks Prof. Varsha Apte.

Network Design and Analysis-----Wang Wenjie Queueing System IV: 1 © Graduate University, Chinese academy of Sciences. Network Design and Analysis Wang.

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

TexPoint fonts used in EMF.

M/M/1 queue λn = λ, (n >=0); μn = μ (n>=1) λ μ λ: arrival rate

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

ECEN4533 Data Communications Lecture #1511 February 2013 Dr. George Scheets n Review C.1 - C.3 n Problems: Web 7, 8, & 9 n Quiz #1 < 11 February (Async.

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

EE6610: Week 6 Lectures.

Outlines Received due 13 March 30 %. NO CLASS Week of March (Spring Break)

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

ECEN4533 Data Communications Lecture #244 March 2013 Dr. George Scheets n Read 4.6 n Problems Web n Corrected Exams u Due 6 March (Live) u One.

ECEN4503 Random Signals Lecture #6 26 January 2014 Dr. George Scheets n Read: 3.2 & 3.3 n Problems: 2.28, 3.3, 3.4, 3.7 (1 st Edition) n Problems: 2.61,

ECEN4503 Random Signals Lecture #24 10 March 2014 Dr. George Scheets n Read 8.1 n Problems , 7.5 (1 st & 2 nd Edition) n Next Quiz on 28 March.

CSCI1600: Embedded and Real Time Software Lecture 19: Queuing Theory Steven Reiss, Fall 2015.

Computer Networking Queueing (A Summary from Appendix A) Dr Sandra I. Woolley.

Maciej Stasiak, Mariusz Głąbowski Arkadiusz Wiśniewski, Piotr Zwierzykowski Model of the Nodes in the Packet Network Chapter 10.

Outlines Received due 13 March %. MID-TERM n Wednesday, 1 March n Start studying NOW! n Work 4 of 5 pages n 1-2 pages of the previous midterm will.

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

ECEN4503 Random Signals Lecture #18 24 February 2014 Dr. George Scheets n Read 5.3 & 5.5 n Problems 5.1, 5.4, 5.11 n Exam #1 Friday n Quiz 4 Results Hi.

1 Queuing Delay and Queuing Analysis. RECALL: Delays in Packet Switched (e.g. IP) Networks End-to-end delay (simplified) = End-to-end delay (simplified)

Basic Queuing Insights Nico M. van Dijk “Why queuing never vanishes” European Journal of Operational Research 99 (1997)

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

Random Variables r Random variables define a real valued function over a sample space. r The value of a random variable is determined by the outcome of.

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

Queuing Theory Simulation & Modeling.

M/G/1 Queue & Renewal Reward Theory

Al-Imam Mohammad Ibn Saud University

Queueing Theory What is a queue? Examples of queues:

Queuing Theory Queuing Theory.

B.Ramamurthy Appendix A

Birth-Death Process Birth – arrival of a customer to the system

TexPoint fonts used in EMF.

Queuing Analysis.

COMP60621 Designing for Parallelism

Queuing Theory III.

Queueing Theory 2008.

Queuing Theory III.

CSE 550 Computer Network Design

Presentation transcript:

ECEN4533 Data Communications Lecture #1818 February 2013 Dr. George Scheets n Problems: 2011 Exam #1 n Corrected Design #1 u Due 18 February (Live) u 1 week after you get them back (DL) n Exam #1: 22 February (Live), < 1 March (DL)

ECEN4533 Data Communications Lecture #1920 February 2013 Dr. George Scheets n Read n Problems: 2012 Exam #1 n Exam #1 22 February (Live), < 1 March (DL)

Possible Test Topics S Reading HW Lectures Anything in the circles is fair game.

Exponentially Distributed Packet Length (Somewhat decent fit to real world traffic) Bytes Bin Count

Little's Rule n Under steady-state conditions E[K(t)] = λ E[T] E[Kq(t)] = λ E[Tq] E[# in server] = λ E[Ts] regardless of PDF's involved.

M/G/1 n Exponentially distributed IAT n Arbitrary packet size distribution n Single Server n E[Tq] = E[Ts 2 ]/[2(1-ρ)] n E[Ts 2 ] = σ Ts 2 + E[Ts] 2

M/M/1 Queues n Exponentially Distributed IAT's n Exponentially Distributed Packet Sizes u E[Ts] = σ Ts if Exponential n Single Server n E[Tq] = ρE[Ts]/(1-ρ) n Multiple Input, Multiple Output Switch? u Repeat analysis once per output trunk u Base on input traffic exiting that trunk

Classical M/M/1 Queuing Theory 0% 100% Offered Load Average Queue Size Dropped Packet Probability

Finite Buffer Queuing Performance 0% 100% Trunk Offered Load Probability of dropped packets Average Delay for delivered packets

M/M/a Queues n Exponentially Distributed IAT's n Exponentially Distrubuted Packets n Multiple Servers (# = a) u Queue servicing "a" output trunks u Trunks have identical loads n M/M/1 versus equal speed M/M/a u EX) 100 Mbps had E[T] = μsec 2x50 Mbps had E[T] = μsec u Want a big trunk to minimize delay thru switch

M/M/1 Queues with Priorities n Exponentially Distributed IAT's n Exponentially Distrubuted Packets n Single Server n Hi priority traffic to head of queue u Gets output more speedily u Packet is server is not prempted n Low priority traffic slower to exit n Overall average ≈ same as M/M/1

Queuing with Priorities 0% 100% Offered Load High Priority Average Delay M/M/1 Low Priority Overall Average Stays ≈ the Same

M/D/1 Queues n Exponentially Distributed IAT's n Fixed Packet Size (i.e. Cells) n Single Server n E[Tq] = ρ[Ts]/[2(1-ρ)] n Given equivalent loads and same average sizes, fixed size cells are moved faster.

Classical Queuing Theory 0% 100% Offered Load M/D/1 ρ 2 /(1-ρ) M/M/1 ρ/(1-ρ) Average # in System

Armed with n The average service time E[Ts] n An equation for E[Time in Queue] or E[Time in System] n Little's Rule u Average # packets = E[Time] E[Packet Arrival Rate] where E[Packet Arrival Rate] = λ packets/second n You can find a large number of parameters u E[T], E[Tq], E[K(t)], E[Kq(t)]