FEATURE ANALYSIS ON QUEUE LENGTH OF ASYMMETRIC TWO-QUEUE POLLING SYSTEM WITH GATED SERVICES *
|
|
- Margery Henry
- 5 years ago
- Views:
Transcription
1 Journal of Theoretcal and Appled Informaton Technoloy 0 th January 03. Vol. 4 No JATIT & LLS. All rhts reserved. ISSN: E-ISSN: FEATURE ANALYSIS ON QUEUE LENGTH OF ASYMMETRIC TWO-QUEUE POLLING SYSTEM WITH GATED SERVICES * WANG XINCHUN, LIU YUMING, CHENG MAN, AND YE QING Department of Physcal and Electroncs, Chuxon Normal Unversty, Chuxon, Chna. Emal: xxxywxch@sna.com, luyum@cxtc.edu.cn, chenm@cxtc.edu.cn, yq@cxtc.edu.cn ABSTRACT On the bass of establshn mathematcal model and defnn the parameters and treatn embedded Marov chans and probablty eneratn functon as math tools, the paper analyzed dscrete-tme, nonsymmetrc dual-threshold servce queue system precsely, and t derved frst order and second order characterstcs of the system. The paper calculates the averae queue lenth and averae watn delay of nformaton roup. Smulaton experment based on system runnn mechansm and theoretcal calculatons have ood consstency. The analyss lad the sold foundaton for research of ated polln system based on asymmetrc mult queue; t further deepens the percepton of asymmetrc ated polln system; t s meannful to domnate polln system flexbly. Keywords: Asymmetrc; Two-Queue; Gated Polln System; Feature Of Averae Queue Lenth; Smulaton And Theoretcal Calculaton. INTRODUCTION As for research dffculty on asymmetrc polln system s too reat, t s enerally that people usually treat analyss and dscusson of performance of the asymmetrc two polln system as the startn-pont so as to lad sold foundaton for the research of asymmetrc mult queues ated polln system. It s enerally beleved that queue servce system based on perodc nqury has many applcatons n communcaton system and computer networ. As for queue servce system based on perodc nqury, the number of nformaton roup, servce tme for nformaton roup and shftn tme at any tme are varable. So, t s qute dffcult to analyze related performance. In the study of asymmetrc polln system Ref - ve some precse resoluton; however, as there are some problems n analyss method the obtaned results are partal under certan qualfyn condtons. On the bass of Ref -9 the paper adopts the method of embedded Marov chans and probablty eneratn functon to resolve dscretetme and polln asymmetrc double ated servce system, deduce one-order and two-order characterstcs of the system, calculates the averae watn delay of the system. The paper draws some useful conclusons by comparn smulaton results on the bass of the runnn mechansm and theoretcal calculatons.. MATHEMATICAL MODEL OF THE SYSTEM Fure. System Structure Model Of Gated Polln System Of Asymmetrc Two Queues.Structure model of the system Fure. System structure model of ated polln system of asymmetrc two queues Cyclc polln asymmetrc and two-queue ated *Funded Proect: The Scence Study Foundaton of Yunnan Provncal Department of Educaton n Chna under Grant NO. Y040 8
2 Journal of Theoretcal and Appled Informaton Technoloy 0 th January 03. Vol. 4 No JATIT & LLS. All rhts reserved. ISSN: E-ISSN: servce system accepts servces accordn the way of FIFO for nformaton roups belonn to the same queue. Both Termnal and Termnal wor n the means of ated servce. In Queue, when the servce for the former ated nformaton roup s expred and new-comn nformaton durn the course of the servce wll be servced at the next perod and swtch to the Queue after one converson perod. Queue fnshes the servce of current ated nformaton roup, then, the system swtches to Queue and performs the next round servce after a shftn tme. The system structure model s llustrated n Fure. System Parameters and Worn Condton For any queue, nformaton roups arrved at any unt tme s ndependent dentcally dstrbuted. Dstrbuton probablty eneral functon, mean and varance of nformaton roup n the queue are ' '' A ( z ) λ = A () σ λ = A ( ) + λ λ respectvely. In the same way, the probablty functon of the shftn tme, mean and varance ' '' are B ( z ), β = B (), σ β = B ( ) + β β respectvely, where, =,. As lon as the buffer storae capacty s lare enouh for each queue, there wll not exsts the loss of roup nformaton. Each customer n the queue s served by the rule of Frst-come, Frst-serve. For the convenence of analyss, the paper defnes stochastc varable u as the shftn tme that water shfts from Queue to Queue + at the tme t n. v s the servce tme for Queue at the tme t n by the water. µ ( u ) s the number of nformaton roups when the water oes nto Queue at the tme u. η ( v ) s the number of nformaton roups when the water oes nto Queue at the tme v. ξ s the number of nformaton roups of Queue at the tme of t n. =,; =, as for non-symmetrcal two queues..3 Status equaton of the system For the system of asymmetrc two-queue ated servce there should be ( ) r λ + () + () βλ ξ n + ) = 0 + η ( v ) + µ ( ) () ( u Resolve (), (8), (9) and (0) ontly, the paper obtans + () ξ ( n ) = ξ( n) + η( v) + µ ( u) At the tme t n+ when queryn ated servce queue..4 Probablty eneratn functon of the system Probablty eneratn functon of the system of asymmetrc two-queue ated servce s G + ( z, z ( n ξ ) = lm E z n = + ) (3) Combned (), () and (3) the paper obtans probablty eneratn functon of the system of asymmetrc two-queue ated servce s G( z, z) = R A z A z G z B A z A z ( ( ) ( )) (, ( ( ) ( ))) G( z, z) = R A z A z G B A z A z z ( ( ) ( )) ( ( ( ) ( )), ) G z z (4) (5) The (, ) n (4) s the probablty eneratn functon of the status dstrbuton of the Queue. The G ( z, z ) n (5) s the probablty eneratn functon of the status dstrbuton of the Queue. 3. ANALYSIS OF THE SYSTEM PERFORMANCE 3. Resolve one-order characterstcs Defne G ( z, z ) ( ) = lm z, z z =,; =, () Solve one-order partal dervatve of (4) and (5) by (), and obtan the follown by reducton ( + β λ ) rλ + () () = () ( + β λ ) rλ () = (8) ( r λ + β λ ) () = (9) = (0) 9
3 Journal of Theoretcal and Appled Informaton Technoloy 0 th January 03. Vol. 4 No JATIT & LLS. All rhts reserved. ISSN: E-ISSN: ( r r + ρ r ) λ () = () ρ ( r r + ρ r ) λ () = () ρ Averae lenth of queue () = ( r + r ) λ (3) ρ ( r + r ) λ () = (4) ρ Averae cycle tme r = r r θ = T θ = = ρ ρ = T + (5) 4. COMPARISON BETWEEN SIMULATION AND THEORETICAL CALCULATION RESULTS Accordn to the mechansm of the system the paper compares computer smulaton wth theoretcal calculaton results. Assume arrval of each queue at any tme slot obeys Posson dstrbuton and smulaton and theoretcal calculaton adopt the same parameters. M = 0 Set polln number. When r = r =, λ = 0. 0, λ = smulaton and theoretcal calculaton results of averae lenth of Queue and varyn wth servce rate s llustrated n Fure. Set polln number M = 3 0. When = r = r, β, β 3 = = smulaton and theoretcal calculaton results of averae lenth of Queue and varyn wth arrval rate s llustrated n Fure 3. Set polln number M = 5 0. When β = β = 0, λ = 0. 0, λ = smulaton and theoretcal calculaton results of averae lenth of Queue and varyn wth shftn tme s llustrated n Fure 4. Assume queues are = 5 0 symmetrcal, set polln number smulaton and theoretcal calculaton results of averae lenth of Queue and varyn wth the varaton of load are llustrated n Fure 5. M 5. ANALYSIS AND DISCUSSION We can obtan t from Fure that the averae watn delay ncreases wth the ncrease of β when λ and γ are fxed. Compare two sets of curves n Fure and you wll fnd that he averae watn delay ncreases remarably f λ s larer. Averae watn delay s larer f λ s larer and when β s fxed. Smulaton and theoretcal resolutons (3) and (4) have ood consstency. Althouh smulaton and theoretcal resolutons approxmately equal, there s a devaton between them. Ths s manly due to fewer statstcs polln, only M = 0. If ncreasn polln number, provn data qualty and decreasn devaton. Averae lenth of watn queue Servce rate Fure. Comparson Between Smulaton And Theoretcal Calculaton Results Of Averae Lenth Of Queue And Varyn Wth Servce Rate Averae lenth of watn queue Arrval rate Fure 3. Comparson Between Smulaton And Theoretcal Calculaton Results Of Averae Lenth Of Queue And Varyn Wth Arrval Rate 30
4 Journal of Theoretcal and Appled Informaton Technoloy 0 th January 03. Vol. 4 No JATIT & LLS. All rhts reserved. ISSN: E-ISSN: We can also obtan t from Fure 3 that the averae watn delay ncreases wth the ncrease of λ when β and γ are fxed. Compare two sets of curves n Fure 3 and you wll fnd that the averae watn delay ncreases remarably f β s larer. Averae watn delay s larer f β s larer and when λ s fxed. Smulaton and theoretcal resolutons (3) and (4) have ood consstency. Smulaton and theoretcal resolutons approxmately equal and there s only lttle devaton between them. Ths s manly due that statstcal polln number has reached M = 3 0. If ncreasn polln number M we can mprove the qualty of data, and further reduce the error. Averae lenth of watn queue Shftn tme Fure 4. Comparson Between Smulaton And Theoretcal Calculaton Results Of Averae Lenth Of Queue And Varyn Wth Shftn Tme Averae lenth of watn queue load Fure 5. Comparson Between Smulaton And Theoretcal Calculaton Results Of Averae Lenth Of Queue And Varyn Wth The Varaton Of Load We can obtan t from Fure 4 that the averae watn delay ncreases wth the ncrease of γ when λ and β are fxed. Compare two sets of curves n Fure 4 and you wll fnd that the averae watn delay ncreases remarably f ρ s larer. Averae watn delay of the ones wth heaver load s larer when shftn tme s fxed. Expermental results and theoretcal expressons (3) and (4) have ood consstency. Smulaton and theoretcal resolutons approxmately equal and there s only lttle devaton between them. Ths s manly due that statstcal polln number has reached M = 3 0. If ncreasn polln number M we can mprove the qualty of data, and further reduce the error. We can also obtan t from Fure 5 that the averae watn delay ncreases wth the ncrease of ρ when γ s fxed. Smulaton and theoretcal resolutons (3) and (4) have ood consstency. The devaton s least. Ths s manly due that statstcal polln number has reached M = 5 0. If ncreasn polln number M we can mprove the qualty of data, and further reduce the error. Compare Fure, 3, 4, 5 we can fure out that bas between smulaton results and theoretcal value further reduce wth the ncrease of polln number M.The experments show the error can be manpulated wthn % f the load of asymmetrc two-queue satsfes ρ and polln number = 8 reaches M 0. Expresson (3) and (4) transform to the Expresson () n Reference [] when the networ s runnn under the crcumstance of symmetry parameters and N =. REFERENCE [] Feruson M J, Amnetzah Y J. Exact results for nonsymmetrc toen rn systems. IEEE Trans Commun, 985, 33 (3): 3-3. [] Evertt D. Smple approxmatons for toen rns. IEEE Trans Commun, 98, 34: 9-. [3] Tanc T, Taahash Y. Exact analyss of asymmetrc polln systems wth snle buffers. IEEE Trans Commun, 988, 3 (0): 9-. [4] Ibe O C, Chen X. Performance analyss of asymmetrc snle-buffer polln systems. Perform Eval, 989, 0: -4. 3
5 Journal of Theoretcal and Appled Informaton Technoloy 0 th January 03. Vol. 4 No JATIT & LLS. All rhts reserved. ISSN: E-ISSN: [5] Ibe O C, Chen X. Approxmate analyss of asymmetrc snle-server toen-passn systems. IEEE Trans Commun, 989, 3 (): 5-5. [] Muheree B, Kwo C K, Lantz A C, Moh W L M. Comments on exact analyss of asymmetrc polln systems wth snle buffers. IEEE Trans Commun, 990, 38 () : [] Zhao Donfen, Zhen Sumn. Messae Watn Tme Analyss for a Polln System wth Gated Servce. Journal of Chna of communcaton, 994, 5(): 8-3. [8] Zhao Donfen. Study on scheduln rules of producton flows wth two prorty control. Informaton and Control, 998, (5): [9] Yu Yn, Zhao Donfen. Performance analyss of exhaustn and ated polln system. Journal of Yunnan Normal Unversty, 00, (4):
Queueing 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 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 informationS Advanced Digital Communication (4 cr) Targets today
S.72-3320 Advanced Dtal Communcaton (4 cr) Convolutonal Codes Tarets today Why to apply convolutonal codn? Defnn convolutonal codes Practcal encodn crcuts Defnn qualty of convolutonal codes Decodn prncples
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng 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 informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationA Simple Inventory System
A Smple Inventory System Lawrence M. Leems and Stephen K. Park, Dscrete-Event Smulaton: A Frst Course, Prentce Hall, 2006 Hu Chen Computer Scence Vrgna State Unversty Petersburg, Vrgna February 8, 2017
More informationA PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS
HCMC Unversty of Pedagogy Thong Nguyen Huu et al. A PROBABILITY-DRIVEN SEARCH ALGORITHM FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS Thong Nguyen Huu and Hao Tran Van Department of mathematcs-nformaton,
More informationx = , so that calculated
Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to
More informationAnalysis 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 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 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 informationFlux-Uncertainty from Aperture Photometry. F. Masci, version 1.0, 10/14/2008
Flux-Uncertanty from Aperture Photometry F. Masc, verson 1.0, 10/14/008 1. Summary We derve a eneral formula for the nose varance n the flux of a source estmated from aperture photometry. The 1-σ uncertanty
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 informationAdaptive Dynamical Polling in Wireless Networks
BULGARIA ACADEMY OF SCIECES CYBERETICS AD IFORMATIO TECHOLOGIES Volume 8, o Sofa 28 Adaptve Dynamcal Pollng n Wreless etworks Vladmr Vshnevsky, Olga Semenova Insttute for Informaton Transmsson Problems
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 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 informationOperating conditions of a mine fan under conditions of variable resistance
Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety
More informationwhere v means the change in velocity, and t is the
1 PHYS:100 LECTURE 4 MECHANICS (3) Ths lecture covers the eneral case of moton wth constant acceleraton and free fall (whch s one of the more mportant examples of moton wth constant acceleraton) n a more
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationon the improved Partial Least Squares regression
Internatonal Conference on Manufacturng Scence and Engneerng (ICMSE 05) Identfcaton of the multvarable outlers usng T eclpse chart based on the mproved Partal Least Squares regresson Lu Yunlan,a X Yanhu,b
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 informationCopyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor
Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data
More informationInternational Journal of Engineering Research and Modern Education (IJERME) Impact Factor: 7.018, ISSN (Online): (
CONSTRUCTION AND SELECTION OF CHAIN SAMPLING PLAN WITH ZERO INFLATED POISSON DISTRIBUTION A. Palansamy* & M. Latha** * Research Scholar, Department of Statstcs, Government Arts College, Udumalpet, Tamlnadu
More informationComputing MLE Bias Empirically
Computng MLE Bas Emprcally Kar Wa Lm Australan atonal Unversty January 3, 27 Abstract Ths note studes the bas arses from the MLE estmate of the rate parameter and the mean parameter of an exponental dstrbuton.
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 informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
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 informationAn Improved multiple fractal algorithm
Advanced Scence and Technology Letters Vol.31 (MulGraB 213), pp.184-188 http://dx.do.org/1.1427/astl.213.31.41 An Improved multple fractal algorthm Yun Ln, Xaochu Xu, Jnfeng Pang College of Informaton
More informationGoodness of fit and Wilks theorem
DRAFT 0.0 Glen Cowan 3 June, 2013 Goodness of ft and Wlks theorem Suppose we model data y wth a lkelhood L(µ) that depends on a set of N parameters µ = (µ 1,...,µ N ). Defne the statstc t µ ln L(µ) L(ˆµ),
More informationLecture 4 Hypothesis Testing
Lecture 4 Hypothess Testng We may wsh to test pror hypotheses about the coeffcents we estmate. We can use the estmates to test whether the data rejects our hypothess. An example mght be that we wsh to
More informationTracking with Kalman Filter
Trackng wth Kalman Flter Scott T. Acton Vrgna Image and Vdeo Analyss (VIVA), Charles L. Brown Department of Electrcal and Computer Engneerng Department of Bomedcal Engneerng Unversty of Vrgna, Charlottesvlle,
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationCase Study of Markov Chains Ray-Knight Compactification
Internatonal Journal of Contemporary Mathematcal Scences Vol. 9, 24, no. 6, 753-76 HIKAI Ltd, www.m-har.com http://dx.do.org/.2988/cms.24.46 Case Study of Marov Chans ay-knght Compactfcaton HaXa Du and
More informationSimulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests
Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth
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 informationResearch Article Green s Theorem for Sign Data
Internatonal Scholarly Research Network ISRN Appled Mathematcs Volume 2012, Artcle ID 539359, 10 pages do:10.5402/2012/539359 Research Artcle Green s Theorem for Sgn Data Lous M. Houston The Unversty of
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
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 informationUncertainty as the Overlap of Alternate Conditional Distributions
Uncertanty as the Overlap of Alternate Condtonal Dstrbutons Olena Babak and Clayton V. Deutsch Centre for Computatonal Geostatstcs Department of Cvl & Envronmental Engneerng Unversty of Alberta An mportant
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 informationmodeling of equilibrium and dynamic multi-component adsorption in a two-layered fixed bed for purification of hydrogen from methane reforming products
modelng of equlbrum and dynamc mult-component adsorpton n a two-layered fxed bed for purfcaton of hydrogen from methane reformng products Mohammad A. Ebrahm, Mahmood R. G. Arsalan, Shohreh Fatem * Laboratory
More informationx i1 =1 for all i (the constant ).
Chapter 5 The Multple Regresson Model Consder an economc model where the dependent varable s a functon of K explanatory varables. The economc model has the form: y = f ( x,x,..., ) xk Approxmate ths by
More informationFlexible Allocation of Capacity in Multi-Cell CDMA Networks
Flexble Allocaton of Capacty n Mult-Cell CDMA Networs Robert Al, Manu Hegde, Mort Naragh-Pour*, Paul Mn Washngton Unversty, St. Lous, MO *Lousana State Unversty, Baton Rouge, LA Outlne Capacty and Probablty
More informationA note on almost sure behavior of randomly weighted sums of φ-mixing random variables with φ-mixing weights
ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA Volume 7, Number 2, December 203 Avalable onlne at http://acutm.math.ut.ee A note on almost sure behavor of randomly weghted sums of φ-mxng
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 informationA Particle Filter Algorithm based on Mixing of Prior probability density and UKF as Generate Importance Function
Advanced Scence and Technology Letters, pp.83-87 http://dx.do.org/10.14257/astl.2014.53.20 A Partcle Flter Algorthm based on Mxng of Pror probablty densty and UKF as Generate Importance Functon Lu Lu 1,1,
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 informationDurban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications
Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department
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 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 informationGEO-SLOPE International Ltd, Calgary, Alberta, Canada Vibrating Beam
GEO-SLOPE Internatonal Ltd, Calgary, Alberta, Canada www.geo-slope.com Introducton Vbratng Beam Ths example looks at the dynamc response of a cantlever beam n response to a cyclc force at the free end.
More informationDetermine the Optimal Order Quantity in Multi-items&s EOQ Model with Backorder
Australan Journal of Basc and Appled Scences, 5(7): 863-873, 0 ISSN 99-878 Determne the Optmal Order Quantty n Mult-tems&s EOQ Model wth Backorder Babak Khabr, Had Nasser, 3 Ehsan Ehsan and Nma Kazem Department
More information4 Analysis of Variance (ANOVA) 5 ANOVA. 5.1 Introduction. 5.2 Fixed Effects ANOVA
4 Analyss of Varance (ANOVA) 5 ANOVA 51 Introducton ANOVA ANOVA s a way to estmate and test the means of multple populatons We wll start wth one-way ANOVA If the populatons ncluded n the study are selected
More informationGeneral viscosity iterative method for a sequence of quasi-nonexpansive mappings
Avalable onlne at www.tjnsa.com J. Nonlnear Sc. Appl. 9 (2016), 5672 5682 Research Artcle General vscosty teratve method for a sequence of quas-nonexpansve mappngs Cuje Zhang, Ynan Wang College of Scence,
More informationANOVA. The Observations y ij
ANOVA Stands for ANalyss Of VArance But t s a test of dfferences n means The dea: The Observatons y j Treatment group = 1 = 2 = k y 11 y 21 y k,1 y 12 y 22 y k,2 y 1, n1 y 2, n2 y k, nk means: m 1 m 2
More informationStatistical inference for generalized Pareto distribution based on progressive Type-II censored data with random removals
Internatonal Journal of Scentfc World, 2 1) 2014) 1-9 c Scence Publshng Corporaton www.scencepubco.com/ndex.php/ijsw do: 10.14419/jsw.v21.1780 Research Paper Statstcal nference for generalzed Pareto dstrbuton
More informationWinter 2008 CS567 Stochastic Linear/Integer Programming Guest Lecturer: Xu, Huan
Wnter 2008 CS567 Stochastc Lnear/Integer Programmng Guest Lecturer: Xu, Huan Class 2: More Modelng Examples 1 Capacty Expanson Capacty expanson models optmal choces of the tmng and levels of nvestments
More informationUsing T.O.M to Estimate Parameter of distributions that have not Single Exponential Family
IOSR Journal of Mathematcs IOSR-JM) ISSN: 2278-5728. Volume 3, Issue 3 Sep-Oct. 202), PP 44-48 www.osrjournals.org Usng T.O.M to Estmate Parameter of dstrbutons that have not Sngle Exponental Famly Jubran
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationStatistics for Economics & Business
Statstcs for Economcs & Busness Smple Lnear Regresson Learnng Objectves In ths chapter, you learn: How to use regresson analyss to predct the value of a dependent varable based on an ndependent varable
More informationOn an Extension of Stochastic Approximation EM Algorithm for Incomplete Data Problems. Vahid Tadayon 1
On an Extenson of Stochastc Approxmaton EM Algorthm for Incomplete Data Problems Vahd Tadayon Abstract: The Stochastc Approxmaton EM (SAEM algorthm, a varant stochastc approxmaton of EM, s a versatle tool
More informationGrey prediction model in world women s pentathlon performance prediction applied research
Avalable onlne www.jocpr.com Journal of Chemcal and Pharmaceutcal Research, 4, 6(6):36-4 Research Artcle ISSN : 975-7384 CODEN(USA) : JCPRC5 Grey predcton model n world women s pentathlon performance predcton
More informationTHE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD
Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS
More informationEcon Statistical Properties of the OLS estimator. Sanjaya DeSilva
Econ 39 - Statstcal Propertes of the OLS estmator Sanjaya DeSlva September, 008 1 Overvew Recall that the true regresson model s Y = β 0 + β 1 X + u (1) Applyng the OLS method to a sample of data, we estmate
More informationBuffer Dumping Management for High Speed Routers
Buffer Dumpng Management for Hgh Speed Routers Carolne Fayet, André-Luc Beylot IT, 9 rue Charles Fourer, 90 Evry Cedex, France carolne.fayet@nt-evry.fr, Groupe des Ecoles des Télécommuncatons ESEEIHT,,
More informationDouble Acceptance Sampling Plan for Time Truncated Life Tests Based on Transmuted Generalized Inverse Weibull Distribution
J. Stat. Appl. Pro. 6, No. 1, 1-6 2017 1 Journal of Statstcs Applcatons & Probablty An Internatonal Journal http://dx.do.org/10.18576/jsap/060101 Double Acceptance Samplng Plan for Tme Truncated Lfe Tests
More informationUNIVERSITY OF TORONTO Faculty of Arts and Science. December 2005 Examinations STA437H1F/STA1005HF. Duration - 3 hours
UNIVERSITY OF TORONTO Faculty of Arts and Scence December 005 Examnatons STA47HF/STA005HF Duraton - hours AIDS ALLOWED: (to be suppled by the student) Non-programmable calculator One handwrtten 8.5'' x
More informationSuppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl
RECURSIVE SPLINE INTERPOLATION METHOD FOR REAL TIME ENGINE CONTROL APPLICATIONS A. Stotsky Volvo Car Corporaton Engne Desgn and Development Dept. 97542, HA1N, SE- 405 31 Gothenburg Sweden. Emal: astotsky@volvocars.com
More informationPOWER AND SIZE OF NORMAL DISTRIBUTION AND ITS APPLICATIONS
Jurnal Ilmah Matematka dan Penddkan Matematka (JMP) Vol. 9 No., Desember 07, hal. -6 ISSN (Cetak) : 085-456; ISSN (Onlne) : 550-04; https://jmpunsoed.com/ POWER AND SIZE OF NORMAL DISTRIBION AND ITS APPLICATIONS
More informationThe Analysis of Convection Experiment
Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 5) The Analyss of Convecton Experment Zlong Zhang School of North Chna Electrc Power Unversty, Baodng 7, Chna 469567@qq.com Keywords:
More informationVariability-Driven Module Selection with Joint Design Time Optimization and Post-Silicon Tuning
Asa and South Pacfc Desgn Automaton Conference 2008 Varablty-Drven Module Selecton wth Jont Desgn Tme Optmzaton and Post-Slcon Tunng Feng Wang, Xaoxa Wu, Yuan Xe The Pennsylvana State Unversty Department
More informationECE697AA Lecture 17. Birth-Death Processes
Tlman Wolf Department of Electrcal and Computer Engneerng /4/8 ECE697AA ecture 7 Queung Systems II ECE697AA /4/8 Uass Amherst Tlman Wolf Brth-Death Processes Solvng general arov chan can be dffcult Smpler,
More informationPHYS 450 Spring semester Lecture 02: Dealing with Experimental Uncertainties. Ron Reifenberger Birck Nanotechnology Center Purdue University
PHYS 45 Sprng semester 7 Lecture : Dealng wth Expermental Uncertantes Ron Refenberger Brck anotechnology Center Purdue Unversty Lecture Introductory Comments Expermental errors (really expermental uncertantes)
More informationA New Grey Relational Fusion Algorithm Based on Approximate Antropy
Journal of Computatonal Informaton Systems 9: 20 (2013) 8045 8052 Avalable at http://www.jofcs.com A New Grey Relatonal Fuson Algorthm Based on Approxmate Antropy Yun LIN, Jnfeng PANG, Ybng LI College
More informationLecture 17 : Stochastic Processes II
: Stochastc Processes II 1 Contnuous-tme stochastc process So far we have studed dscrete-tme stochastc processes. We studed the concept of Makov chans and martngales, tme seres analyss, and regresson analyss
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
More informationAmplification and Relaxation of Electron Spin Polarization in Semiconductor Devices
Amplfcaton and Relaxaton of Electron Spn Polarzaton n Semconductor Devces Yury V. Pershn and Vladmr Prvman Center for Quantum Devce Technology, Clarkson Unversty, Potsdam, New York 13699-570, USA Spn Relaxaton
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 informationGlobal Sensitivity. Tuesday 20 th February, 2018
Global Senstvty Tuesday 2 th February, 28 ) Local Senstvty Most senstvty analyses [] are based on local estmates of senstvty, typcally by expandng the response n a Taylor seres about some specfc values
More informationChapter 7 Channel Capacity and Coding
Wreless Informaton Transmsson System Lab. Chapter 7 Channel Capacty and Codng Insttute of Communcatons Engneerng atonal Sun Yat-sen Unversty Contents 7. Channel models and channel capacty 7.. Channel models
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 informationMeenu Gupta, Man Singh & Deepak Gupta
IJS, Vol., o. 3-4, (July-December 0, pp. 489-497 Serals Publcatons ISS: 097-754X THE STEADY-STATE SOLUTIOS OF ULTIPLE PARALLEL CHAELS I SERIES AD O-SERIAL ULTIPLE PARALLEL CHAELS BOTH WITH BALKIG & REEGIG
More informationLecture Randomized Load Balancing strategies and their analysis. Probability concepts include, counting, the union bound, and Chernoff bounds.
U.C. Berkeley CS273: Parallel and Dstrbuted Theory Lecture 1 Professor Satsh Rao August 26, 2010 Lecturer: Satsh Rao Last revsed September 2, 2010 Lecture 1 1 Course Outlne We wll cover a samplng of the
More informationChapter 8 Indicator Variables
Chapter 8 Indcator Varables In general, e explanatory varables n any regresson analyss are assumed to be quanttatve n nature. For example, e varables lke temperature, dstance, age etc. are quanttatve n
More informationFirst Year Examination Department of Statistics, University of Florida
Frst Year Examnaton Department of Statstcs, Unversty of Florda May 7, 010, 8:00 am - 1:00 noon Instructons: 1. You have four hours to answer questons n ths examnaton.. You must show your work to receve
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 informationThe Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method
Journal of Electromagnetc Analyss and Applcatons, 04, 6, 0-08 Publshed Onlne September 04 n ScRes. http://www.scrp.org/journal/jemaa http://dx.do.org/0.46/jemaa.04.6000 The Exact Formulaton of the Inverse
More information1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys
More informationImprovement of Histogram Equalization for Minimum Mean Brightness Error
Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 3 Improvement of Hstogram Equalzaton for Mnmum Mean Brghtness Error AAPOG PHAHUA*,
More informationLecture 6: Introduction to Linear Regression
Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6
More informationTwo Methods to Release a New Real-time Task
Two Methods to Release a New Real-tme Task Abstract Guangmng Qan 1, Xanghua Chen 2 College of Mathematcs and Computer Scence Hunan Normal Unversty Changsha, 410081, Chna qqyy@hunnu.edu.cn Gang Yao 3 Sebel
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationStatistical analysis using matlab. HY 439 Presented by: George Fortetsanakis
Statstcal analyss usng matlab HY 439 Presented by: George Fortetsanaks Roadmap Probablty dstrbutons Statstcal estmaton Fttng data to probablty dstrbutons Contnuous dstrbutons Contnuous random varable X
More informationUniqueness of Weak Solutions to the 3D Ginzburg- Landau Model for Superconductivity
Int. Journal of Math. Analyss, Vol. 6, 212, no. 22, 195-114 Unqueness of Weak Solutons to the 3D Gnzburg- Landau Model for Superconductvty Jshan Fan Department of Appled Mathematcs Nanjng Forestry Unversty
More informationAS-Level Maths: Statistics 1 for Edexcel
1 of 6 AS-Level Maths: Statstcs 1 for Edecel S1. Calculatng means and standard devatons Ths con ndcates the slde contans actvtes created n Flash. These actvtes are not edtable. For more detaled nstructons,
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Experments- MODULE LECTURE - 6 EXPERMENTAL DESGN MODELS Dr. Shalabh Department of Mathematcs and Statstcs ndan nsttute of Technology Kanpur Two-way classfcaton wth nteractons
More information