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The Optimal Multiple Multicast Problem on WDM Ring 演講者:丁德榮 弘光科技大學 資訊管理系助理教授 兼電算中心主任 Mail: [email protected] 1 Outline • • • • • • Introduction Multicast Problem on WDM Multiple Multicast Problem on WDM Ring Solution Methods Results Conclusion and Further Research Topics 2 What is WDM • Wavelength Division Multiplexing (WDM) – Each wavelength is an independent communication channel – Multiple wavelengths channels can be multiplexed into one fiber wavlength wavlength wavlength n Opitcal Fiber 3 Why WDM? • Provide huge bandwidth using fiber – Fiber has about 50 terabits per second – Multiple WDM channels provide huge aggregate bandwidth in a single fiber • Avoid the bottleneck of increasing baud rate – Current peak rate is about only 10 Gbps – Implementation of higher bit rate using fiber for longdistance transmission is more difficult – Multiple WDM channels with peak rate can achieve huge capacity • Upgrade network capacity without fiber redeployment 4 Optical Components in WDM Networking • Optical Transmitter – Tunable transmitter – Fixed transmitter • Transmit at a fixed wavelength • Optical Receivers (Filters) – Tunable receiver – Fixed receiver • Filter out one or multiple wavelengths from 5 Optical Components in WDM Networking Wavelength multiplexer & demultiplexer 1 2 1 1,2,…,n 1,2,…,n 2 n n Multiplexer Demultiplexer 6 Optical Components in WDM Networking • Wavelength router Wavelength Demux. 1,.., N Wavelength Mux. 1,.., N Optical Switch 1,.., N 1,.., N Optical Switch 1,.., N 1,.., N Optical Switch Arrayed WDM Receiver Arrayed WDM Trans mitter Arrayed WDM Receiver Arrayed WDM Trans mitter Arrayed WDM Receiver Arrayed WDM Trans mitter Local source and sink 7 Optical Components in WDM Networking • Wavelength converter – Main function: convert the input wavelength from one to another – Used to raise wavelength utilization and reduce call blocking rate c s Wavelength Converter s = 1,2,…,N c = 1,2,…,N 8 Two Kinds of WDM-based LAN • Single-hop systems – The source node’s transmitter and the destination node’s receiver always tune to the same wavelength. – Direct transmission without store-and-forward by intermediate nodes. – Transmission coordination is necessary to avoid channel collision and receiver collision . • Multi-hop systems – Only some pair of nodes have direct transmission. – Traffic between two nodes may be stored-and-forwarded via intermediate nodes. – Wavelength converter is need 9 Wavelength-Routed Network • Light-path: the all-optical communication channel between two nodes. Wavelength Router d g 2 3 a b h 1 i 4 6 5 c e j f 10 Wavelength-Routed Network • Constraints – Wavelength continuity • A light-path is required to be on the same wavelength throughout its path. • Wavelength converter can be used to change the wavelength in one light-path. – Different light-paths traversing the same fiber must be on different wavelengths 11 Research Problems • • • • Virtual topology embedding Topological optimization Virtual topology reconfiguration Routing and wavelength assignment (RWA) • Optimization problems due to using wavelength converters • Multicast problem • Placement Problem 12 Multicast Problem on WDM • Multicast is a point to multipoint communication, by which a source node sends messages to multiple destination nodes. • A light-tree, as a point to multipoint extension of a light-path, is a tree in the physical topology and occupies the same wavelength in all fiber links in the tree. • Definition: given an multicast request in a WDM network system, compute a set of routing trees and assign wavelengths to them such the cost is minimized. 13 Multiple Multicast Problem on WDM Ring • WDM Model – Single-hop WDM network – All Optical Network – Ring – Multicast Capability (light-splitting capability) – Static Traffic 14 Problem Definition • Ring network G(V,E) – V: the set of nodes – E: the set of links – bi-directional link – W wavelengths per link。 15 Problem Definition • r groups of multicasts， – – – – Mi={si, Di}，i=1, 2, …, r, 1≦ki≦n；where Di={d1i, d2i, …, dkii } be the destination si :source For each multicast Mi={si, Di}，a multicast tree MTi is need – Construct a multicast forest MF=Ui=1,2,…r MTi。 – Construct MF with wavelength continuity constraint, such the number of used wavelengths is minimized。 16 OMMP • Optimal multiple multicast problem, OMMP • 給定一個WDM網路與r個多點傳送的需求所成的 集合M={Mi={si, Di}，i=1, 2, …, r, 1≦ki≦n}，建 立一個多點傳送樹林，並決定每一個多點傳送樹 之波長通道指派，使的所需求的波長通道為最少。 • OMMP is a NP-hard problem • Since RWA(NP-hard) is a special case of OMMP • RWA on Ring is a NP-hard problem. 17 Example 18 Possible Assignment of Example 19 Observation • Each MTi can be constructed by： – 建立一個順時針方向的路徑：Pc(si, dl-1i) – 建立一個逆時針方向的路徑：Pr(si, dl+1i) – 建立兩個路徑，一個順時針與逆時針之路徑 Pr(si, dl’i) 與Pc(si, dl’i)，對某一個l’D。 20 Model Objective : Min y wW w s.t. k c x 1 , e P wc k wW k r x 1 , e P wr k wW wM ec k xwc k x wr yw , w W , e E wM er k k xwc , xwr {0,1}, c M y w {0,1}, w W 21 Solution Methods • Heuristic Algorithms • Genetic Algorithms 22 Heuristic Algorithms • Two phases – Routing Phase: • R1: Maximal-gap Routing • R2: Minimal Load Routing – Assignment Phase: • A1: Greedy Method • A2: Approximation Method: 7/4-approximation algorithm 23 Maximal Gap Routing 24 Greedy Method 25 Genetic Algorithm 26 Genetic Algorithm • • • • • • Chromosome Encoding Objective Function Penalty Function Crossover Mutation Selection 27 Chromosome Encoding • routing gene • MGi={mgik, i=1,...,r; k=1,2} AGi={agik, i=1,...,r; k=1,2} • r: number of connections. r=4 mg11 mg12 mg 12 mg 22 7 1 2 7 ... ... 1 2 mg1r mg r2 ag1 ag1 ag 12 ag 22 3 8 1 2 2 2 ... ag 1r ag r2 3 4 28 Example of chromosome encoding 8 1 2 3 7 6 4 5 29 Wavelength gene if (there is one element ag ik , such ag ik j ) and (mgik si ); 1 y j for i 1,2,..., r; k 1,2) 0 otherwise 30 Objective Function • Objective function W Objective function y j j 1 • The assignment represented by the connection may not constraint-satisfy, thus, a penalty function should be included in objective function. 31 Penalty Function • Assume both connections c1=(1,2) and c2=(1,4) are assigned to wavelength 1 with clockwise direction, then conflict occurred. • Penalty should be defined. • How to detect the conflict in a connection gene? • A conflict-detection algorithm should be developed. • O(M2) pairs of connections should be examined. • The conflict between two connections can be detected in constant time O(1). 32 Conflict-detection Algorithm • Construct four bipartite graph AA, AB, BA, BB, • Node: connection • Edge: conflict occurred – A: clockwise direction – B: counter-clockwise direction 33 Experiments • Run on PC with a Pentium III 1GHz CPU and 512MB RAM. • For nodes n=100, 200, 300 • Two sets of multicast requests are randomly generated. – Specific – Random • MAXM={5, 10} : the maximal number destinations in D. 34 Specific Set • Ranges Ai = { j | n*(i-1)/5+1 ≦ j ≦ n*i/5 } • The source and destination nodes of multicast Mi, i=1,2,...,r are randomly selected from nodes in Ai and two of which are n*(i-1)/5+1 and n*i/5. • The lower bound of the minimal used wavelengths of the set Mspecific is n/5. 35 Specific n=100 (MAXM =5 or 10) 36 Specific n=200 (MAXM =5 or 10) 37 Specific n=300 (MAXM =5 or 10) 38 39 Random n=100 (MAXM =5 or 10) 40 Random n=200 (MAXM =5 or 10) 41 Random n=300 (MAXM =5 or 10) 42 43 More Improvement 44 More Improvement 45 Conclusion and Further Research • Proposed – Mathematic Model for multiple multicast problem on WDM ring – Several Heuristic Algorithms – Genetic Algorithms • Further Research in the problem – Lower bound proof – CPLEX package to found optimal solution – Other Soft-computing method • Simulated Annealing, Tabu search, Ant algorithm, Scatter search 46 Further Extension • Dynamic traffic case: minimize blocking probability • Allow dynamic joining and leaving multicast group • Different WDM Model – Multi-hop WDM – Partial Multicast Capacity – Different Network Topology: Mesh, General Network • Other research problem – Group Communication Problem 47