Annales Informatca AI 1 (2003) 277-284 Annales Informatca Lubln-Polona Secto AI http://www.annales.umcs.lubln.pl/ Desgnng of multchannel optcal communcaton systems topologes crtera optmzaton Mrosław Hajder, Mrosław Mazure, Paweł Dymora Faculty of Electrcal and Computer Engneerng, Rzeszów Unversty of Technology, ul. Wncentego Pola 2, 35-959 Rzeszów, Poland Abstract Ths paper presents the ssues necessary to solve n the desgnng process of multchannel optcal communcaton systems topologes. The man desgn assumpton s the acceptance of multchannelng n communcaton system realzaton. In partcular, the bascs of desgnng physcal and logcal topologes are shown. Also cost aspects of physcal and logcal topologes realzaton are shown. 1. Introducton The tass solved by means of present telenformatc systems can be classfed nto two man groups. We can number the tass related to executng communcaton operatons between the parallel processng system elements n the frst group. The other group of tass s related wth assurance necessty of data transfer envronment for typcal nformaton servces.e.: fle transfer, voce and pcture transmsson, teleconferences etc. Desgnng of multchannel optcal communcaton systems s a very complex computatonal problem. Its am s to create lns wth gven characterstcs connectng any par of networ nodes wth each other. In the desgnng process we can dstngush two man stages: desgnng of physcal topology and desgnng of logcal topology. Specfyng n the networ structure physcal and logcal elements allows to get a number of orgnal possbltes, such as: possblty to specfy a set of logcal topologes n the confnes of one physcal topology, whose archtecture fulfl the requrements of run applcatons; possblty to buld topologes usng the pont to pont channels; realzaton smplfcaton of broadcast and multcast networ communcaton procedures; mprovement of physcal communcaton channels use effcency. Correspondng author: e-mal address: mremaz@prz.rzeszow.pl
The above advantages are characterstc of all multchannel systems but the possblty of other effcent use has appeared only n optcal systems. 2. Desgnng process elements Topologcal desgnng of multchannel optcal communcaton networs conssts of a number of mutually related steps. In the frst step, physcal topology s created whch s reflecton of optcal fber routes connectng real system nodes. In the second step projecton of the logcal topology on the physcal topology s performed. Ths process should tae nto consderaton requrements whch logcal topology should fulfl and also possblty of realzaton on the resources of physcal networ. Because ths tas s most often NP-hard computatonal problem that s why desgnng of logcal topology s splt nto four not necessarly dependent desgnng problems. These problems are: - desgnng of correct vrtual topology, whose transmttng nodes are drectly connected wth recevng nodes wth the assumpton that a number of optcal transmtters and recevers s mnmal; - desgnng of optcal routes on the physcal topology wth the assumpton that a number of avalable wavelengths s lmted; - selecton of wavelengths for dfferent optcal routes wth the assumpton that a number of avalable wavelengths s lmted; - pacets routng on the bass of vrtual topology routes wth the assumpton that transmttng and bufferng delays of the nformaton n the networ are mnmal. In the thrd step, on the bass of manner analyss of the logcal topology projecton on the physcal topology the type of buldng optcal networ s chosen. Optcal communcaton networs classfcaton s shown n Fg. 1. Optcal communcaton networs Broadcast Pont to pont Wavelength Routng Sngle-hop Multhop Statc Dynamc Lnear Fg. 1. Optcal communcaton networs classfcaton
3. Desgnng of physcal topology Desgnng of physcal topology n a partcular way affects on future functonng of the whole communcaton system. Partcularly physcal topology parameters defne such characterstcs as; lfeness, relablty, capacty, delays, etc. The most used optmzaton crteron s the networ realzaton cost and ts coheson coeffcent. Desgnng of physcal topology, partcularly desgnng of optcal fber routes connectng ndvdual nodes, must be closely connected wth the desgnng process of logcal networ. The entre networ capacty wll be specfed only at a physcal not logcal level. Because of that desgnng processes of physcal and logcal topologes should be related. In the desgnng process of physcal topology the heurstc algorthms creatng dendrte topology can be used and next wth the genetc approach the topologcal characterstcs could be mproved n order to ncrease ts maxmal capacty and coheson coeffcent. 4. Desgnng of logcal topology The projecton problem of the requred vrtual topology on the gven physcal topology s formally descrbed below. The followng nputs to ths problem are gven: G = V, E composed of weghted, undrected graph 1. The physcal topology p ( p) where V s a set of networ nodes and E p s a set of lns connectng nodes. The fact of graph undrecton results from that lns n physcal networs are of b-drectonal character. Graph nodes correspond to the networ nodes (pacet swtch) and lns correspond to the fbers connectng the mentoned nodes. Because lns are undrected, each ln may have two fbers or two multplexed transmsson channels based on the same fber. Each ln has weght whch corresponds to the dstance between the nodes. The node D D swtches wth wavelength routng mared as s joned to p( ) p( ) where D ( ) p s called node physcal degree whch equals to a number of physcal lns gong out (or gong n) of the node. 2. The number of avalable wavelength channels n each physcal fber s equal to M. 3. The matrx of N N elements s a flow matrx where N - s a number of networ nodes. Flows between the nodes and j are placed n (,j) table element. Traffc stream may be asymmetrc.e. the traffc between the nodes and j may be dfferent from the traffc between the nodes j and. 4. The number of lasers and flters whch are networ transmtters and recevers respectvely.
Our goal s to specfy the followng elements: G = V, E defned as a graph whch has the node 1. The vrtual topology ( ) v v output degree equal to the number of transmtters n the node and node nput degree equal to the number of recevers n the node. Nodes n the vrtual topology correspond to the physcal topology nodes. Each ln between the par of the vrtual topology nodes corresponds to the drected, completely optcal connecton routes between corresponded physcal topology nodes. Each of these lns may use many dfferent physcal connecton routes. Very mportant desgnng process element s to get so-called optmal routng n whch t s possble to create communcaton networ wth a lmted number of wavelength n each physcal channel. 2. The wavelength for the optcal routes such that f any two optcal routes share the same optcal channel they must use dfferent wavelength oblgatory. 3. Sze and confguraton of the optcal swtches n the ntermedary nodes. Some of the logcal topology s defned, and allocaton of wavelength could be determned by sze and swtches confguraton. We could put together ths fascnatng problem as an optmalzaton one. In ths case we wll use the followng symbols: - s or d are used as the upper or lower ndexes, descrbng the source and destnaton of pacets respectvely; - or j are representng begnnng and fnal optcal path nodes; - m and n denote the fnal paths,whch are contaned n the optcal path. Input data of the algorthm: Number of nodes N Maxmum number of the wavelength based on the sngle fber M Physcal topology P, where Pnm = P = 1 only f drect connecton exsts between the nodes; nm, = 1,2,..., N. If connecton does not exst, then P = P = 0. In both cases optcal connectons are treated as duplex. nm Dstance matrx s defned as an optcal dstance d between the nodes m and n. More often ths dstance s expressed as the essental tme for sendng the optcal sgnal between a par of nodes. Therefore, accordng to pror assumptons, optcal lnes are consdered duplex d = dnm and d = 0 f P = 0. Number of transmtters n the node s equal to T ( T 1 ). Lewse, a number of recevers n the node s equal to R ( R 1 ).
The flow matrx λ, descrbes an average traffc rate between the nodes s and d, where, = 1,2,..., N. The traffc rate for λ ss = 0. Therefore, we assume, that frequency of the pacet appearance n the note s and ts length, characterzes exponental arrangement. Therefore, standard of the queue M / M /1 could be employed to descrbe each and ever one networ connecton. The value λ should be expressed n each per pacet per second. Capacty of each channel s equal to C. Fndng varable Vrtual topology s descrbed by the nonsymmetrcal adjacency matrx V. The value V = 1 f presented topology conssts of the optcal path between the nodes and j. Otherwse, f there n no connectng path V = 0. We must become aware that the above statement n contrast to the prevously descrbed optcal channels does not mean, that vrtual channels should be duplex, for example V = 1 does not mean V = 1. Routng, the parameter j λ descrbes traffc between s and d nodes through the ntermedate vrtual ln V. It s notced, that stream from node s to node d can be separated nto two dfferent components, whch use dfferent sets of optcal paths. Routng n physcal topology, the varable p = 1 f and only f optcal connecton P exsts n the vrtual path V. Otherwse, p = 0. Wavelength color coverng, the value c = 1 varable f the path starts wth the node and ends wth the node j contans color, where = 1,2,..., M. Otherwse, c = 0. Dependences: In vrtual topology the connectvty matrx V : V T, (14) j V Rj j. (15) The above equatons are true only f all the transmtters n the node and all the recevers n the node j are used. In the physcal route the parameters p : p P, (16)
In vrtual topology traffc parameters Optcal paths color coverng p V, (17) pm = pn f, j (18) m n pn = V, (19) n pmj = V.. (20) n λ : λ 0, (21) λsj = λ, (22) j λd = λ, (23) λ = λ f s, (24) j λ V C. (25), c : c = V, (26) p c 1,,. (27) Crtera of the optmalzaton: Mnmzng of the delay: 1 mn λ p d + C λ. (28) Mnmzng of the ntal load (equvalent to mnmzng of the maxmum flow of the ln): C mn max λ max, j. (29) mn max λ Equatons explanaton. The prevously presented equatons are based on the prncple to sustan stream and source, and also on none-conflct routng. None-
conflct routng means that two optcal paths ncluded n the same optcal fber cannot share the same wavelength. Equatons (1) and (2) guarantee, that the number of optcal lnes, receved and sent, n the optcal paths of each node, at least s equal to nput or output node degree. Equatons (3) and (4) nvoe the followng problem, p can only exst f there s a physcal fber equvalent to our optcal path. Formulas (5)-(7) are multple equatons characterzng route from the source to ts destnaton. However, equatons (8) to (12) are responsble for pacet routng n the vrtual networ, they guarantee that t s possble to overload path channel wth many dfferent flows of steam. Equaton (13) requres that the optcal path could be assembled wth only one color. Formula (14), restrcts a number of colors, so colors utlzed n dfferent paths are mutually exclusve and are cancellng each other n one physcal connecton. Equatons (15) and (16) descrbe two possble optmalzaton crtera. In formula (15) n the deepest parenthess, the frst component s ted to propagaton delay of connecton, whch s utlzed by the optcal path. The second component s ted to queue delay and also durng transfers of the pacets through the optcal ln, usng for each optcal path the followng queue type M/M/1. If we assume, that routng wll be base of the shortest path n physcal topology then meanng of ths value p wll be establshed. Addtonally, f we omt all of the delays n the optmalzaton queue n formula (15) and f we mae smplfcaton to the formula λ p d, whch s consder as a lnear programmng, n whch all of the varables numercal soluton, but the varables V and λ do not requre them. c requre complete The role of the functon descrbed by (16) s also non-lnear and t s descrbed as a maxmum sze mnmalzaton of any flow through optcal path. Ths s also connected wth the vrtual topology creaton process, whch has to maxmze accessble load, f the matrx flow s ncreasng. Concluson In concluson to the presented analyss, we could presume that modern metallc transmsson envronment does not meet the requrements presented before hgh capacty transmsson envronment. Therefore t s requred to utlze hgh capacty transmsson envronments based on the optcal cables. The hgh effcency could be acheved only f use wavelength methods for multplcty dvsons. In order to use completely all the features of the hgh capacty optcal networ, we are requred to buld them on the base of rregular physcal topology. Therefore, the desgn of the logcal topology s not only lmted to descrpton of the networ that connects partcular nodes, but also requres the
descrpton of the possble ways to mplement logcal topology, based on the physcal source. Stablty of the topology, guarantee perfect mnmalzaton of the routng messagng procedure n the networ. Therefore, the mportance for real tme help des servces, such as voce transmsson, vdeoconferences or e-commerce, maes vrtual topology the only optmal soluton. In another wor, the attenton was focused manly on the resstance toward fault-tolerance communcaton, defntons and analyss of the standard topology. References [1] Hajder M., Mazure M., Dymora P., Vrtual topologes of multnode wde networs, Poznań Unversty of Technology, Poznań, (2002) 197. [2] Bannster J.A., Fratta L., Topologcal Desgn of the Wavelength-Dvson Optcal Networ, n proc. IEEE INFOCOM 90, San Francsco, CA., (1990) 1005. [3] Muherjee B., Banerjee D., Ramamurthy S., Muherjee A.: Some Prncples for Desgnng a Wde-Area WDM Optcal Networ, IEEE, (1996). [4] Xn Y., Rousas G., Perros H. G., On the Desgn of MPλS Networs, Department of Computer Scence North Calforna State Unversty, (1997). [5] Acampora A.S., A Multchannel Multhop Local Lghtwave Networ, n proc. GLOBECOM 87 Toyo, Japan, (1993). [6] Marsan M.A., Banco A., Leonard E., Ner F., A Comparson of Regular Topologes for All- Optcal Networs, n proc. INFOCOM 93 San Francsco, (1993). [7] Karasan E., Ayanoglu E., Performance of WDM Transport Networs, IEEE J. Selected Areas Commun., (1998). [8] Gen M., Cheng R., Genetc Algorthms and Engneerng Optmzaton, John Wley & Sons Inc., New Yor, (2000). Powered by TCPDF (www.tcpdf.org)