Departure Process from a M/M/m/ Queue
|
|
- Ezra Flynn
- 5 years ago
- Views:
Transcription
1 Dearture rocess fro a M/M// Queue Q - (-) Q Q3 Q4 (-) Knowledge of the nature of the dearture rocess fro a queue would be useful as we can then use t to analyze sle cases of queueng networs as shown. The ey result here s that the dearture rocess fro a M/M// queue s also osson wth the sae rate as the arrval rate enterng the queue. It should also be noted that the result of randoly slttng or cobnng ndeendent osson rocesses also yelds a osson rocess Coyrght Sanay K. Bose The result on the dearture rocess of a M/M// queue follows fro Bure s Theore. Ths theore states that - [A] The dearture rocess fro a M/M// queue s osson n nature. [B] For a M/M// queue at each te t the nuber of custoers n the syste s ndeendent of the sequence of dearture tes ror to t. [C] For a M/M// FCFS queue gven a custoer dearture at te t the arrval te of ths custoer s ndeendent of the dearture rocess ror to t. Coyrght Sanay K. Bose
2 Coyrght Sanay K. Bose 3 Te Reversblty roerty of Irreducble Aerodc Marov Chans Consder a dscrete te rreducble aerodc Marov Chan... n- n n... for whch the transton robabltes are gven to be. Now consder the sae chan bacwards n te.e. the chan... n n Ths would also be a Marov Chan snce we can show that * State Transton robablty of the Reverse Chan Coyrght Sanay K. Bose 4 The Marov Chan s consdered to be te reversble for the secal case where *. The reverse chan wll have the followng roertes - The reversed chan s also rreducble and aerodc le the forward chan The reversed chan has the sae statonary state dstrbuton as the forward chan The chan s te reversble only f the detaled balance equaton holds for
3 How can we handle queues where the servce te dstrbuton s not exonental? [A] If we can exress the actual servce te as cobnatons of exonentally dstrbuted te ntervals then the Method of Stages ay be used. (Secton.9) [B] The M/G/ queue and ts varatons ay be analyzed. (Chaters 3 and 4) [C] Aroxaton ethods ay be used f the ean and varance of the servce te are gven. (GI/G/ aroxaton of Secton 6.) Coyrght Sanay K. Bose 5 Method of Stages Stage /µ Stage /µ Consder a M/-// exale where the actual servce te s the su of two rando varables each of whch s exonentally dstrbuted. State of the syste reresented as (n ) where n s the total nuber of custoers n the syste where the custoer currently beng served s at Stage n... State () reresents the state when the syste s ety () ( ) ( ) µ µ State Transton µ µ Dagra of the Syste ( ) ( ) Coyrght Sanay K. Bose 6 3
4 Balance Equatons for the Syste µ ( µ ) ( µ ( µ ) ( µ etc... ) ) µ µ µ µ 3 (.38) These Balance Equatons ay be solved along wth the arorate Noralzaton Condton to obtan the state robabltes of the syste. Once these are nown erforance araeters of the queue ay be arorately evaluated. Coyrght Sanay K. Bose 7 The ethod llustrated for the M/-// exale ay be extended for the followng tyes systes.. Have stages of servce tes - ore rows n the state transton dagra. Fnte Nuber of Watng ostons n the Queue - ae the arrval rate a functon of the nuber n the syste and ae t go to zero once all the watng ostons have been flled 3. Multle Servers - aroxate ths by allowng ore than one ob to enter servce at a te 4. More General Servce Te Dstrbutons - see next slde Coyrght Sanay K. Bose 8 4
5 For ore general servce te dstrbutons the Method of Stages ay be used f the Lalace Transfor of the df of the servce te ay be reresented as a ratonal functon of s L B (s)n(s)/d(s) wth sle roots. Entry Stage µ α α -α -α Stage µ Ths leads to - L ( s) ( α B Ext Wth ultle stages le ths the L.T. of the servce te df wll be of the for - ) α... α ( α ) µ s µ L ( s) B β β s µ Coyrght Sanay K. Bose 9 Gven a servce te df as L B (s)n(s)/d(s) wth sle roots -. Obtan the ultle stage reresentaton n the for shown earler. Draw the corresondng state transton dagra and dentfy the flows between the varous states 3. Wrte and solve the flow balance equatons along wth the noralzaton condton to obtan the state robabltes 4. Use the state robabltes to obtan the requred erfroance araeters Coyrght Sanay K. Bose 5
6 Queues wth Bul (or Batch) Arrvals (Secton.) M [] osson Batch Arrval rocess Batches arrvng as a osson rocess wth exonentally dstrbuted nter-arrval tes between batches Batch sze Nuber of obs n a batch (rando varable) Average Batch Arrval Rate β r r obs n a batch r. β ( β r z r β r rβ r r Coyrght Sanay K. Bose The M [] /M/ Queue µ ( for ) µ β for Balance Equatons Though these ay be solved n the standard fashon we wll consder a soluton aroach for drectly obtanng ( the Generatng Functon for the nuber n the syste. For ths we would need to ultly the th equaton above by z and su fro to. ( µ ) z µ z z β z ( n n n z Coyrght Sanay K. Bose 6
7 Slfyng we get µ ( µ )[ ( ] [ ( z µ ( ( µ ( z[ β( ] z] ( β ( β Defne ρ as the offered traffc µ Note that () s effectvely the sae as the Noralzaton Condton. Usng ths we get ρ µ ( ρ)( ( µ ( z[ β ( ] Therefore (.4) We can nvert ( or exand t as a ower seres n z to get the state robablty dstrbuton. The ean nuber N n the syste ay be drectly calculated fro ( as - d( ρ( β β ) N (.43) dz ( ) z ρ Coyrght Sanay K. Bose 3 The M [] /-/-/K Queue Batch Arrval Queue wth Fnte Caacty For oeratng queues of ths tye one ust also secfy the batch accetance strategy to be followed f a batch of sze or ore arrrves n a syste where the nuber of watng ostons avalable s less than. artal Batch Accetance Strategy (BAS) Whole Batch Accetance Strategy (WBAS) Randoly choose as any obs fro the batch as ay be accoodated n the buffer Accet the batch only f all ts obs ay be accoodated; otherwse reect all obs of the batch Coyrght Sanay K. Bose 4 7
8 M [ /M/-/- tyes of queues ay be oerated and analyzed under ether the BAS or the WBAS strategy See Secton. where ths analyss s done for a M [ /M/s/s queue. The state dstrbuton for ths queue are gven by φ... s µ (.46) where φ β... Coyrght Sanay K. Bose 5 8
Analysis of Discrete Time Queues (Section 4.6)
Analyss of Dscrete Tme Queues (Secton 4.6) Copyrght 2002, Sanjay K. Bose Tme axs dvded nto slots slot slot boundares Arrvals can only occur at slot boundares Servce to a job can only start at a slot boundary
More informationEquilibrium Analysis of the M/G/1 Queue
Eulbrum nalyss of the M/G/ Queue Copyrght, Sanay K. ose. Mean nalyss usng Resdual Lfe rguments Secton 3.. nalyss usng an Imbedded Marov Chan pproach Secton 3. 3. Method of Supplementary Varables done later!
More informationA Performance Model of Space-Division ATM Switches with Input and Output Queueing *
A Perforance Model of Sace-Dvson ATM Swtches wth Inut and Outut Queueng * Guogen Zhang Couter Scence Deartent Unversty of Calforna at Los Angeles Los Angeles, CA 94, USA Wlla G. Bulgren Engneerng Manageent
More informationApplied Stochastic Processes
STAT455/855 Fall 23 Appled Stochastc Processes Fnal Exam, Bref Solutons 1. (15 marks) (a) (7 marks) The dstrbuton of Y s gven by ( ) ( ) y 2 1 5 P (Y y) for y 2, 3,... The above follows because each of
More informationThe Dirac Equation. Elementary Particle Physics Strong Interaction Fenomenology. Diego Bettoni Academic year
The Drac Equaton Eleentary artcle hyscs Strong Interacton Fenoenology Dego Betton Acadec year - D Betton Fenoenologa Interazon Fort elatvstc equaton to descrbe the electron (ncludng ts sn) Conservaton
More informationMarkov model for analysis and modeling of Distributed Coordination Function of Multirate IEEE Mateusz Wielgosz
Marov odel for analyss and odelng of Dstruted Coordnaton Functon of Multrate IEEE 802.11 Mateusz elgosz 1 Introducton Dstruted Coordnaton Functon Creatng a Marov odel Solvng the chan Collson roalty and
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationBirth Death Processes
Brth Death rocesses 79 Brth Death rocesses ohamed, 3.... - K+ + States of the rocess may reresent a count of someth ( number of acet n a queue, The oulaton of a cty, the number of customers n store) +
More informationDiscrete Memoryless Channels
Dscrete Meorless Channels Source Channel Snk Aount of Inforaton avalable Source Entro Generall nos, dstorted and a be te varng ow uch nforaton s receved? ow uch s lost? Introduces error and lts the rate
More information6. Stochastic processes (2)
Contents Markov processes Brth-death processes Lect6.ppt S-38.45 - Introducton to Teletraffc Theory Sprng 5 Markov process Consder a contnuous-tme and dscrete-state stochastc process X(t) wth state space
More information6. Stochastic processes (2)
6. Stochastc processes () Lect6.ppt S-38.45 - Introducton to Teletraffc Theory Sprng 5 6. Stochastc processes () Contents Markov processes Brth-death processes 6. Stochastc processes () Markov process
More informationSource-Channel-Sink Some questions
Source-Channel-Snk Soe questons Source Channel Snk Aount of Inforaton avalable Source Entro Generall nos and a be te varng Introduces error and lts the rate at whch data can be transferred ow uch nforaton
More informationNetwork of Markovian Queues. Lecture
etwork of Markovan Queues etwork of Markovan Queues ETW09 20 etwork queue ed, G E ETW09 20 λ If the frst queue was not empty Then the tme tll the next arrval to the second queue wll be equal to the servce
More informationSystem in Weibull Distribution
Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co
More informationON A CLASS OF RENEWAL QUEUEING AND RISK PROCESSES
ON A CLASS OF RENEWAL QUEUEING AND RISK ROCESSES K.K.Thap a, M.J.Jacob b a Departent of Statstcs, SNMC, M.G.Unversty, Kerala INDIA b Departent of Matheatcs, NITC Calcut, Kerala - INDIA UROSE:- In ths paper,
More informationSuggested solutions for the exam in SF2863 Systems Engineering. June 12,
Suggested solutons for the exam n SF2863 Systems Engneerng. June 12, 2012 14.00 19.00 Examner: Per Enqvst, phone: 790 62 98 1. We can thnk of the farm as a Jackson network. The strawberry feld s modelled
More informationMarkov chains. Definition of a CTMC: [2, page 381] is a continuous time, discrete value random process such that for an infinitesimal
Markov chans M. Veeraraghavan; March 17, 2004 [Tp: Study the MC, QT, and Lttle s law lectures together: CTMC (MC lecture), M/M/1 queue (QT lecture), Lttle s law lecture (when dervng the mean response tme
More informationFuzzy approach to solve multi-objective capacitated transportation problem
Internatonal Journal of Bonformatcs Research, ISSN: 0975 087, Volume, Issue, 00, -0-4 Fuzzy aroach to solve mult-objectve caactated transortaton roblem Lohgaonkar M. H. and Bajaj V. H.* * Deartment of
More informationMultipoint Analysis for Sibling Pairs. Biostatistics 666 Lecture 18
Multpont Analyss for Sblng ars Bostatstcs 666 Lecture 8 revously Lnkage analyss wth pars of ndvduals Non-paraetrc BS Methods Maxu Lkelhood BD Based Method ossble Trangle Constrant AS Methods Covered So
More informationIS 709/809: Computational Methods in IS Research. Simple Markovian Queueing Model
IS 79/89: Comutatoal Methods IS Research Smle Marova Queueg Model Nrmalya Roy Deartmet of Iformato Systems Uversty of Marylad Baltmore Couty www.umbc.edu Queueg Theory Software QtsPlus software The software
More informationCOS 511: Theoretical Machine Learning
COS 5: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #0 Scrbe: José Sões Ferrera March 06, 203 In the last lecture the concept of Radeacher coplexty was ntroduced, wth the goal of showng that
More informationOur focus will be on linear systems. A system is linear if it obeys the principle of superposition and homogenity, i.e.
SSTEM MODELLIN In order to solve a control syste proble, the descrptons of the syste and ts coponents ust be put nto a for sutable for analyss and evaluaton. The followng ethods can be used to odel physcal
More informationTCOM 501: Networking Theory & Fundamentals. Lecture 7 February 25, 2003 Prof. Yannis A. Korilis
TCOM 501: Networkng Theory & Fundamentals Lecture 7 February 25, 2003 Prof. Yanns A. Korls 1 7-2 Topcs Open Jackson Networks Network Flows State-Dependent Servce Rates Networks of Transmsson Lnes Klenrock
More informationManaging Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration
Managng Caacty Through eward Programs on-lne comanon age Byung-Do Km Seoul Natonal Unversty College of Busness Admnstraton Mengze Sh Unversty of Toronto otman School of Management Toronto ON M5S E6 Canada
More informationAdvanced Topics in Optimization. Piecewise Linear Approximation of a Nonlinear Function
Advanced Tocs n Otmzaton Pecewse Lnear Aroxmaton of a Nonlnear Functon Otmzaton Methods: M8L Introducton and Objectves Introducton There exsts no general algorthm for nonlnear rogrammng due to ts rregular
More informationChapter 5: Root Locus
Chater 5: Root Locu ey condton for Plottng Root Locu g n G Gven oen-loo tranfer functon G Charactertc equaton n g,,.., n Magntude Condton and Arguent Condton 5-3 Rule for Plottng Root Locu 5.3. Rule Rule
More informationEE513 Audio Signals and Systems. Statistical Pattern Classification Kevin D. Donohue Electrical and Computer Engineering University of Kentucky
EE53 Audo Sgnals and Systes Statstcal Pattern Classfcaton Kevn D. Donohue Electrcal and Couter Engneerng Unversty of Kentucy Interretaton of Audtory Scenes Huan erceton and cognton greatly eceeds any couter-based
More informationBAYESIAN CURVE FITTING USING PIECEWISE POLYNOMIALS. Dariusz Biskup
BAYESIAN CURVE FITTING USING PIECEWISE POLYNOMIALS Darusz Bskup 1. Introducton The paper presents a nonparaetrc procedure for estaton of an unknown functon f n the regresson odel y = f x + ε = N. (1) (
More informationHandling Overload (G. Buttazzo, Hard Real-Time Systems, Ch. 9) Causes for Overload
PS-663: Real-Te Systes Handlng Overloads Handlng Overload (G Buttazzo, Hard Real-Te Systes, h 9) auses for Overload Bad syste desgn eg poor estaton of worst-case executon tes Sultaneous arrval of unexpected
More information( ) 2 ( ) ( ) Problem Set 4 Suggested Solutions. Problem 1
Problem Set 4 Suggested Solutons Problem (A) The market demand functon s the soluton to the followng utlty-maxmzaton roblem (UMP): The Lagrangean: ( x, x, x ) = + max U x, x, x x x x st.. x + x + x y x,
More informationAlgorithms for factoring
CSA E0 235: Crytograhy Arl 9,2015 Instructor: Arta Patra Algorthms for factorng Submtted by: Jay Oza, Nranjan Sngh Introducton Factorsaton of large ntegers has been a wdely studed toc manly because of
More informationContinuous Time Markov Chains
Contnuous Tme Markov Chans Brth and Death Processes,Transton Probablty Functon, Kolmogorov Equatons, Lmtng Probabltes, Unformzaton Chapter 6 1 Markovan Processes State Space Parameter Space (Tme) Dscrete
More informationHidden Markov Model Cheat Sheet
Hdden Markov Model Cheat Sheet (GIT ID: dc2f391536d67ed5847290d5250d4baae103487e) Ths document s a cheat sheet on Hdden Markov Models (HMMs). It resembles lecture notes, excet that t cuts to the chase
More informationQueueing Networks II Network Performance
Queueng Networks II Network Performance Davd Tpper Assocate Professor Graduate Telecommuncatons and Networkng Program Unversty of Pttsburgh Sldes 6 Networks of Queues Many communcaton systems must be modeled
More informationThe Multiple Classical Linear Regression Model (CLRM): Specification and Assumptions. 1. Introduction
ECONOMICS 5* -- NOTE (Summary) ECON 5* -- NOTE The Multple Classcal Lnear Regresson Model (CLRM): Specfcaton and Assumptons. Introducton CLRM stands for the Classcal Lnear Regresson Model. The CLRM s also
More informationConvergence of random processes
DS-GA 12 Lecture notes 6 Fall 216 Convergence of random processes 1 Introducton In these notes we study convergence of dscrete random processes. Ths allows to characterze phenomena such as the law of large
More informationOn the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals
On the relatonshps among queue lengths at arrval departure and random epochs n the dscrete-tme queue wth D-BMAP arrvals Nam K. Km Seo H. Chang Kung C. Chae * Department of Industral Engneerng Korea Advanced
More informationXiangwen Li. March 8th and March 13th, 2001
CS49I Approxaton Algorths The Vertex-Cover Proble Lecture Notes Xangwen L March 8th and March 3th, 00 Absolute Approxaton Gven an optzaton proble P, an algorth A s an approxaton algorth for P f, for an
More informationExcess Error, Approximation Error, and Estimation Error
E0 370 Statstcal Learnng Theory Lecture 10 Sep 15, 011 Excess Error, Approxaton Error, and Estaton Error Lecturer: Shvan Agarwal Scrbe: Shvan Agarwal 1 Introducton So far, we have consdered the fnte saple
More informationApplied Mathematics Letters
Appled Matheatcs Letters 2 (2) 46 5 Contents lsts avalable at ScenceDrect Appled Matheatcs Letters journal hoepage: wwwelseverco/locate/al Calculaton of coeffcents of a cardnal B-splne Gradr V Mlovanovć
More informationNotes prepared by Prof Mrs) M.J. Gholba Class M.Sc Part(I) Information Technology
Inverse transformatons Generaton of random observatons from gven dstrbutons Assume that random numbers,,, are readly avalable, where each tself s a random varable whch s unformly dstrbuted over the range(,).
More informationInternational Journal of Mathematical Archive-9(3), 2018, Available online through ISSN
Internatonal Journal of Matheatcal Archve-9(3), 208, 20-24 Avalable onlne through www.ja.nfo ISSN 2229 5046 CONSTRUCTION OF BALANCED INCOMPLETE BLOCK DESIGNS T. SHEKAR GOUD, JAGAN MOHAN RAO M AND N.CH.
More informationAn application of generalized Tsalli s-havrda-charvat entropy in coding theory through a generalization of Kraft inequality
Internatonal Journal of Statstcs and Aled Mathematcs 206; (4): 0-05 ISS: 2456-452 Maths 206; (4): 0-05 206 Stats & Maths wwwmathsjournalcom Receved: 0-09-206 Acceted: 02-0-206 Maharsh Markendeshwar Unversty,
More informationChapter 8 Balances on Nonreactive Processes 8.1 Elements of Energy Balances Calculations 8.1a Reference States A Review
Chater 8 Balances on Nonreactve Processes 8.1 Elements of Energy Balances Calculatons 8.1a Reference States A Revew We can never know the absolute values of U and H for a seces at a gven state. t Fortunately,
More informationSolutions for Homework #9
Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE II LECTURE - GENERAL LINEAR HYPOTHESIS AND ANALYSIS OF VARIANCE Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 3.
More informationPower-sum problem, Bernoulli Numbers and Bernoulli Polynomials.
Power-sum roblem, Bernoull Numbers and Bernoull Polynomals. Arady M. Alt Defnton 1 Power um Problem Fnd the sum n : 1... n where, n N or, usng sum notaton, n n n closed form. Recurrence for n Exercse Usng
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article
Avalable onlne www.jocr.co Journal of Checal and Pharaceutcal Research,, 6(5:95-956 Research Artcle ISSN : 975-738 CODEN(USA : JCPRC5 Analyss of fault tree ortance of CNC achne tools based on BDD Je Yu,
More informationExpected Value and Variance
MATH 38 Expected Value and Varance Dr. Neal, WKU We now shall dscuss how to fnd the average and standard devaton of a random varable X. Expected Value Defnton. The expected value (or average value, or
More informationContinuous Time Markov Chain
Contnuous Tme Markov Chan Hu Jn Department of Electroncs and Communcaton Engneerng Hanyang Unversty ERICA Campus Contents Contnuous tme Markov Chan (CTMC) Propertes of sojourn tme Relatons Transton probablty
More informationApproccio Statistico all'analisi di Sistemi Caotici e Applicazioni all'ingegneria dell'informazione
Arocco tatstco all'anals d stem Caotc e Alcazon all'ingegnera dell'informazone Ganluca ett 3 Rccardo Rovatt 3 D. d Ingegnera Unverstà d Ferrara D. d Elettronca, Informatca e stemstca - Unverstà d Bologna
More informationComparing two Quantiles: the Burr Type X and Weibull Cases
IOSR Journal of Mathematcs (IOSR-JM) e-issn: 78-578, -ISSN: 39-765X. Volume, Issue 5 Ver. VII (Se. - Oct.06), PP 8-40 www.osrjournals.org Comarng two Quantles: the Burr Tye X and Webull Cases Mohammed
More informationConfidence intervals for weighted polynomial calibrations
Confdence ntervals for weghted olynomal calbratons Sergey Maltsev, Amersand Ltd., Moscow, Russa; ur Kalambet, Amersand Internatonal, Inc., Beachwood, OH e-mal: kalambet@amersand-ntl.com htt://www.chromandsec.com
More informationEcon107 Applied Econometrics Topic 3: Classical Model (Studenmund, Chapter 4)
I. Classcal Assumptons Econ7 Appled Econometrcs Topc 3: Classcal Model (Studenmund, Chapter 4) We have defned OLS and studed some algebrac propertes of OLS. In ths topc we wll study statstcal propertes
More informationReview: Discrete Event Random Processes. Hongwei Zhang
Revew: Dscrete Event Random Processes Hongwe Zhang http://www.cs.wayne.edu/~hzhang Outlne Markov chans and some renewal theory Markov chan Renewal processes, renewal reward processes, Markov renewal processes
More informationPattern Classification
attern Classfcaton All materals n these sldes were taken from attern Classfcaton nd ed by R. O. Duda,. E. Hart and D. G. Stork, John Wley & Sons, 000 wth the ermsson of the authors and the ublsher Chater
More informationOn the Calderón-Zygmund lemma for Sobolev functions
arxv:0810.5029v1 [ath.ca] 28 Oct 2008 On the Calderón-Zygund lea for Sobolev functons Pascal Auscher october 16, 2008 Abstract We correct an naccuracy n the proof of a result n [Aus1]. 2000 MSC: 42B20,
More informationOn the Transient and Steady-State Analysis of a Special Single Server Queuing System with HOL Priority Scheduling
96 On the Transent and Steady-State Analyss of a Specal On the Transent and Steady-State Analyss of a Specal Sngle Server Queung Syste wth HOL Prorty Schedulng Faou Kaoun Duba Uversty College, College
More informationOrder Full Rate, Leadtime Variability, and Advance Demand Information in an Assemble- To-Order System
Order Full Rate, Leadtme Varablty, and Advance Demand Informaton n an Assemble- To-Order System by Lu, Song, and Yao (2002) Presented by Png Xu Ths summary presentaton s based on: Lu, Yngdong, and Jng-Sheng
More informationInteractive Markov Models of Evolutionary Algorithms
Interactve Markov Models of Evolutonary Algorths Hang Ma, Dan Son, Mnru Fe, and Hongwe Mo Abstract Evolutonary algorths are global otzaton ethods that have been used n any real-world alcatons. In ths aer
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationResponse time in a tandem queue with blocking, Markovian arrivals and phase-type services
Operatons Research Letters 33 (25) 373 381 Operatons Research Letters wwwelsevercom/locate/dsw Response tme n a tandem queue wth blockng, Markovan arrvals and phase-type servces B Van Houdt a,,1, Attahru
More informationMixture of Gaussians Expectation Maximization (EM) Part 2
Mture of Gaussans Eectaton Mamaton EM Part 2 Most of the sldes are due to Chrstoher Bsho BCS Summer School Eeter 2003. The rest of the sldes are based on lecture notes by A. Ng Lmtatons of K-means Hard
More informationLecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES
COMPUTATIONAL FLUID DYNAMICS: FDM: Appromaton of Second Order Dervatves Lecture APPROXIMATION OF SECOMD ORDER DERIVATIVES. APPROXIMATION OF SECOND ORDER DERIVATIVES Second order dervatves appear n dffusve
More informationIntroduction to Continuous-Time Markov Chains and Queueing Theory
Introducton to Contnuous-Tme Markov Chans and Queueng Theory From DTMC to CTMC p p 1 p 12 1 2 k-1 k p k-1,k p k-1,k k+1 p 1 p 21 p k,k-1 p k,k-1 DTMC 1. Transtons at dscrete tme steps n=,1,2, 2. Past doesn
More informationIdentification of Modal Parameters from Ambient Vibration Data by Modified Eigensystem Realization Algorithm *
Journal of Aeronautcs, Astronautcs and Avaton, Seres A, Vol.42, No.2.079-086 (2010) 79 Identfcaton of Modal Paraeters fro Abent Vbraton Data by Modfed Egensyste ealzaton Algorth * Dar-Yun Chang **, Chang-Sheng
More informationGeneral Results of Local Metric Dimensions of. Edge-Corona of Graphs
Internatonal Matheatcal Foru, Vol 11, 016, no 16, 793-799 HIKARI Ltd, www-hkarco htt://dxdoorg/101988/f0166710 General Results of Local Metrc Densons of Edge-Corona of Grahs Rnurwat Deartent of Matheatcs,
More informationApplication of Queuing Theory to Waiting Time of Out-Patients in Hospitals.
Applcaton of Queung Theory to Watng Tme of Out-Patents n Hosptals. R.A. Adeleke *, O.D. Ogunwale, and O.Y. Hald. Department of Mathematcal Scences, Unversty of Ado-Ekt, Ado-Ekt, Ekt State, Ngera. E-mal:
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationJournal of Global Research in Computer Science A MARKOV CHAIN MODEL FOR ROUND ROBIN SCHEDULING IN OPERATING SYSTEM
Volue 2, No 6, June 20 Journal of Global Research n Coputer Scence RESEARCH AER Avalable Onlne at wwwjgrcsnfo A MARKOV CHAIN MODEL FOR ROUND ROBIN SCHEDULING IN OERATING SYSTEM Deepak Ssoda *, Dr Sohan
More information3. Tensor (continued) Definitions
atheatcs Revew. ensor (contnued) Defntons Scalar roduct of two tensors : : : carry out the dot roducts ndcated ( )( ) δ δ becoes becoes atheatcs Revew But, what s a tensor really? tensor s a handy reresentaton
More informationComputation of Higher Order Moments from Two Multinomial Overdispersion Likelihood Models
Computaton of Hgher Order Moments from Two Multnomal Overdsperson Lkelhood Models BY J. T. NEWCOMER, N. K. NEERCHAL Department of Mathematcs and Statstcs, Unversty of Maryland, Baltmore County, Baltmore,
More informationPriority Queuing with Finite Buffer Size and Randomized Push-out Mechanism
ICN 00 Prorty Queung wth Fnte Buffer Sze and Randomzed Push-out Mechansm Vladmr Zaborovsy, Oleg Zayats, Vladmr Muluha Polytechncal Unversty, Sant-Petersburg, Russa Arl 4, 00 Content I. Introducton II.
More informationDigital Signal Processing
Dgtal Sgnal Processng Dscrete-tme System Analyss Manar Mohasen Offce: F8 Emal: manar.subh@ut.ac.r School of IT Engneerng Revew of Precedent Class Contnuous Sgnal The value of the sgnal s avalable over
More informationDetermination of the Confidence Level of PSD Estimation with Given D.O.F. Based on WELCH Algorithm
Internatonal Conference on Inforaton Technology and Manageent Innovaton (ICITMI 05) Deternaton of the Confdence Level of PSD Estaton wth Gven D.O.F. Based on WELCH Algorth Xue-wang Zhu, *, S-jan Zhang
More informationAssignment 5. Simulation for Logistics. Monti, N.E. Yunita, T.
Assgnment 5 Smulaton for Logstcs Mont, N.E. Yunta, T. November 26, 2007 1. Smulaton Desgn The frst objectve of ths assgnment s to derve a 90% two-sded Confdence Interval (CI) for the average watng tme
More informationModule 9. Lecture 6. Duality in Assignment Problems
Module 9 1 Lecture 6 Dualty n Assgnment Problems In ths lecture we attempt to answer few other mportant questons posed n earler lecture for (AP) and see how some of them can be explaned through the concept
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationj) = 1 (note sigma notation) ii. Continuous random variable (e.g. Normal distribution) 1. density function: f ( x) 0 and f ( x) dx = 1
Random varables Measure of central tendences and varablty (means and varances) Jont densty functons and ndependence Measures of assocaton (covarance and correlaton) Interestng result Condtonal dstrbutons
More informationQuasi-Static transient Thermal Stresses in a Robin's thin Rectangular plate with internal moving heat source
31-7871 Weely Scence Research Journal Orgnal Artcle Vol-1, Issue-44, May 014 Quas-Statc transent Theral Stresses n a Robn's n Rectangular late w nternal ovng heat source D. T. Solane and M.. Durge ABSTRACT
More informationCS-433: Simulation and Modeling Modeling and Probability Review
CS-433: Smulaton and Modelng Modelng and Probablty Revew Exercse 1. (Probablty of Smple Events) Exercse 1.1 The owner of a camera shop receves a shpment of fve cameras from a camera manufacturer. Unknown
More informationFermi-Dirac statistics
UCC/Physcs/MK/EM/October 8, 205 Fer-Drac statstcs Fer-Drac dstrbuton Matter partcles that are eleentary ostly have a type of angular oentu called spn. hese partcles are known to have a agnetc oent whch
More informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More informationLINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables
LINEAR REGRESSION ANALYSIS MODULE VIII Lecture - 7 Indcator Varables Dr. Shalabh Department of Maematcs and Statstcs Indan Insttute of Technology Kanpur Indcator varables versus quanttatve explanatory
More informationEP523 Introduction to QFT I
EP523 Introducton to QFT I Toc 0 INTRODUCTION TO COURSE Deartment of Engneerng Physcs Unversty of Gazante Setember 2011 Sayfa 1 Content Introducton Revew of SR, QM, RQM and EMT Lagrangan Feld Theory An
More informationModule 2. Random Processes. Version 2 ECE IIT, Kharagpur
Module Random Processes Lesson 6 Functons of Random Varables After readng ths lesson, ou wll learn about cdf of functon of a random varable. Formula for determnng the pdf of a random varable. Let, X be
More informationEstimation: Part 2. Chapter GREG estimation
Chapter 9 Estmaton: Part 2 9. GREG estmaton In Chapter 8, we have seen that the regresson estmator s an effcent estmator when there s a lnear relatonshp between y and x. In ths chapter, we generalzed the
More informationSeveral generation methods of multinomial distributed random number Tian Lei 1, a,linxihe 1,b,Zhigang Zhang 1,c
Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 205) Several generaton ethods of ultnoal dstrbuted rando nuber Tan Le, a,lnhe,b,zhgang Zhang,c School of Matheatcs and Physcs, USTB,
More informationOn Pfaff s solution of the Pfaff problem
Zur Pfaff scen Lösung des Pfaff scen Probles Mat. Ann. 7 (880) 53-530. On Pfaff s soluton of te Pfaff proble By A. MAYER n Lepzg Translated by D. H. Delpenc Te way tat Pfaff adopted for te ntegraton of
More informationCOMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS
More informationDistributions /06. G.Serazzi 05/06 Dimensionamento degli Impianti Informatici distrib - 1
Dstrbutons 8/03/06 /06 G.Serazz 05/06 Dmensonamento degl Impant Informatc dstrb - outlne densty, dstrbuton, moments unform dstrbuton Posson process, eponental dstrbuton Pareto functon densty and dstrbuton
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationECONOMICS 351*-A Mid-Term Exam -- Fall Term 2000 Page 1 of 13 pages. QUEEN'S UNIVERSITY AT KINGSTON Department of Economics
ECOOMICS 35*-A Md-Term Exam -- Fall Term 000 Page of 3 pages QUEE'S UIVERSITY AT KIGSTO Department of Economcs ECOOMICS 35* - Secton A Introductory Econometrcs Fall Term 000 MID-TERM EAM ASWERS MG Abbott
More informationLecture 4: November 17, Part 1 Single Buffer Management
Lecturer: Ad Rosén Algorthms for the anagement of Networs Fall 2003-2004 Lecture 4: November 7, 2003 Scrbe: Guy Grebla Part Sngle Buffer anagement In the prevous lecture we taled about the Combned Input
More informationSOJOURN TIME IN A QUEUE WITH CLUSTERED PERIODIC ARRIVALS
Journal of the Operatons Research Socety of Japan 2003, Vol. 46, No. 2, 220-241 2003 he Operatons Research Socety of Japan SOJOURN IME IN A QUEUE WIH CLUSERED PERIODIC ARRIVALS Da Inoue he oko Marne and
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationThe Degree Distribution of Random Birth-and-Death Network with Network Size Decline
The Degree Dstrbuton of Random Brth-and-Death etwork wth etwork Sze Declne Xaojun Zhang *, Hulan Yang School of Mathematcal Scences, Unversty of Electronc Scence and Technology of Chna, Chengdu 673, P.R.
More information1 Convex Optimization
Convex Optmzaton We wll consder convex optmzaton problems. Namely, mnmzaton problems where the objectve s convex (we assume no constrants for now). Such problems often arse n machne learnng. For example,
More information