TUFTS UNIVERSITY DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING ES 152 ENGINEERING SYSTEMS Spring Lesson 14. Queue System Theory

B. Maddah ENMG 622 ENMG /27/07

B. Maddah ENMG 622 ENMG 5 3/27/7 Queueig Theory () What is a queueig system? A queueig system cosists of servers (resources) that provide service to customers (etities). A Customer requestig service will

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

Queuig Theory Basic properties, Markovia models, Networks of queues, Geeral service time distributios, Fiite source models, Multiserver queues Chapter 8 Kedall s Notatio for Queuig Systems A/B/X/Y/Z: A

First come, first served (FCFS) Batch

Queuig Theory Prelimiaries A flow of customers comig towards the service facility forms a queue o accout of lack of capacity to serve them all at a time. RK Jaa Some Examples: Persos waitig at doctor s

http://www.xelca.l/articles/ufo_ladigsbaa_houte.aspx imulatio Output aalysis 3/4/06 This lecture Output: A simulatio determies the value of some performace measures, e.g. productio per hour, average queue

CS/ECE 715 Spring 2004 Homework 5 (Due date: March 16)

CS/ECE 75 Sprig 004 Homework 5 (Due date: March 6) Problem 0 (For fu). M/G/ Queue with Radom-Sized Batch Arrivals. Cosider the M/G/ system with the differece that customers are arrivig i batches accordig

The statistical pattern of the arrival can be indicated through the probability distribution of the number of the arrivals in an interval.

Itroductio Queuig are the most freuetly ecoutered roblems i everyday life. For examle, ueue at a cafeteria, library, bak, etc. Commo to all of these cases are the arrivals of objects reuirig service ad

A queueing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service,

Queuig System A queueig system ca be described as customers arrivig for service, waitig for service if it is ot immediate, ad if havig waited for service, leavig the service after beig served. The basic

Simulation of Discrete Event Systems

Simulatio of Discrete Evet Systems Uit 9 Queueig Models Fall Witer 2014/2015 Uiv.-Prof. Dr.-Ig. Dipl.-Wirt.-Ig. Christopher M. Schlick Chair ad Istitute of Idustrial Egieerig ad Ergoomics RWTH Aache Uiversity

Announcements. Queueing Systems: Lecture 1. Lecture Outline. Topics in Queueing Theory

Aoucemets Queueig Systems: Lecture Amedeo R. Odoi October 4, 2006 PS #3 out this afteroo Due: October 9 (graded by 0/23) Office hours Odoi: Mo. 2:30-4:30 - Wed. 2:30-4:30 o Oct. 8 (No office hrs 0/6) _

Queueing theory and Replacement model

Queueig theory ad Replacemet model. Trucks at a sigle platform weigh-bridge arrive accordig to Poisso probability distributio. The time required to weigh the truck follows a expoetial probability distributio.

Reliability and Queueing

Copyright 999 Uiversity of Califoria Reliability ad Queueig by David G. Messerschmitt Supplemetary sectio for Uderstadig Networked Applicatios: A First Course, Morga Kaufma, 999. Copyright otice: Permissio

TCOM 501: Networking Theory & Fundamentals. Lecture 3 January 29, 2003 Prof. Yannis A. Korilis

TCOM 5: Networkig Theory & Fudametals Lecture 3 Jauary 29, 23 Prof. Yais A. Korilis 3-2 Topics Markov Chais Discrete-Time Markov Chais Calculatig Statioary Distributio Global Balace Equatios Detailed Balace

Chapter 11 Output Analysis for a Single Model. Banks, Carson, Nelson & Nicol Discrete-Event System Simulation

Chapter Output Aalysis for a Sigle Model Baks, Carso, Nelso & Nicol Discrete-Evet System Simulatio Error Estimatio If {,, } are ot statistically idepedet, the S / is a biased estimator of the true variace.

There is no straightforward approach for choosing the warmup period l.

B. Maddah INDE 504 Discrete-Evet Simulatio Output Aalysis () Statistical Aalysis for Steady-State Parameters I a otermiatig simulatio, the iterest is i estimatig the log ru steady state measures of performace.

4.6 M/M/s/s Loss Queueing Model

4.6 M/M// Lo Queueig Model Characteritic 1. Iterarrival time i expoetial with rate Arrival proce i Poio Proce with rate 2. Iterarrival time i expoetial with rate µ Number of ervice i Poio Proce with rate

Output Analysis (2, Chapters 10 &11 Law)

B. Maddah ENMG 6 Simulatio Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should be doe

Birth-Death Processes. Outline. EEC 686/785 Modeling & Performance Evaluation of Computer Systems. Relationship Among Stochastic Processes.

EEC 686/785 Modelig & Perforace Evaluatio of Couter Systes Lecture Webig Zhao Deartet of Electrical ad Couter Egieerig Clevelad State Uiversity webig@ieee.org based o Dr. Raj jai s lecture otes Relatioshi

SINGLE-CHANNEL QUEUING PROBLEMS APPROACH

SINGLE-CHANNEL QUEUING ROBLEMS AROACH Abdurrzzag TAMTAM, Doctoral Degree rogramme () Dept. of Telecommuicatios, FEEC, BUT E-mail: xtamta@stud.feec.vutbr.cz Supervised by: Dr. Karol Molár ABSTRACT The paper

Discrete Mathematics and Probability Theory Spring 2016 Rao and Walrand Note 19

CS 70 Discrete Mathematics ad Probability Theory Sprig 2016 Rao ad Walrad Note 19 Some Importat Distributios Recall our basic probabilistic experimet of tossig a biased coi times. This is a very simple

1 Introduction to reducing variance in Monte Carlo simulations

Copyright c 010 by Karl Sigma 1 Itroductio to reducig variace i Mote Carlo simulatios 11 Review of cofidece itervals for estimatig a mea I statistics, we estimate a ukow mea µ = E(X) of a distributio by

c. Explain the basic Newsvendor model. Why is it useful for SC models? e. What additional research do you believe will be helpful in this area?

1. Research Methodology a. What is meat by the supply chai (SC) coordiatio problem ad does it apply to all types of SC s? Does the Bullwhip effect relate to all types of SC s? Also does it relate to SC

Limit Theorems. Convergence in Probability. Let X be the number of heads observed in n tosses. Then, E[X] = np and Var[X] = np(1-p).

Limit Theorems Covergece i Probability Let X be the umber of heads observed i tosses. The, E[X] = p ad Var[X] = p(-p). L O This P x p NM QP P x p should be close to uity for large if our ituitio is correct.

NOTES ON DISTRIBUTIONS

NOTES ON DISTRIBUTIONS MICHAEL N KATEHAKIS Radom Variables Radom variables represet outcomes from radom pheomea They are specified by two objects The rage R of possible values ad the frequecy fx with which

Increasing timing capacity using packet coloring

003 Coferece o Iformatio Scieces ad Systems, The Johs Hopkis Uiversity, March 4, 003 Icreasig timig capacity usig packet colorig Xi Liu ad R Srikat[] Coordiated Sciece Laboratory Uiversity of Illiois e-mail:

Generalized Semi- Markov Processes (GSMP)

Geeralized Semi- Markov Processes (GSMP) Summary Some Defiitios Markov ad Semi-Markov Processes The Poisso Process Properties of the Poisso Process Iterarrival times Memoryless property ad the residual

PROPERTIES OF AN EULER SQUARE

PROPERTIES OF N EULER SQURE bout 0 the mathematicia Leoard Euler discussed the properties a x array of letters or itegers ow kow as a Euler or Graeco-Lati Square Such squares have the property that every

Final Review for MATH 3510

Fial Review for MATH 50 Calculatio 5 Give a fairly simple probability mass fuctio or probability desity fuctio of a radom variable, you should be able to compute the expected value ad variace of the variable

Lecture 5: April 17, 2013

TTIC/CMSC 350 Mathematical Toolkit Sprig 203 Madhur Tulsiai Lecture 5: April 7, 203 Scribe: Somaye Hashemifar Cheroff bouds recap We recall the Cheroff/Hoeffdig bouds we derived i the last lecture idepedet

Empirical Distributions

Empirical Distributios A empirical distributio is oe for which each possible evet is assiged a probability derived from experimetal observatio. It is assumed that the evets are idepedet ad the sum of the

Discrete Mathematics and Probability Theory Summer 2014 James Cook Note 15

CS 70 Discrete Mathematics ad Probability Theory Summer 2014 James Cook Note 15 Some Importat Distributios I this ote we will itroduce three importat probability distributios that are widely used to model

Introduction to probability Stochastic Process Queuing systems. TELE4642: Week2

Itroductio to probability Stochastic Process Queuig systems TELE4642: Week2 Overview Refresher: Probability theory Termiology, defiitio Coditioal probability, idepedece Radom variables ad distributios

Probability, Expectation Value and Uncertainty

Chapter 1 Probability, Expectatio Value ad Ucertaity We have see that the physically observable properties of a quatum system are represeted by Hermitea operators (also referred to as observables ) such

B. Maddah ENMG 622 ENMG /20/09

B. Maddah ENMG 6 ENMG 5 5//9 Queueig Theory () Distributio of waitig time i M/M/ Let T q be the waitig time i queue of a ustomer. The it a be show that, ( ) t { q > } =. T t e Let T be the total time of

Basis for simulation techniques

Basis for simulatio techiques M. Veeraraghava, March 7, 004 Estimatio is based o a collectio of experimetal outcomes, x, x,, x, where each experimetal outcome is a value of a radom variable. x i. Defiitios

Queueing Theory (Part 3)

Queueig Theory art 3 M/M/ Queueig Sytem with Variatio M/M/, M/M///K, M/M//// Queueig Theory- M/M/ Queueig Sytem We defie λ mea arrival rate mea ervice rate umber of erver > ρ λ / utilizatio ratio We require

NUMERICAL METHODS FOR SOLVING EQUATIONS

Mathematics Revisio Guides Numerical Methods for Solvig Equatios Page 1 of 11 M.K. HOME TUITION Mathematics Revisio Guides Level: GCSE Higher Tier NUMERICAL METHODS FOR SOLVING EQUATIONS Versio:. Date:

Topic 10: Introduction to Estimation

Topic 0: Itroductio to Estimatio Jue, 0 Itroductio I the simplest possible terms, the goal of estimatio theory is to aswer the questio: What is that umber? What is the legth, the reactio rate, the fractio

Axioms of Measure Theory

MATH 532 Axioms of Measure Theory Dr. Neal, WKU I. The Space Throughout the course, we shall let X deote a geeric o-empty set. I geeral, we shall ot assume that ay algebraic structure exists o X so that

STAT 350 Handout 19 Sampling Distribution, Central Limit Theorem (6.6)

STAT 350 Hadout 9 Samplig Distributio, Cetral Limit Theorem (6.6) A radom sample is a sequece of radom variables X, X 2,, X that are idepedet ad idetically distributed. o This property is ofte abbreviated

On Poisson Bulk Arrival Queue: M / M /2/ N with. Balking, Reneging and Heterogeneous servers

Applied Mathematical Scieces, Vol., 008, o. 4, 69-75 O oisso Bulk Arrival Queue: M / M // with Balkig, Reegig ad Heterogeeous servers M. S. El-aoumy Statistics Departmet, Faculty of Commerce, Dkhlia, Egypt

Topic 9: Sampling Distributions of Estimators

Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be

A Question. Output Analysis. Example. What Are We Doing Wrong? Result from throwing a die. Let X be the random variable

A Questio Output Aalysis Let X be the radom variable Result from throwig a die 5.. Questio: What is E (X? Would you throw just oce ad take the result as your aswer? Itroductio to Simulatio WS/ - L 7 /

Series: Infinite Sums

Series: Ifiite Sums Series are a way to mae sese of certai types of ifiitely log sums. We will eed to be able to do this if we are to attai our goal of approximatig trascedetal fuctios by usig ifiite degree

Estimating the Population Mean - when a sample average is calculated we can create an interval centered on this average

6. Cofidece Iterval for the Populatio Mea p58 Estimatig the Populatio Mea - whe a sample average is calculated we ca create a iterval cetered o this average x-bar - at a predetermied level of cofidece

t distribution [34] : used to test a mean against an hypothesized value (H 0 : µ = µ 0 ) or the difference

EXST30 Backgroud material Page From the textbook The Statistical Sleuth Mea [0]: I your text the word mea deotes a populatio mea (µ) while the work average deotes a sample average ( ). Variace [0]: The

A statistical method to determine sample size to estimate characteristic value of soil parameters

A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig

Discrete Mathematics and Probability Theory Spring 2012 Alistair Sinclair Note 15

CS 70 Discrete Mathematics ad Probability Theory Sprig 2012 Alistair Siclair Note 15 Some Importat Distributios The first importat distributio we leared about i the last Lecture Note is the biomial distributio

MIXED REVIEW of Problem Solving

MIXED REVIEW of Problem Solvig STATE TEST PRACTICE classzoe.com Lessos 2.4 2.. MULTI-STEP PROBLEM A ball is dropped from a height of 2 feet. Each time the ball hits the groud, it bouces to 70% of its previous

Randomized Algorithms I, Spring 2018, Department of Computer Science, University of Helsinki Homework 1: Solutions (Discussed January 25, 2018)

Radomized Algorithms I, Sprig 08, Departmet of Computer Sciece, Uiversity of Helsiki Homework : Solutios Discussed Jauary 5, 08). Exercise.: Cosider the followig balls-ad-bi game. We start with oe black

Math 113 Exam 3 Practice

Math Exam Practice Exam will cover.-.9. This sheet has three sectios. The first sectio will remid you about techiques ad formulas that you should kow. The secod gives a umber of practice questios for you

Sums, products and sequences

Sums, products ad sequeces How to write log sums, e.g., 1+2+ (-1)+ cocisely? i=1 Sum otatio ( sum from 1 to ): i 3 = 1 + 2 + + If =3, i=1 i = 1+2+3=6. The ame ii does ot matter. Could use aother letter

Topic 9: Sampling Distributions of Estimators

Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be

Sequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence

Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece 1, 1, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet

Statisticians use the word population to refer the total number of (potential) observations under consideration

6 Samplig Distributios Statisticias use the word populatio to refer the total umber of (potetial) observatios uder cosideratio The populatio is just the set of all possible outcomes i our sample space

Recursive Algorithms. Recurrences. Recursive Algorithms Analysis

Recursive Algorithms Recurreces Computer Sciece & Egieerig 35: Discrete Mathematics Christopher M Bourke cbourke@cseuledu A recursive algorithm is oe i which objects are defied i terms of other objects

Goodness-of-Fit Tests and Categorical Data Analysis (Devore Chapter Fourteen)

Goodess-of-Fit Tests ad Categorical Data Aalysis (Devore Chapter Fourtee) MATH-252-01: Probability ad Statistics II Sprig 2019 Cotets 1 Chi-Squared Tests with Kow Probabilities 1 1.1 Chi-Squared Testig................

HOMEWORK #10 SOLUTIONS

Math 33 - Aalysis I Sprig 29 HOMEWORK # SOLUTIONS () Prove that the fuctio f(x) = x 3 is (Riema) itegrable o [, ] ad show that x 3 dx = 4. (Without usig formulae for itegratio that you leart i previous

Chapter 22. Comparing Two Proportions. Copyright 2010, 2007, 2004 Pearson Education, Inc.

Chapter 22 Comparig Two Proportios Copyright 2010, 2007, 2004 Pearso Educatio, Ic. Comparig Two Proportios Read the first two paragraphs of pg 504. Comparisos betwee two percetages are much more commo

Topic 9: Sampling Distributions of Estimators

Topic 9: Samplig Distributios of Estimators Course 003, 2016 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be

6.041/6.431 Spring 2009 Final Exam Thursday, May 21, 1:30-4:30 PM.

6.041/6.431 Sprig 2009 Fial Exam Thursday, May 21, 1:30-4:30 PM. Name: Recitatio Istructor: Questio Part Score Out of 0 2 1 all 18 2 all 24 3 a 4 b 4 c 4 4 a 6 b 6 c 6 5 a 6 b 6 6 a 4 b 4 c 4 d 5 e 5 7

Test of Statistics - Prof. M. Romanazzi

1 Uiversità di Veezia - Corso di Laurea Ecoomics & Maagemet Test of Statistics - Prof. M. Romaazzi 19 Jauary, 2011 Full Name Matricola Total (omial) score: 30/30 (2 scores for each questio). Pass score:

The Interval of Convergence for a Power Series Examples

The Iterval of Covergece for a Power Series Examples To review the process: How to Test a Power Series for Covergece. Fid the iterval where the series coverges absolutely. We have to use the Ratio or Root

Approximations and more PMFs and PDFs

Approximatios ad more PMFs ad PDFs Saad Meimeh 1 Approximatio of biomial with Poisso Cosider the biomial distributio ( b(k,,p = p k (1 p k, k λ: k Assume that is large, ad p is small, but p λ at the limit.

1 Generating functions for balls in boxes

Math 566 Fall 05 Some otes o geeratig fuctios Give a sequece a 0, a, a,..., a,..., a geeratig fuctio some way of represetig the sequece as a fuctio. There are may ways to do this, with the most commo ways

Castiel, Supernatural, Season 6, Episode 18

13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio

1036: Probability & Statistics

036: Probability & Statistics Lecture 0 Oe- ad Two-Sample Tests of Hypotheses 0- Statistical Hypotheses Decisio based o experimetal evidece whether Coffee drikig icreases the risk of cacer i humas. A perso

( ) = p and P( i = b) = q.

MATH 540 Radom Walks Part 1 A radom walk X is special stochastic process that measures the height (or value) of a particle that radomly moves upward or dowward certai fixed amouts o each uit icremet of

Analysis of a queueing model with service threshold

Rochester Istitute of Techology RIT Scholar Works Theses Thesis/Dissertatio Collectios 2-7-2 alysis of a queueig model with service threshold Kathry Graf Follow this ad additioal works at: http://scholarworks.rit.edu/theses

Lecture 2: Monte Carlo Simulation

STAT/Q SCI 43: Itroductio to Resamplig ethods Sprig 27 Istructor: Ye-Chi Che Lecture 2: ote Carlo Simulatio 2 ote Carlo Itegratio Assume we wat to evaluate the followig itegratio: e x3 dx What ca we do?

Stochastic Matrices in a Finite Field

Stochastic Matrices i a Fiite Field Abstract: I this project we will explore the properties of stochastic matrices i both the real ad the fiite fields. We first explore what properties 2 2 stochastic matrices

Activity 3: Length Measurements with the Four-Sided Meter Stick

Activity 3: Legth Measuremets with the Four-Sided Meter Stick OBJECTIVE: The purpose of this experimet is to study errors ad the propagatio of errors whe experimetal data derived usig a four-sided meter

AP Statistics Review Ch. 8

AP Statistics Review Ch. 8 Name 1. Each figure below displays the samplig distributio of a statistic used to estimate a parameter. The true value of the populatio parameter is marked o each samplig distributio.

Chapter 22. Comparing Two Proportions. Copyright 2010 Pearson Education, Inc.

Chapter 22 Comparig Two Proportios Copyright 2010 Pearso Educatio, Ic. Comparig Two Proportios Comparisos betwee two percetages are much more commo tha questios about isolated percetages. Ad they are more

9. Simulation lect09.ppt S Introduction to Teletraffic Theory - Fall

lect09.ppt S-38.145 - Itroductio to Teletraffic Theory - Fall 2001 1 Cotets Itroductio Geeratio of realizatios of the traffic process Geeratio of realizatios of radom variables Collectio of data Statistical

Modeling and Performance Analysis with Discrete-Event Simulation

Simulatio Modelig ad Performace Aalysis with Discrete-Evet Simulatio Chapter 5 Statistical Models i Simulatio Cotets Basic Probability Theory Cocepts Useful Statistical Models Discrete Distributios Cotiuous

A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence

Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece,, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet as

The coalescent coalescence theory

The coalescet coalescece theory Peter Beerli September 1, 009 Historical ote Up to 198 most developmet i populatio geetics was prospective ad developed expectatios based o situatios of today. Most work

SNAP Centre Workshop. Basic Algebraic Manipulation

SNAP Cetre Workshop Basic Algebraic Maipulatio 8 Simplifyig Algebraic Expressios Whe a expressio is writte i the most compact maer possible, it is cosidered to be simplified. Not Simplified: x(x + 4x)

Agreement of CI and HT. Lecture 13 - Tests of Proportions. Example - Waiting Times

Sigificace level vs. cofidece level Agreemet of CI ad HT Lecture 13 - Tests of Proportios Sta102 / BME102 Coli Rudel October 15, 2014 Cofidece itervals ad hypothesis tests (almost) always agree, as log

Discrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 18

EECS 70 Discrete Mathematics ad Probability Theory Sprig 2013 Aat Sahai Lecture 18 Iferece Oe of the major uses of probability is to provide a systematic framework to perform iferece uder ucertaity. A

MA131 - Analysis 1. Workbook 3 Sequences II

MA3 - Aalysis Workbook 3 Sequeces II Autum 2004 Cotets 2.8 Coverget Sequeces........................ 2.9 Algebra of Limits......................... 2 2.0 Further Useful Results........................

Section 11.8: Power Series

Sectio 11.8: Power Series 1. Power Series I this sectio, we cosider geeralizig the cocept of a series. Recall that a series is a ifiite sum of umbers a. We ca talk about whether or ot it coverges ad i

Unit 5. Gases (Answers)

Uit 5. Gases (Aswers) Upo successful completio of this uit, the studets should be able to: 5. Describe what is meat by gas pressure.. The ca had a small amout of water o the bottom to begi with. Upo heatig

Statistics 511 Additional Materials

Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability

Statistical Inference (Chapter 10) Statistical inference = learn about a population based on the information provided by a sample.

Statistical Iferece (Chapter 10) Statistical iferece = lear about a populatio based o the iformatio provided by a sample. Populatio: The set of all values of a radom variable X of iterest. Characterized

Summary: CORRELATION & LINEAR REGRESSION. GC. Students are advised to refer to lecture notes for the GC operations to obtain scatter diagram.

Key Cocepts: 1) Sketchig of scatter diagram The scatter diagram of bivariate (i.e. cotaiig two variables) data ca be easily obtaied usig GC. Studets are advised to refer to lecture otes for the GC operatios

STA Learning Objectives. Population Proportions. Module 10 Comparing Two Proportions. Upon completing this module, you should be able to:

STA 2023 Module 10 Comparig Two Proportios Learig Objectives Upo completig this module, you should be able to: 1. Perform large-sample ifereces (hypothesis test ad cofidece itervals) to compare two populatio

THE POTENTIALS METHOD FOR A CLOSED QUEUEING SYSTEM WITH HYSTERETIC STRATEGY OF THE SERVICE TIME CHANGE

Joural of Applied Mathematics ad Computatioal Mechaics 5, 4(), 3-43 www.amcm.pcz.pl p-issn 99-9965 DOI:.75/amcm.5..4 e-issn 353-588 THE POTENTIALS METHOD FOR A CLOSED QUEUEING SYSTEM WITH HYSTERETIC STRATEGY

Data Analysis and Statistical Methods Statistics 651

Data Aalysis ad Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasii/teachig.html Suhasii Subba Rao Review of testig: Example The admistrator of a ursig home wats to do a time ad motio

Chapter Vectors

Chapter 4. Vectors fter readig this chapter you should be able to:. defie a vector. add ad subtract vectors. fid liear combiatios of vectors ad their relatioship to a set of equatios 4. explai what it

PRACTICE PROBLEMS FOR THE FINAL

PRACTICE PROBLEMS FOR THE FINAL Math 36Q Fall 25 Professor Hoh Below is a list of practice questios for the Fial Exam. I would suggest also goig over the practice problems ad exams for Exam ad Exam 2 to

Roberto s Notes on Infinite Series Chapter 1: Sequences and series Section 3. Geometric series

Roberto s Notes o Ifiite Series Chapter 1: Sequeces ad series Sectio Geometric series What you eed to kow already: What a ifiite series is. The divergece test. What you ca le here: Everythig there is to

Half Life Worksheet Extra Practice

Half Life Worksheet Extra Practice ) Fluorie- has a half life of approximately 5 secods. What fractio of the origial uclei would remai after miute? ) Iodie-3 has a half life of 8 days. What fractio of

Notes on iteration and Newton s method. Iteration

Notes o iteratio ad Newto s method Iteratio Iteratio meas doig somethig over ad over. I our cotet, a iteratio is a sequece of umbers, vectors, fuctios, etc. geerated by a iteratio rule of the type 1 f

Nonequilibrium Excess Carriers in Semiconductors

Lecture 8 Semicoductor Physics VI Noequilibrium Excess Carriers i Semicoductors Noequilibrium coditios. Excess electros i the coductio bad ad excess holes i the valece bad Ambiolar trasort : Excess electros

9. Simulation. lect09.ppt S Introduction to Teletraffic Theory - Fall Literature

lect09.ppt S-38.45 - Itroductio to Teletraffic Theory - Fall 999 Literature I. Mitrai (98) Simulatio techiques for discrete evet systems Cambridge Uiversity Press, Cambridge A.M. Law ad W. D. Kelto (98,

APPLICATION OF EMPIRICAL BAYESIAN ESTIMATION TO THE OPTIMAL DECISION OF A SERVER-DEPENDENT QUEUING SYSTEM

Yugoslav Joural of Operatios Research 5 (005, umber, 9-07 AIATIO OF EMIRIA BAYESIA ESTIMATIO TO THE OTIMA DEISIO OF A SERVER-DEEDET UEUIG SYSTEM ei-hu I Departmet of Trasportatio ad ommuicatio Maagemet

Massachusetts Institute of Technology

6.0/6.3: Probabilistic Systems Aalysis (Fall 00) Problem Set 8: Solutios. (a) We cosider a Markov chai with states 0,,, 3,, 5, where state i idicates that there are i shoes available at the frot door i

ECE 901 Lecture 12: Complexity Regularization and the Squared Loss

ECE 90 Lecture : Complexity Regularizatio ad the Squared Loss R. Nowak 5/7/009 I the previous lectures we made use of the Cheroff/Hoeffdig bouds for our aalysis of classifier errors. Hoeffdig s iequality

10. Comparative Tests among Spatial Regression Models. Here we revisit the example in Section 8.1 of estimating the mean of a normal random

Part III. Areal Data Aalysis 0. Comparative Tests amog Spatial Regressio Models While the otio of relative likelihood values for differet models is somewhat difficult to iterpret directly (as metioed above),