Many-to-Many Traffic Grooming in WDM Mesh Networks

Similar documents
Support vector machines for regression

Graphical rules for SU(N)

Effectiveness and Efficiency Analysis of Parallel Flow and Counter Flow Heat Exchangers

SVMs for regression Multilayer neural networks

Module 3: Element Properties Lecture 5: Solid Elements

SVMs for regression Non-parametric/instance based classification method

Pattern Generation for Two Dimensional. cutting stock problem.

Abhilasha Classes Class- XII Date: SOLUTION (Chap - 9,10,12) MM 50 Mob no

CENTROID (AĞIRLIK MERKEZİ )

CENTROID (AĞIRLIK MERKEZİ )

CENTROID (AĞIRLIK MERKEZİ )

Section 2.1 Special Right Triangles

Pythagorean Theorem and Trigonometry

Dennis Bricker, 2001 Dept of Industrial Engineering The University of Iowa. MDP: Taxi page 1

ME 501A Seminar in Engineering Analysis Page 1

Performance Comparison of Three-Phase Shunt Active Power Filter Algorithms

On Pfaff s solution of the Pfaff problem

Algebra: Function Tables - One Step

*GMT62* *20GMT6201* Mathematics. Unit T6 Paper 2 (With calculator) Higher Tier [GMT62] MONDAY 11 JUNE 3.00 pm 4.15 pm. 1 hour 15 minutes.

Symmetry Labeling of Molecular Energies

Physics 41 Chapter 22 HW Serway 7 th Edition

THIS PAGE DECLASSIFIED IAW E

Chapter Runge-Kutta 2nd Order Method for Ordinary Differential Equations

Multivariate Ratio Estimator of the Population Total under Stratified Random Sampling

Gravity Drainage Prior to Cake Filtration

4.3 The Sine Law and the Cosine Law

Mathematically, integration is just finding the area under a curve from one point to another. It is b

VECTORS VECTORS VECTORS VECTORS. 2. Vector Representation. 1. Definition. 3. Types of Vectors. 5. Vector Operations I. 4. Equal and Opposite Vectors

Partially Observable Systems. 1 Partially Observable Markov Decision Process (POMDP) Formalism

Econ 401A Three extra questions John Riley. Homework 3 Due Tuesday, Nov 28

e a = 12.4 i a = 13.5i h a = xi + yj 3 a Let r a = 25cos(20) i + 25sin(20) j b = 15cos(55) i + 15sin(55) j

Effectiveness of Split-Plot Design over Randomized Complete Block Design in Some Experiments

Multicommodity Distribution System Design

Research on Complex Networks Control Based on Fuzzy Integral Sliding Theory

Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC

COMP4630: λ-calculus

Chemical Reaction Engineering

Product Layout Optimization and Simulation Model in a Multi-level Distribution Center

Lecture 6: Coding theory

Cyclic Codes BCH Codes

Effects of polarization on the reflected wave

A = h w (1) Error Analysis Physics 141

Trigonometry. Trigonometry. Solutions. Curriculum Ready ACMMG: 223, 224, 245.

How to Find the Derivative of a Function: Calculus 1

Neural Network (Basic Ideas) Hung-yi Lee

MAT 1275: Introduction to Mathematical Analysis

Figure XX.1.1 Plane truss structure

Controller Design for Networked Control Systems in Multiple-packet Transmission with Random Delays

Learning Enhancement Team

1 + t5 dt with respect to x. du = 2. dg du = f(u). du dx. dg dx = dg. du du. dg du. dx = 4x3. - page 1 -

MATHEMATICS PAPER & SOLUTION

Periodic Learning of B-spline Models for Output PDF Control: Application to MWD Control

Observations on harmonic Progressions *

Chemical Reaction Engineering

Logarithms and Exponential Functions. Gerda de Vries & John S. Macnab. match as necessary, or to work these results into other lessons.

Lecture Note 4: Numerical differentiation and integration. Xiaoqun Zhang Shanghai Jiao Tong University

3. Using your answers to the two previous questions, evaluate the Mratio

Stanford University CS254: Computational Complexity Notes 7 Luca Trevisan January 29, Notes for Lecture 7

Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]

1/4/13. Outline. Markov Models. Frequency & profile model. A DNA profile (matrix) Markov chain model. Markov chains

Math 324 Advanced Financial Mathematics Spring 2008 Final Exam Solutions May 2, 2008

DYNAMIC ANALYSIS OF SEMI-RIGID FRAMES

Iranian Journal of Mathematical Chemistry, Vol. 5, No.2, November 2014, pp

Polynomial Interpolation

Applied Statistics Qualifier Examination

P a g e 5 1 of R e p o r t P B 4 / 0 9

Chapter 4. Interaction of Many-Electron Atoms with Electromagnetic Radiation

Study on the Normal and Skewed Distribution of Isometric Grouping

Chapter 5 Worked Solutions to the Problems

Exact Inference: Introduction. Exact Inference: Introduction. Exact Inference: Introduction. Exact Inference: Introduction.

The proof is a straightforward probabilistic extension of Palfrey and Rosenthal (1983). Note that in our case we assume N

Section 3.1: Derivatives of Polynomials and Exponential Functions

Numerical Differentiation

PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

Boundary Value Problems. Lecture Objectives. Ch. 27

The Projective Quarter Symmetric Metric Connections and Their Curvature Tensors

Order of Accuracy. ũ h u Ch p, (1)

Research Article Application of Functionals in Creating Inequalities

we have E Y x t ( ( xl)) 1 ( xl), e a in I( Λ ) are as follows:

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o

Chapter Newton-Raphson Method of Solving a Nonlinear Equation

Energy Balance of Solar Collector

Solution Set #3

Performance Modeling of Hierarchical Memories

M/G/1/GD/ / System. ! Pollaczek-Khinchin (PK) Equation. ! Steady-state probabilities. ! Finding L, W q, W. ! π 0 = 1 ρ

ELASTIC-VISCOPLASTIC HOMOGENIZATION ANALYSIS OF PLAIN-WOVEN GFRP LAMINATES WITH MISALIGNED PLAIN FABRICS

5.1 We will begin this section with the definition of a rational expression. We

MAGIC058 & MATH64062: Partial Differential Equations 1

Some results on a cross-section in the tensor bundle

Math 20C Multivariable Calculus Lecture 5 1. Lines and planes. Equations of lines (Vector, parametric, and symmetric eqs.). Equations of lines

PLEASE DO NOT TURN THIS PAGE UNTIL INSTRUCTED TO DO SO THEN ENSURE THAT YOU HAVE THE CORRECT EXAM PAPER

Computing data with spreadsheets. Enter the following into the corresponding cells: A1: n B1: triangle C1: sqrt

Lab 6 Derivatives and Mutant Bacteria

1 The concept of limits (p.217 p.229, p.242 p.249, p.255 p.256) 1.1 Limits Consider the function determined by the formula 3. x since at this point

AVL trees. AVL trees

Polynomial Interpolation

Lecture 4: Piecewise Cubic Interpolation

Chapter 2 Differentiation

NON-DETERMINISTIC FSA

Estimating Delays. Gate Delay Model. Gate Delay. Effort Delay. Computing Logical Effort. Logical Effort

Transcription:

Mny-to-Mny Trff Groomng n WDM Mes Networks Mommd A. Se Amed E. K Deprtment of Eetr nd Computer Engneerng, Iow Stte Unversty, Ames, IA 50011 Em: {mse,k}@stte.edu Astrt In y-to-y ommunton, sesson onssts of group of users (we tem memers) were e one of te memers trnsmts ts trff to oter memers n te group. Ts pper studes te proem of provsonng yto-y sessons wt su-wveengt grnurtes n WDM mes networks. Our ojetve s to mnmze te numer of trnsevers requred. We study te proem n networks wt nd wtout opt spttng ptes. For networks wtout opt spttng ptes, we use n opt ppro w s n extenson of tt ntrodued n [8] for te y-to-one trff groomng proem. For networks wt opt spttng ptes, we ntrodue nove u-sed ppro were e sesson s routed troug y-to-one tree from te memers to entr u node, nd ten troug mutst tree from te u node k to te memers. At te u node, network odng s performed y nery omnng te trff unts reeved from te memers. Tese omntons re ten groomed nd devered k to te memers usng gt-tree(s). Numer resuts from ot pproes re presented nd ompred. I. INTRODUCTION In opt wveengt dvson mutpexng (WDM) networks, trff groomng ws ntrodued to redue te uge gp etween ndwdt requrements of user sessons nd te ndwdt of wveengt nne. For exmpe, n MPEG ompressed HDTV nne requres ess tn 20 Mps of ndwdt we te ndwdt of wveengt nne my re 10 Gps. In ddton to determnng te vrtu topoogy nd te routng nd wveengt ssgnment of e of te wveengt nnes, te trff groomng proem des wt te ntegent ssgnment of su-wveengt trff deds onto te exstng wveengt nnes. Most of te work n ts re s foused on unst trff [1], [2], [3]. For survey of dvnes n unst trff groomng, te reder s referred to [4]. In te reent yers, more nd more of te trff n g perfore networks eomng of te mutpont type. Ts trff type nudes mutst, y-to-one nd y-toy. In y-to-y, sesson onssts of group of users (we tem memers) were e one of tese memers trnsmts ts trff to oter memers n te group. Onded vdeo dstruton nd fe dstruton re exmpes of mutst pptons, we resoure dsovery nd dt oeton re exmpes of y-to-one pptons. In te se of y-to-y were sever users ntert togeter, mutmed onferenng, dstne ernng, dstruted smutons, Ts reser ws supported n prt y grnt CNS-0626741 from te Nton Sene Foundton. nd oortve proessng re some of te pptons. Sne WDM networks provde te pty to ommodte tese g-ndwdt pptons, fndng effent wys of provsonng tese pptons t te opt yer eome promnent. Trff groomng for mutst nd y-to-one trff types een studed n te terture [5], [6], [8]. For n ount of reent dvnes n mutst trff groomng, te reder s referred to [7]. To te est of our knowedge, te proem of y-to-y trff groomng n WDM networks s not een ddressed efore. In ts proem, one s gven set of y-to-y sessons wt rtrry su-wveengt trff deds nd te ojetve s to mnmze te numer of eetron ports w re used to dd or drop ertn wveengt t node (e.g., numer of trnsevers). In order to effetvey support mutst nd y-to-y trff types, nodes n WDM network must e e to dupte nomng trff nto mutpe opes e gong to dfferent output port. Two mn node rtetures were proposed n te terture to mpement ts funtonty. In te frst one, nodes n ony dupte n nomng opt sgn y ppyng opt-eetron-opt (O/E/O) onverson to te sgn nd dupton tkes pe n te eetron domn, we refer to networks wt tese nodes s non-spttng networks. In te seond one, nodes re pe of spttng te nomng sgn n te opt domn. Terefore, dupton n tke pe n te opt domn, we refer to networks wt tese nodes s spttng networks. In ts pper, we study te y-to-y trff groomng proem n ot spttng nd non-spttng networks. Te rest of te pper s orgnzed s foows. In Seton II, we propose te gtpt ppro nd te u-sed ppro to sove te y-to-y trff groomng proem n non-spttng nd spttng WDM networks, respetvey. In Seton III, we formute n MILP s n nyt mode for te u-sed ppro. Numer resuts from ot pproes re presented nd ompred n Seton IV, we te pper s onuded n Seton V. II. MANY-TO-MANY TRAFFIC GROOMING: NON-SPLITTING VERSUS SPLITTING NETWORKS A. Mny-to-Mny Trff Groomng n non-spttng Networks In non-spttng networks, gtpts w e te ony opt ommunton nnes ve to provson y-to-y

sessons. To opty sove te y-to-y trff groomng proem, we ve generzed te y-to-one MILP n [8] to ommodte sessons of mutpe soures nd mutpe destntons. E soure n te soure set trnsmts ts trff to destntons n te destnton set. Aordngy, yto-y sesson w smpy e represented s sesson wose soure set nd destnton set re te sme nd tey orrespond to te memers of te y-to-y sesson. In ts mode, y-to-y sesson n trverse mutpe gtpts from ny memer to ny oter memer n te group, we te gtpt tsef n trverse mutpe fers. Te ojetve s to mnmze te tot numer of trnsevers. For te rest of te pper, we refer to ts ppro s te gtpt ppro nd refer to te generzed MILP s LP-MILP. We do not nude te LP-MILP n ts pper due to spe mttons; owever, t s ve onne [10] for nterested reders. B. Mny-to-Mny Trff Groomng n Spttng Networks In spttng networks, gt-trees, n ddton to gtpts, n e used to provson y-to-y sessons. In ts seton, we ntrodue nove u-sed ppro to provson y-to-y sessons n spttng networks. In ts ppro, of te memers, n sesson wt N memers, send ter trff unts to entr u node w n e ny node n te network nudng te memers temseves. Ts u node ten nery omnes te trff unts reeved to generte N 1 nery ndependent omntons (A proess known s network odng [9]). Tese omntons must so e nery ndependent from te orgn trff unts reeved from te memers. Afterwrds, te N 1 omntons re groomed nd devered k to te memers usng gt-tree(s). E of te memers w e e to reover te orgn trff unty nery omnng ts own trff unt wt te reeved omntons (e.g., sovng N nery ndependent omntons), see Fg. (1.). For smpty, we ssume tt te ner omntons re performed usng oeffents tken from fed of sze 2. Aso we mke te ssumpton tt te memers n sesson ve te sme trff ded. Ts ssumpton s needed to ftte network odng t te u node y performng twse XOR on equ szed dt unts. C. A Comprtve Exmpe Consder te exmpe sown n Fg. 1, were nodes A, B nd C re memers of y-to-y sesson. E one of te memers needs to send one unt of trff denoted s, nd respetvey to te oter two memers. For te ske of ts exmpe, we ssume tt te pty of wveengt nne (groomng ftor) s two unts of trff. In te nonspttng network se, Fgure 1.() ustrtes te opt provsonng of te sesson y te gtpt ppro, w requres tot of 6 trnsevers. In te spttng network se, Fgure 1.() ustrtes te provsonng of te sesson y te u-sed ppro. Note tt e of te memers A nd C w e e to reover te orgn trff unty ddng + wt ter own trff unt moduo 2. Ts ppro requres tot of 7 trnsevers, w osts one more trnsever tn te gtpt ppro. On te oter nd, f, nd re two unts of trff nsted of one, ten te opt provsonng y te gtpt ppro, n te non-spttng network se, s sown n Fgure 1.(), w requres tot of 12 trnsevers. However, n te spttng network se, te u-sed ppro, s sown n Fgure 1.(d), requres tot of 10 trnsevers, w sves 2 trnsevers ompred to te gtpt ppro., A B C A B C,+,+, (), A B C () Fg. 1. A B C + () (d) + Trnsever Lgtpt Lgt-tree Lgtpt Appro vs. Hu-sed Appro III. HUB-BASED APPROACH: MILP FORMULATION Te y-to-y trff groomng proem under te used ppro s fory defned s foows: Gven te network topoogy, numer of wveengts per fer, groomng ftor nd set of y-to-y sesson requests wt rtrry su-wveengt trff deds, determne, for e sesson, ow to: 1) Opty seet u node. 2) Opty fnd y-to-one tree to dever te trff from te memers to te u node, we t memersto-u journey. 3) Opty fnd mutst tree to dever te ner omntons from te u node k to te memers, we t u-to-memers journey. Te memers-to-u journey my trverse mutpe gtpts from e of te memers to te u, we te u-tomemers journey my trverse mutpe gt-tree(s) from te u to te memers. We note tt gt-tree n our mode s ssoted wt sesson, e.g, wen we sy gt-tree eongng to sesson s we men gt-tree tt t s rooted t te u of s nd ts eves re te memers of s. Lgtpts nd gt-trees my groom trff from dfferent sessons nd trff from dfferent memers wtn sesson. Te ojetve of te optmzton proedure s to mnmze te tot numer of trnsevers requred. In ts seton, we formute n MILP, w we refer to s te HUB-MILP, to sove te y-to-y trff groomng proem n spttng networks under te u-sed ppro. Te foowng nottons re used n te MILP: N P W g tot numer of nodes n te network. nry numer equs to 1 f tere s dreted fer nk from node m to node n. numer of wveengts per fer, w we set rge enoug to gurntee fese souton. groomng ftor.

K tot numer of sessons n te network. m s te set of memers n sesson s, were 1 K. N s numer of memers n sesson s ; N s = m s. t s numer of unts of trff deded y e of te memers n sesson s, were 1 t s g. B s nry numer equs to 1 f sesson s s s one of ts memers. Q A very rge nteger; Q K N. T R n numer of trnsevers t node n. LPj w numer of gtpts from node to node j on wveengt w. numer of gtpts from node to node j on LP j Z s,k j X s j I s E s, wveengts; LP j = w LP j w. nry numer equs to 1 f tere s gtpt from to j tt uses fer on wveengt w. nry numer equs to 1 f te trff strem orgntng from memer k m s nd termntng t te u of s s usng gtpt from to j. re numer equs to te mount of trff rred on gtpt(s) from to j due to k m s. nry numer equs to 1 f node s te u node for sesson s. nry numer equs to 1 f sessons s nd sre node s ter u node. Es s nry numer equs to 1 f sessons s nd sre te sme u node. We note tt ts s te dsjunton of Es s, for vues of ; Es s = 1. LTs w numer of gt-treeeongng to sesson s on wveengt w. numer of gt-treeeongng to sesson s on wveengts; LT s = w LT s w. re numer equs to te produt of LT s nd I s LT s A s R s,w U s T s. nry numer equs to 1 f tere s gt-tree eongng to sesson s wt root (u of s ) to ef (memer m s ) pt tt uses fer on wveengt w. nry numer equs to 1 f t est one of te root (u of s ) to ef (memer m s ) pts of gt-tree eongng to sesson s uses fer nk on wveengt w. nry numer equs to 1 f sesson s s routed on gt-tree eongng to sesson. re numer equs to te mount of trff rred on gt-tree(s) eongng to sesson due to memers n sesson s. Ojetve Funton: Sujet to: Mnmze: n T R n Numer of trnsevers: Te foowng onstrnt ensures tt t te soure nd t te destnton of e gtpt tere s trnsever present. Aso, t ensures tt t te root nd t te eves of e gt-tree tere s trnsever present. T R (LP j + LP j ) + LT s B s j:j s + A s s : / m s Te nonner term A s n e omputed usng te foowng set of ner onstrnts (togeter wt te mnmzton n te ojetve funton): A s Lgtpt eve onstrnts: m = m:p m =1 n:p n =1 m:p mx=1 (1) QI s Q + LT s s, (2) A s LT s s, (3) n = n:p jn =1 m:p mj =1 mx = n:p xn=1 jn = 0, j, w (4) mj = LP w j, j, w (5) xn, j, w, x (, j) Constrnts (4), (5) nd (6) togeter ensure tt for e gtpt from to j tere s orrespondng pys pt from to j not usng fers omng nto or outgong from j nd stsfyng te wveengt ontnuty. Lgt-tree eve onstrnts: In ts set of onstrnts, we vsuze gt-tree eongng to sesson s s set of pts, e orgntng from te root of te gt-tree (u of s ) nd termntng t one of ts eves (one of te memers of s ). We refer to tese pts s root-to-ef pts. Te foowng onstrnt ensures tt no root-to-ef pt s routed on fer nk omng nto te root. m:p m =1 m (6) (1 I s )Q s, m s,, w (7) Te foowng onstrnt ensures tt no root-to-ef pt s routed on fer nk outgong from te ef. n = 0 s, m s, w (8) n:p n =1 Te foowng onstrnts ensure tt for e ef of gt-tree tere soud e root-to-ef pt orgntng from te root. s, m s,, w : n:p n =1 n:p n =1 n n LTs w (1 I s )Q (9) LTs w + (1 I s )Q (10) Te foowng onstrnts ensure tt for e ef of gt-tree tere soud e root-to-ef pt termntng t te ef. LT w s QI s s, m s, w (11)

LT w s + QI s s, m s, w (12) Te foowng onstrnts ensure te wveengt ontnuty of root-to-ef pt. s, m s, w, x : Rmx s,,w Rxn s,,w (13) m:p mx=1 m:p mx=1 mx n:p xn=1 n:p xn=1 xn QI s x (14) Te foowng onstrnts ensure tt te sme wveengt s used on root-to-ef pts tt eong to te sme gt-tree. s, (, k) m s, w : m:p mk =1 m:p mk =1 R s,k,w mk R s,k,w mk (I s + (I s + I s k )Q (15) + I s k )Q (16) Te foowng onstrnts set te vre R s,w s te dsjunton of for vues of. R s,w /Q s, w, m, n : p = 1 (17) m s R s,w m s s, w, m, n : p = 1 (18) Te foowng onstrnt ensures tt for ny wveengt w on ny fer nk no more tn one gtpt or gt-tree n e present. s R s,w + j 1 w, m, n : p = 1 (19) Hu node seeton onstrnts: Te foowng onstrnt ensures tt tere s exty one u node for e sesson. I s = 1 s (20) Te foowng onstrnts set te vre E s, onjunton of te vres I s E s, E s, (I s I s nd I. s te + I )/2 s,, (21) + I 1 s,, (22) Te foowng onstrnts set te vre E s dsjunton of Es s, for vues of. E s E s s te E s, /Q s, (23) E s, s, (24) Memers-to-u journey onstrnts: In ts set of onstrnts, we vsuze te memersto-u journey of sesson s set of strems, e orgntng from memer nd termntng t te u. E of tese strems, w we refer to s memer-tou strems, my trverse mutpe gtpts from te memer to te u. Te foowng onstrnt ensures tt memer-to-u strem nnot e routed on gtpt omng nto te memer. Z s,k k = 0 s, k m s (25) : k Te foowng onstrnt ensures tt memer-to-u strem nnot e routed on gtpt outgong from te u. Z s,k (1 I s )Q s, k ms, k (26) : Te foowng onstrnt ensures tt for e memerto-u strem, tere s gtpt orgntng from te memer uness t s te u. : k Z s,k k = 1 I s k s, k m s (27) Te foowng onstrnt ensures tt for e memerto-u strem, tere s gtpt termntng t te u. : x : Z s,k I s s, k m s, k (28) Te foowng onstrnt ensures te ontnuty of memer-to-u strem on mutpe gtpts. Z s,k x = Z s,k xj + I s x s, k m s, x k j:j (x,k) (29) Te foowng onstrnt determnes te ext mount of trff rred on gtpt(s) from node to node j due to memers k m s. X s j = t s Z s,k j s,, j (30) k m s Te foowng onstrnt determnes te tot numer of gtpt(s) needed from node to node j. LP j ( s X s j )/g, j (31) Hu-to-memers journey onstrnts: In ts set of onstrnts, we determne w gt-tree(s) re used n te u-to-memers journey of sesson. Te foowng onstrnt ensures tt te u-to-memers journey of sesson nnot e routed on gt-tree of noter sesson uness te two sessons sre te sme u node. U s E s s, (32) Te foowng onstrnt ensures tt e memer of sesson must e reed y t est one of te gt-trees used n te u-to-memers journey of te sesson. Us s 1 s, m s (33) : m s

Te foowng onstrnt determnes te ext mount of trff rred on gt-tree(s) eongng to sesson due to memers n sesson s. T s = U s t s (N s 1) s, (34) Ts represents te tot mount of trff fter odng te trff unts trnsmtted y te memers of sesson s t te u node of sesson. Te foowng onstrnt determnes te tot numer of gt-trees needed for sesson s. spttng networks, we ve ntrodued te u-sed ppro tt omnes opt spttng nd network odng to provson te sessons. We ve onuded tt te gtpt ppro s etter oe wen trff deds of sessons re retvey ow (t < g/2) we te u-sed ppro s etter oe wen trff deds of sessons re retvey g (t > g/2). LT s ( T s )/g s (35) IV. NUMERICAL RESULTS In ts seton, we ompre te gtpt ppro nd te u-sed ppro usng LP-MILP nd HUB-MILP, respetvey. In our experments, we onsder te network sown n Fg. 2 w sed on te Aene Reser Network [11]. E nk s omposed of two undreton fers n opposte dretons, nd te numer of wveengt nnes n e fer, W, s set to 4. Trff deds re nteger mutpes of OC-3 rtes, we wveengt nne s pty of OC-48; ene, te groomng ftor, g, s 16. We run 6 rndom experments s foows, e experment s 5 y-to-y sessons were te sze of e sesson s rndoy seeted etween [2,4]. Te memers n e sesson re rndoy seeted etween [0,9] nd te trff deded y e of te memers n sesson s rndoy seeted etween [1,16]. For e experment, we defne t = s N s t s / s N s, to e te verge mount of trff deded y memer n ts experment. Te opt souton from LP-MILP nd HUB-MILP for e of tese experments s otned usng te CPLEX sover [12]. Te numer of trnsevers (T R) requred y e of te experments s sown n Te I. Due to spe mttons, we do not sow te tu provsonng of sessons n te 6 experments. However, Fg. 2 ustrtes te provsonng of sessons 1 nd 4 n Exp. #1 (sown n Te II) usng te HUB-MILP. From te resuts we onude tt te gtpt ppro s etter oe wen trff deds of sessons re retvey ow (t < g/2), see Exps. 5 nd 6, we te u-sed ppro s etter oe wen trff deds of sessons re retvey g (t > g/2), see Exps. 2 nd 3. Te reson for ts s tt gt-trees re not effent n groomng trff nd terefore wen trff deds re retvey ow (t < g/2), te u-sed ppro do not perform we. On te oter nd, gtpts re very effent n groomng trff nd terefore te gtpt ppro performetter wen trff deds re retvey ow (t < g/2). V. CONCLUSIONS In ts pper, we ve studed te y-to-y trff groomng proem n ot spttng nd non-spttng WDM networks. In non-spttng networks, we ve generzed te mode n [8] to provde n opt gtpt ppro. In Fg. 2. Aene Reser Network (wt two ddton nks): Provsonng of s 1 nd s 4 n Exp. #1 usng te HUB-MILP. Note tt te two sessons re groomed on gtpt 3 5 nd on gt-tree 5 (3, 9) were u(s 1 )=u(s 4 )=5 TABLE I NUMBER OF TRANSCEIVERS (TR) COMPARISON BETWEEN THE LIGHTPATH AND THE HUB-BASED APPROACHES Exp # 1 2 3 4 5 6 t 8.3 11.8 9.8 7.5 5.3 4.4 LP-MILP(TR) 28 36 38 30 20 18 HUB-MILP(TR) 28 32 34 29 23 22 TABLE II INPUT PARAMETERS FOR EXPERIMENT #1 Sesson Memers Trff Deds s 1 (3,5) 3 s 2 (1,2,7) 14 s 3 (0,6,8) 7 s 4 (3,5,9) 5 s 5 (4,9) 12 REFERENCES [1] E. Modno, Trff Groomng n WDM Networks IEEE Communtons pp. 124-129, Juy 2001. [2] O. Gerste, R. Rmswm, nd G. Ssk, Cost-effetve Trff Groomng n WDM Rngs, IEEE/ACM Trnstons on Networkng, Ot. 2000. [3] K. Zu nd B. Mukerjee, Trff Groomng n WDM Mes Network, IEEE Journ on Seeted Ares n Communtons, Jn 2002. [4] R. Dutt nd G. N. Rousks, Trff groomng n WDM networks: pst nd future, IEEE Network, vo. 16, no. 6, pp. 4656, Nov./De. 2002. [5] R. U-Mustf nd A. E. K, Desgn nd provsonng of WDM networks wt mutst trff groomng, IEEE J. Seet. Ares Commun., vo. 24, no. 4, pp. 3753, Apr. 2006. [6] G. Cowdry nd C. S. R. Murty, Groomng of mutst sessons n wdm mes networks, n Worksop on Trff Groomng, 2004. [7] K, A. E., Agortms for Mutst Trff Groomng n WDM Mes Networks, IEEE Communtons Nov. 2006. [8] R. U-Mustf nd A. E. K, Mny-to-one Trff Groomng wt Aggregton n WDM Networks IEEE Journ on Seeted Ares n Communton, vo. 24, no. 8, August 2006. [9] R. Aswede, N. C, S. R. L, nd R. W. Yeung, Network nformton fow IEEE Trns. Inf. Teory vo. 46, no. 4, pp. 12041216, Ju. 2000. [10] ttp://epe.ee.stte.edu/n/downods/lp-milp.pdf [11] Te Aene Reser Network, ttp://ene.nternet2.edu/. [12] ttp://www.og.om/produts/pex/

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback