ELECTRONIC WAVELENGTH TRANSLATION IN OPTICAL NETWORKS Mlan Kovacevc Anthony Acampora Department of Electrcal Engneerng Center for Telecommuncatons Research Columba Unversty, New York, NY 0027-6699 Abstract { In ths paper we study the benets of electronc (regeneratve) wavelength translaton n optcal networks provdng wavelength channel crcut-swtchng among users. The electronc translaton means that an optcal sgnal on one wavelength s converted to electroncs then converted agan nto an optcal sgnal on another wavelength. A prevous study has demonstrated that wavelength translaton can sgncantly mprove the performance of a large mesh network. In ths paper we consder an optcal network archtecture based on a mesh topology where each node s suppled wth an array of W transmtters recevers (where W s the number of wavelengths). For ths archtecture we study eectveness of electronc wavelength translaton as a low cost alternatve to all-optcal wavelength translaton. We propose wavelength assgnment algorthms over a gven routng path whch mnmze the number of wavelength changes. The results of our performance study for a statc routng mesh network show that electronc translaton wth such algorthms can be almost as eectve as all-optcal wavelength translaton. In fact, the performance of electronc translaton converge to those of all-optcal translaton as the sze of a large mesh ncreases. the path between them (.e., the wavelength s beng routed along the path). Wavelength translaton ntroduces more exblty n establshng connectons by allowng a connecton to use derent wavelengths along the path. If wavelength translaton s used, t s enough to have at least one wavelength avalable on each lnk of the path between a par of statons. Wavelength translaton clearly reduces constrants n settng up connectons, whch results n lower connecton blockng probablty. Fgure llustrates the advantage of wavelength translaton. Suppose that we wsh to set up a connecton between statons A C n Fgure, that Recever array User Laser array I. INTRODUCTION Wavelength demultplexer Wavelength multplexer An all-optcal network based on wavelength dvson multplexng (WDM) wavelength routng appears to be a vable cdate for a new wde area telecommuncatons nfrastructure [, 2, 3]. Such a network conssts of bers joned by dynamcally controllable cross-connects (.e., wavelength selectve swtches) whch provde purely optcal transport between pars of network access statons (see Fgure ). Each access staton s equpped wth W optcal transcevers, each operatng on a dstnct wavelength, the optcal core enables the establshment of so-called clear optcal channels whch nterconnect the access statons. The optcal core, tself, contans wavelength selectve swtches, such that each wavelength - ndexed channel created by a gven access staton can be ndvdually routed to a possbly dstnct recevng access staton. Connectons at the optcal level are purely crcut-swtched, the lmted connectvty among access statons seen at the optcal level can be overcome by means of a multhop packet overlay, thereby permttng unlmted user-to-user connectvty, as seen at the vrtual crcut level. Together wth wavelength routng, wavelength translaton (also known as wavelength converson) s vewed as an mportant capablty for enablng scalablty mprovng the performance of optcal networks, s an essental feature of multhop networks [4]. In networks wthout wavelength translaton, two users are connected by usng the same wavelength on every lnk (ber) of The work presented heren was performed for the Optcal Network Technology Consortum was supported by the Advanced Research Project Agency under contract MDA-972-92-H-000. Wavelength selectve swtch Network access staton D d A a Fgure : A wavelength routng network each ber lnk carres up to two wavelengths (W W 2). If no wavelength translaton s allowed, such a connecton cannot be establshed, snce W, whch s avalable on lnk bc, s not avalable on lnk ab, W 2, whch s avalable on lnk ab, s not avalable on lnk bc. In the case where wavelength translaton s permtted, W B b W2 C c e E
the connecton from A to C can be establshed usng W 2 on the access lnk Aa the network lnk ab, W on the network lnk bc the access lnk cc. In the case of all-optcal translaton the wavelength change s performed optcally by wavelength converters embedded wthn network swtches. Several studes on all-optcal wavelength translaton have recently been reported. In [] a crcut-swtched alloptcal network wth statc routng wthout wavelength translaton s consdered. In [5] wavelength translaton s studed n a crcut-swtched all-optcal network wth dynamc routng a lmted number of wavelength converters. In [6] analytcal lower bounds for blockng probablty n networks wth wthout wavelength translaton are obtaned. In all of these studes, t s shown that wavelength translaton reduces blockng. However, the performance mprovement demonstrated n these studes does not appear to be sgncant. In [7], the eect of all-optcal wavelength translaton on performance s studed n statc-routng crcutswtched networks wth derent topologes. It s shown that there s no sgncant performance mprovement when the optcal wavelength translaton s used n centralzed swtch or rng topology networks. However, t also shown that optcal wavelength translaton sgncantly mproves performance of large mesh networks. A major obstacle n usng optcal wavelength translaton s that all-optcal wavelength converters are stll beng developed n laboratores. Even when they become commercally avalable, t can be expected that they wll be very expensve. Ths observaton motvates us to consder an electronc (regeneratve) wavelength translaton as a low-cost alternatve to all-optcal translaton. Electronc wavelength translaton means that an optcal channel s translated from one wavelength to another by an access staton assocated wth a swtchng node. In ths paper, we evaluate electronc translaton n the optcal network archtecture shown n Fgure [2]. We are partcularly nterested n a large network wth a mesh topology, snce t s shown that ths s the case where wavelength translaton s the most useful. We consder the case where a network access staton s connected to each wavelength selectve swtch. We also assume that the network s crcut-swtched wth statc routng (.e., a connecton between a par of statons always uses the same path). Dynamc or alternate routng may provde better performance, but ts analyss s more complex. Snce we are prmarly nterested n a relatve comparson of the schemes wth electronc optcal translaton, wthout wavelength translaton, the performance study for statc routng s sucent. The electronc wavelength translaton s llustrated n Fgure 2. In ths example, the connecton usng wavelength W on lnk In cannot use the same wavelength on lnk Out. Thus, the connecton s sent to the network access staton whch retransmts t on wavelength W 2. The connecton then contnues on wavelength W2 over lnk Out. Therefore, the staton serves merely as a cross-connect. Note, however, that the electronc wavelength translaton consumes resources of access statons. In ths example, a new connecton cannot be ntated from the staton, snce all the wavelengths on the staton's access lnk to the network (In0) are occuped. However, n a large mesh network where the expected number of hops s large, each staton uses only a small fracton of ts resources (.e.,transmtters recevers). The network lnks are the bottlenecks not the access lnks. In order to see ths, let us consder a mesh network where the average number of network hops s H where each network lnk s evenly loaded. Let us assume that no electronc wavelength translaton s performed. In such a case, each connecton wll consume one nput one output access lnk, on the average, H network lnks. Thus, W W In In2 In0 E/O Network access staton O/E Wavelength selectve swtch Out0 Out Out2 Fgure 2: Electronc wavelength translaton the oered load on the network lnks wll be about H tmes hgher than the oered load on the access lnks. As the network sze ncreases, H also ncreases, thus the access lnks become less utlzed than the network lnks. For example, f each staton has 5 transmtters 5 recevers, the average load per staton s (whch means that each staton transmts receves, on the average, one connecton all the tme), the average utlzaton of the statons' resources s only 20%. As the network sze ncreases, the load per staton needs to be reduced to mantan the same blockng probablty, as a result, the statons' utlzaton s further reduced. Ths observaton leads to the dea that those resources can be used for wavelength translaton. As we show n the paper, the reducton n blockng due to wavelength translaton capablty more than osets the ncrease n blockng as a result of the ncrease n load on the network access lnks caused by electronc translaton. The paper s organzed as follows. In Secton II, we present algorthms for assgnng wavelengths over a gven routng path whch tend to mnmze the number of wavelength translatons. In Secton III, we study performance n bdrectonal mesh-torus networks. We present results of our smulaton studes compare performance of networks wth optcal electronc wavelength translaton wthout wavelength translaton. II. WAVELENGTH ASSIGNMENT ALGORITHMS The objectve of a wavelength assgnment algorthm s to mnmze blockng of connecton requests. It s shown n [] that the optmal wavelength assgnment s a NP-complete problem, gven that all connecton requests ther routng paths are known n advance. In ths paper, we consder a crcut-swtched network where connectons are set up released dynamcally. In such a network, the optmal assgnment s not feasble, snce future connecton arrvals departures cannot be predcted. Therefore, we consder heurstc algorthms. A reasonable heurstc s to choose a wavelength assgnment whch mnmzes the number of wavelength changes per connecton, snce the number of changes aects load on access lnks, thus, blockng probablty. As was already mentoned, we assume that a network access staton s connected to each wavelength selectve swtch. The wavelength assgnment algorthms presented n ths secton can be eas- W W2 W
0 2 3 W W2 0 2 3 Fgure 3: Graph of the routng path ly moded to apply to a more general case where the number of access statons per swtch can also be zero or greater then one. Let us consder a n-hop routng path (.e., t conssts of n network lnks) from a source to a destnaton. In order to nd an optmal wavelength assgnment, we create a drected graph whch represents ths path, as shown n Fgure 3. We can now map the problem of ndng a wavelength assgnment whch mnmzes the number of wavelength translatons nto the problem of ndng the mnmum cost path n ths graph. In order to do ths, we assgn cost to the edges whch correspond to busy wavelengths cost to the edges whch correspond to dle wavelengths on network lnks. We also assgn a nte cost greater than 0 to the edges whch correspond to dle wavelengths on access lnks (we wll specfy the actual cost later n ths secton). Let C (k) () be the mnmum cost of establshng a connecton over the rst k network hops f the wavelength used on the k-th hop s, let l (k) () be the cost of usng wavelength on the k-th hop. Let n (k) o () n (k) () be the cost of enterng extng the network at node k on wavelength, respectvely. Let P (k) () be the wavelength to be used on the (k? )-th hop, gven that wavelength used on the k-th hop s, let W (k) be the wavelength chosen for the k-th hop of the path. At the end of the rst network hop, we have C () () = n () o () + l () () () We can dene the cost of transfer from wavelength to wavelength j at k-th ntermedate staton to be c (k) (; j) = n (k) () + n (k) o (j) 6= j 0 = j Let w (k?) be the wavelength on the (k? )-th network hop whch preceeds wavelength on the k-th hop such that C (k?) (w (k?) )+c (k) (w (k?) ; ) < C (k?) (j)+c (k) (j; ) j < w (k?) (3) C (k?) (w (k?) )+c (k) (w (k?) ; ) C (k?) (j)+c (k) (j; ) j w (k?) (4) Ths means practcally that w (k?) s the wavelength whch mnmzes the cost, f there s more than one wavelength whch yelds the mnmum cost, the one wth the smallest ndex s chosen. The dea behnd ths strategy s to pack more calls to wavelengths wth lower ndexes. It has been shown that such a "rst-t" heurstc has a postve eect on performance [, 7]. We then have C (k) () = C (k?) (w (k?) ) + c (k) (w (k?) ; ) + l (k) () k > (5) (2) The total cost s then P (k) () = w (k?) (6) C tot() = C (n) () + n (n) () (7) The wavelength used on the last hop s w (n) such that C tot(w (n) ) < C tot(j) j < w (n) (8) C tot(w (n) ) C tot(j) j w (n) (9) The wavelength assgnment s then W (n) = w (n) (0) W (k) = P (k+) (W (k+) ) k < n () In order to determne the mnmum cost wavelength assgnment we stll need to assgn costs to graph edges whch correspond to dle wavelengths on network access lnks. Derent cost assgnments result n derent algorthms. Speccally, we consder the followng two algorthms: Algorthm A: The cost of edges correspondng to dle wavelengths on access lnks s. Such an algorthm mnmzes the number of wavelength changes per connecton. Algorthm B: The cost of edges correspondng to dle wavelengths on access lnks of ntermedate statons s nversely proportonal to the resdual capacty of the access lnks (the cost of edges correspondng to dle wavelengths on the source's destnaton's access lnks s stll ). Thus, such a scheme tends to avod electronc translaton on hghly utlzed statons. Let b (k) b (k) o be the number of busy wavelengths on the ncomng outgong access lnks at the k-th ntermedate staton. The cost of transfer from wavelength to wavelength j ( 6= j) at ths staton s then c (k) (; j) = ( K?b (k) + K?b (k) o b (k) ; b (k) o < K otherwse (2) where K s a parameter whch satses 0 < K W. Thus, electronc wavelength translaton s performed only f the number of busy wavelengths on the access lnks s less than K. Note that the prevously descrbed method for ndng wavelength assgnments can also be appled to the cases wth no wavelength translaton wth optcal wavelength translaton. For
example, c (k) (; j) = ; 6= j corresponds to the case where no wavelength translaton s permtted, the algorthm produces the "rst-t" wavelength assgnment. On the other h, c (k) (; j) = 0; 8; j corresponds to the case where optcal wavelength translaton s performed. In ths paper, we consder algorthms for wavelength assgnment over a predetermned routng path. Note, however, that the same algorthms could be used even f the routng s dynamc. For example, f an algorthm shows that a connecton establshment cannot make further progress on a gven lnk, an attempt to proceed on an alternate lnk can be made. The wavelength assgnment procedure s relatvely smple ts computatonal complexty grows as O(HW 2 ), where H s the number of hops W s the number of wavelengths. III. PERFORMANCE STUDY In our performance study, we consder a class of optcal networks based on mesh topologes n whch the number of hops per connectons can be large. It has been shown n [7] that n such networks the wavelength translaton capablty can sgncantly mprove network performance. As a representatve of ths class, we analyze a bdrectonal n n mesh network where n s an odd number. We choose ths topology because t s symmetrc thus relatvely smple to study. In ths topology, nodes are organzed nto a two-dmensonal grd where the nodes of the rst the last row column of the grd are connected, thus formng a torus, as shown n Fgure 4. Each node has four neghbors to whch t s Otherwse choose a lnk on the y axs. Repeat the procedure untl both D x D y become zero (.e., untl the connecton reaches the destnaton). In ths performance study, we also use the followng assumptons: Each crcut connecton uses an entre wavelength channel. Each lnk has the same number of wavelengths. Pont-to-pont trac. Trac dstrbuton s unform. Due to the symmetry of the topology the routng algorthm, the load on each lnk s the same. Posson arrvals exponental servce tmes. Connecton arrvals on each lnk have Posson dstrbuton. The average duraton of a connecton s exponentally dstrbuted. No queueng of connecton requests. blocked, t s mmedately dscarded. A. Results If a connecton s We present here the results obtaned by smulatons. Fgure 5 shows blockng probablty versus network load for a bdrectonal mesh network, where each optcal ber carres 0 wavelengths. The sold curves correspond to the case where wavelength Blockng probablty 0. 0.0 0.00 wthout w. trans. wth el. w. t.-alg B, K=5 wth el. w. t.-alg. A wth el. w. t.- Alg B, K=0 wth opt. w. t. 0.000 00 200 300 400 500 600 700 Fgure 5: Blockng probablty versus network load for a bdrectonal mesh network. The number of wavelengths s 0. Fgure 4: A mesh-torus network wth bdrectonal lnks connected by bdrectonal lnks. A network access staton a wavelength selectve swtch are assocated wth each node. Snce we are consderng crcut swtched communcatons, our analyss wll be focused on the typcal performance parameters of a crcut swtched system, namely, blockng probablty network load. In the bdrectonal mesh network, we use the followng determnstc routng algorthm for choosng lnks of the path: Let D x D y be the shortest dstance n the number of hops from the destnaton along the x y axs, respectvely. If D x D y choose a lnk on the x axs to get closer to the destnaton. translaton s performed electroncally, usng Algorthms A B, descrbed n the prevous secton. For Algorthm B, results for two values of parameter K (K = 5 K = 0) are shown. The dashed the dotted curves correspond respectvely to the cases where there s no wavelength translaton, where wavelength translaton s performed optcally. Smulaton studes show that Algorthm B performs the best when K = 0 (.e. K = W ), ts performance are only slghtly better than those of Algorthm A. Snce Algorthm A s smpler, we perform further smulaton studes usng only ths algorthm. Fgure 6 shows blockng probablty versus network load for a bdrectonal mesh network, Fgure 7 for a 0 0 network. The number of wavelengths n both cases s 5. We notce that the derence n performance between electronc optcal wavelength translatons dmnshes wth an ncrease n network
sze. On the other h, the derence between the electronc translaton scheme the scheme wth no wavelength translaton wdens wth an ncrease n network sze. Blockng probablty 0. 0.0 0.00 wthout w. trans. wth el. w. t.-alg. A wth opt. w. t. Number of wavelength changes per conn. 0. 0.0 0.00 0.000 wth el. w. trans.-alg. A 50 00 50 200 250 0.000 50 00 50 200 250 Fgure 8: The average number of wavelength changes versus network load for a bdrectonal mesh network. The number of wavelengths s 5. Fgure 6: Blockng probablty versus network load for a bdrectonal mesh network. The number of wavelengths s 5. 0 If we compare Fgures 5 6 we see that the ncrease n the number of wavelengths from 5 to 0 wdens the derence n performance between optcal, electronc non- translaton schemes. 0. Number of wavelength changes per conn. wth el. w. trans.-alg. A Blockng probablty 0.0 0.00 wthout w. trans. wth el. w. t.-alg. A wth opt. w. t. 0. 0 200 400 600 800 000 200 400 Fgure 9: The average number of wavelength changes versus network load for a 00 bdrectonal mesh network. The number of wavelengths s 5. 0.000 0 200 400 600 800 000 200 400 Fgure 7: Blockng probablty versus network load for a 0 0 bdrectonal mesh network. The number of wavelengths s 5. Fgure 8 shows the average number of wavelength changes per connecton, C, versus network load for a bdrectonal mesh network, Fgure 9 for a 0 0 network. We see that the average number of wavelength translatons per connecton grows wth the ncrease n the oered network load. However, even for very hgh loads, the number of translatons s relatvely small compared to the average number of hops. For example, n a network where H = 5:5, C s less than one, n a 0 0 network, where H = 50:5, C s less than 5. Fgures 0 show blockng probablty versus the sze of a bdrectonal mesh network for a xed network oered load when the number of wavelengths s 5 0, respectvely. Fgure shows blockng probablty versus the network sze n a bdrec- Blockng probablty 0. 0.0 0.00 0.000 e-05 wthout w. trans. wth el. w. t.-alg. A wth opt. w. trans. 0 00 Square root of the number of statons Fgure 0: Blockng probablty versus network sze n a bdrectonal mesh network. The number of wavelengths s 5, the network oered load s 00 Erlangs.
tonal mesh network when the number of wavelengths s 0. When Blockng probablty 0. 0.0 0.00 0.000 e-05 0 Square root of the number of statons wthout w. trans. wth el. w. t.-alg. A wth opt. w. trans. Fgure : Blockng probablty versus network sze n a bdrectonal mesh network. The number of wavelengths s 0, the network oered load s 500 Erlangs. [3] B. Mukherjee et al. Some prncples for desgnng a wde-area optcal network. In Proceedngs of IEEE INFOCOM '94, volume, pages 0{9, Toronto, Canada, June 994. [4] A. S. Acampora. A multchannel multhop local lghtwave network. In Proceedngs of GLOBECOM '87, pages 37.5.{37.5.9, Tokyo, Japan, November 987. [5] Kuo-Chun Lee Vctor O. K. L. A wavelengthconvertble optcal network. Journal of Lghtwave Technology, (5/6):962{970, May/June 993. [6] Rajv Ramaswam Kumar N. Svarajan. Optmal routng wavelength assgnment n all-optcal networks. In Proceedngs of IEEE INFOCOM '94, volume 2, pages 970{979, Toronto, Canada, June 994. [7] Mlan Kovacevc Anthony Acampora. On wavelength translaton n all-optcal networks. In Proceedngs of IEEE IN- FOCOM '95, volume 2, pages 43{422, Boston, Massachusetts, Aprl 995. the network sze s small, the electronc wavelength translaton s not very eectve. In fact, we see from the gures that n a 3 3 5 5 networks, the electronc wavelength translaton scheme performs slghtly worse than f no wavelength translaton s takng place. Ths can be explaned by hgh loads on staton access lnks, whch are further ncreased by performng electronc translaton. As the network sze ncreases, electronc wavelength translaton becomes more eectve approaches the performance of optcal wavelength translaton. In any case, the performance of electronc optcal translaton do not der sgncantly. As the number of wavelengths ncreases, the derence n performance between the two translaton schemes wdens, but n all cases, t dmnshes wth an ncrease n the network sze. The prevous results demonstrate that the performance of the electronc wavelength translaton scheme are only slghtly worse than those when wavelength translaton s performed optcally. Ths suggests that electronc translaton s a good alternatve to the all-optcal wavelength translaton. IV. CONCLUSION From the prevous results we see that electronc wavelength translaton can sgncantly mprove the performance of a large mesh network. The derence n performance between optcal electronc translaton s margnal t dmnshes wth an ncrease n network sze. Snce electronc wavelength translaton does not requre addtonal optcal components, t represents a much more economcal, but stll very eectve alternatve to optcal wavelength translaton. References [] I. Chlamtac, A. Ganz, G. Karm. Purely optcal networks for terabt communcaton. In Proceedngs of IEEE INFOCOM '89, volume 3, pages 887{896, Ottawa, Canada, Aprl 989. [2] C. A. Brackett, A.S. Acampora, et al. A scalable multwavelength multhop optcal network: A proposal for research on all-optcal networks. Journal of Lghtwave Technology, (5/6):736{753, May/Jun 993.