MAINTENANCE-IMMUNE DESIGN OF SPAN-RESTORABLE MESH NETWORKS

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1 MAINTENANCE-IMMUNE DESIGN OF SPAN-RESTORABLE MESH NETWORKS John Doucette, Wayne D. Grover TRLabs, # th Avenue, Edmonton, Alberta, Canada T5K 2P7 and Department of Electrcal & Computer Engneerng, Unversty of Alberta, Edmonton, Alberta Contact Phone: (780) Emal: {doucette, Abstract In contemplatng mesh-based networkng, some operators have expressed concern about the possble effects of span mantenance actons on network restorablty, and hence avalablty. We consder ths problem for span-restorable networks and provde two man advances. One s a b-crtera optmzaton method that allows a controlled trade-off between the cost of spare capacty and the reducton of restorablty rsk, through enhancement of the ablty to roll to protecton on the same span wthout exportng any workng flow onto other spare channels of the network as a whole. The second approach drectly desgns the spare capacty of a span-restorable network so that t s 00% mmune to rsk of restorablty loss due to mantenance actons. Ths approach s mathematcally smlar to the problem of desgnng for 00% restorablty for dual-falure scenaros but requres sgnfcantly less addtonal capacty. The mantenance mmune desgn concept can easly be adapted to provde mantenance mmunty for prorty servce paths only. Other desrable sde-effects of the spare capacty addtons for mantenance mmunty are further enhancement of the actual dual-falure restorablty levels and further expanson of the protected workng capacty envelope provded for dynamc servce path provsonng.. INTRODUCTION Most often n the desgn of survvable networks, the goal s to wthstand any sngle physcal falure at a tme. Some recent work has begun to look at the problem of desgnng for dual-falure restorablty, although the capacty costs of complete dual-falure restorablty are very hgh []. A more practcal obectve may be to consder that only hgh-prorty servce paths mght warrant a desgn guarantee of dual-falure restorablty as n [2]. Whle t mght seem rather hypothetcal to worry about the occurrence of dual (ndependent) physcal falures, a sngle physcal falure coupled wth a span mantenance operaton elsewhere may create a stuaton that s n many regards lke a dual falure [3]. One maor vendor has wrtten, servce outages can be caused by unplanned servce-affectng falures or scheduled mantenance and upgrade events and consders the ssue n ther equpment desgns [4]. In a mesh-restorable network, a span mantenance state can be somewhat lke (or exactly equvalent) to a falure f the mantenance procedure nvolves rollng the workng capacty on to spare capacty of the same span, or out nto the network. Gven the extent and rate of growth of some networks, the correspondng frequency of mantenance actons for upgrades or repars may be much hgher than the rate of actual falures. Several ndustry colleagues have therefore suggested to us that mantenance states coupled wth sngle falures may be even more mportant and practcal to consder than desgnng aganst all combnatons of dual-falure scenaros themselves. In ths regard, recent work n [3] provded an analyss of the theoretcal rsk of sngle-falure restorablty loss n span-restorable (SR) mesh networks under all combnatons of mantenance and sngle-falure states. Our present am s to go beyond analyss n ths area, and look nto delberate changes n the synthess of such networks so as to ether mtgate, or even elmnate, mantenance-related rsk to the restorablty of such networks. The current focus s lmted to span-restorable (or the correspondng lnk-protected) mesh networks where restoraton occurs (or protecton paths are predefned) between the end nodes of a faled span drectly. The general ssue of a theoretcal loss of protecton levels durng mantenance states s not specfc to span-restorable networks, however. In a BLSR rng-based network, for example, the rsk s contaned to other spans of the same rng only, but the

2 magntude of the rsk s of 00% protecton loss. In shared backup path protected (SBPP) networks, the ssue has s ust as real but to our knowledge t has ust not been studed yet. One reason for the present nterest n span-restorable networks s the fndng n [3] that even under mnmal capacty optmal desgn, the theoretcal rsk of restorablty loss never reached 00% on any span, and was most often well below 00%. Ths suggests a certan natural ablty of these networks to support a guarantee of mmunty aganst mantenance-related effects to prorty customers. Followng ths observaton t s natural to ask f we could not go even farther to enhance and control these mmunty characterstcs by desgn. An addtonal reason for nterest n span restoraton (or protecton) s the concept of a protected workng capacty envelope, whch span-restorable networks naturally provde for servce provsonng. Span-restorable networks protect the bearer capacty of the network drectly wth protocols embedded wthn the logcal transport layer. In an optcal network wth OXC-based restoraton or protecton at the lghtwave channel, waveband or whole-fber level, ths means that re-routng for survvablty s completely transparent to payload types and there are no explct provsonng operatons requred n the servce layer to provde for survvablty. The servce layer merely routes over a shortest path, desgnates the protecton prorty or class, and receves a confrmaton that the path s protected when routed wthn the current envelope of protected workng span capactes. A vast number of combned routng states are all protected wthn ths envelope as ndvdual demands arrve and depart. In contrast to SBPP, where explct arrangements for protecton are referred nto the servce provsonng problem for every path, span restoraton thus offers an alternatve operatonal paradgm that may appeal to many operators: that of provsonng over protected capacty versus explctly provsonng protecton. In the cases below where spare capacty s added to the baselne desgn to acheve mantenance mmunty, the range of nherently protected composte routng states supported by the network s only further expanded as a sde effect. The falure resstance and the state-space of supported pont-to-pont demand combnatons of the workng capacty envelope are both enhanced... Functonal Models for Span Mantenance Actons Let us now explan the dfferent functonal models for how varous procedures for dvertng workng capacty durng mantenance affect alteratons n the network spare capacty dstrbuton, and hence may also affect ts theoretcal restorablty should a real falure occur whle n that state. We understand that t s normal practce n rng-based networks (and transmsson systems wth APS) to speak of roll-toprotecton as a way of movng workng capacty over to spare capacty on the same span to facltate repars or upgrades on workng channels or fbers. A smlar logcal concept apples n a mesh network but the roll-to-protecton model becomes more general. Fgure llustrates four dfferent basc functonal models for the restorablty-related effect of span mantenance, and termnology for referrng to them. fully contaned (w( s ): fully exported: any excess spare remans all spare wthdrawn workng rolls to protecton workng externally rerouted partally contaned (w( > s ): all spare used up some workng rolls to protecton and excess externally rerouted Fgure Basc models for how span mantenance actons can affect network restorablty. In the fully contaned model all workng capacty, w, s dverted (or rolled ) over to spare capacty, s, on the mantenance span tself, wth no need for external dverson reroutng. Ths s only possble f s 2

3 w. The effectve amount of spare capacty remanng avalable to the network for protecton uses s s,eff = s w. In the partally contaned model as much workng capacty as possble frst uses the same-span protecton channels. Then, any further workng capacty as needed (.e., w,eff = w s ) s dverted to flow out over the network spares n general. In the fully exported model all workng capacty s referred out to the network for detourng and all spare capacty of the span s wthdrawn from network use. Ths would occur when the span mantenance acton requres complete turndown of all the span capacty. From the standpont of network restorablty effects, ths s the worst case as t s functonally ndstngushable from a complete cut on the span. Desgnng to support ths knd of mantenance acton wthout loss of restorablty s therefore mathematcally dentcal to desgnng for 00% restorablty to all dual-falure consderatons. We need not consder ths model further as methods for complete dual-falure restorablty are already provded n [] and [2]. It wll, however, stll serve as a benchmark of comparatve nterest for our results. In general, therefore, dependng on the relatve s and w capactes on the span, we can get nstances of fully or partally contaned mantenance states. If the amount of spare capacty, s, on a span undergong mantenance exceeds (or equals) ts workng capacty, w, then the net effect s a wthdrawal of w unts of spare capacty on span, leavng s,eff = s w remanng spare capacty on span for use n restoraton of falures on another span, actng as the full contaned model. If the amount of spare capacty s not suffcent to contan the rollover wthn the span (.e., w > s ), then the w,eff = w s remanng paths are dverted n a mesh-lke way over the spare capacty dstrbuted throughout the network, actng as the partally contaned model. The w,eff dverted through the network are handled ust as f span restoraton was beng performed on these lghtpaths. All three models for the effects of mantenance consume spare capacty and so could result n a network state where there may not be enough spare capacty remanng to acheve full restoraton of the faled channels on another span should t fal whle n the mantenance state..2. Concept of Mantenance-Related Rsk Felds The concept of rsk felds, or the theoretcal exposure to restorablty loss elsewhere n the network as a result of a mantenance acton, was ntroduced n [3]. A rsk feld represents the extent to whch a specfc locaton and type of span mantenance acton wll mpar the achevable restoraton levels of other spans should they fal whle n that mantenance state. For a gven mantenance acton, every other span has a rsk feld value equvalent to ts loss of restorablty (.e., the percentage of wavelengths crossng t that s no longer restorable f that span fals). Work n [3] showed that under the partally contaned model, restorablty loss due to mantenance actons on some spans could extend through half the network s spans, wth some spans sufferng 50% or more theoretcal loss of restorablty. However, unlke n rngs, no span was ever seen to suffer the 00% restorablty rsk that arses on same-rng spans due to span mantenance. A typcal rsk feld s llustrated conceptually n Fgure Fgure 2 Illustratng the concept of a rsk feld for restorablty loss for a span (M) under mantenance. The mantenance span s marked M and the numbers on other spans are the percentage loss of restorablty should that span fal whle span M s under mantenance. The total magntude of the rsk feld due to a mantenance acton on a certan span s then defned as the sum of the number of all unt-hop 3 28 M

4 workng channels that lose ther restorablty. For span M n Fgure 2, the total rsk feld magntude s 204, or the sum of the ndvdual rsk feld values for each span experencng loss of restorablty. Averaged over all spans as mantenance spans, we obtan the average rsk feld magntude for span mantenance n that network. Loss of restorablty due to mantenance actons can arse as a result of two man causes: spare capacty contenton and replacement path falure. Spare capacty contenton refers to a stuaton where upon falure, the restoraton mechansm s unable to fnd suffcent restoraton routes for all of the faled workng paths because mantenance replacement paths have made use of requred spare capacty. The outcome n such cases can depend on the adaptablty of the restoraton mechansm. Replacement path falure refers to a stuaton where the physcal falure strkes a span where spare capacty s currently beng used to support one or more of the mantenance dverson paths..3. Outlne and Obectves Obvously any rsk of restorablty loss s undesrable f t can be avoded, so n Secton 2 we test some deas for frst reducng the extent and magntude of mantenance-related rsk felds. Ths yelds some smple changes to the basc capacty desgn models that can mprove the nherent ablty to cope wth mantenance actons, wth lttle added cost. In Secton 3 we then ask more generally: How could we optmally nvest n addtonal capacty to acheve complete mmunty to mantenance states? How does ths compare to the capacty needed for full dual-falure restorablty? We present our expermental methods n Secton 4, and provde results n Secton 5. We close wth a summary dscusson n Secton MAINTENANCE AWARE BI-CRITERIA DESIGN METHOD A smple observaton when consderng partally contaned roll-to-protecton s that rsk felds wll be mnmzed by maxmzng the extent to whch dverted workng paths are contaned on spare capacty of the same span. By ts nature, partally contaned roll-to-protecton wll only consume network spare capacty f ts own spare capacty s exceeded by ts workng capacty. Should the span s workng capacty exceed ts spare, then addtonal spare capacty dstrbuted throughout the network wll also be utlzed to affect the mantenance dverson. So we expect that the closer we get to w s for each span, the lower the theoretcal rsk feld wll be. The desgn model for Mantenance Aware Spare Capacty Assgnment (MA-SCA) takes the form of a b-crtera nteger programmng (IP) model. The dea s to smultaneously mnmze the cost of spare capacty plus a pseudo-cost or penalty term based on the number of workng channels that cannot be dverted wthn ther own spans. Whle ths does not elmnate the loss of restorablty due to mantenance actons, t can have two effects on the soluton, dependng on the weght (α) placed on the penalty term. At relatvely lght α the effect wll be solely to bas the soluton towards selectng amongst costequvalent solutons for an actual dstrbuton of spare capactes that has a better overall matchng n terms of w s. At hgher α values the effect wll be to nvest n addtonal spare capacty to further enhance the number of fully contaned spans (.e., those where s w ). Ths s smlar to the recent use of a b-crtera desgn technque to secondarly optmze spare capacty to shorten the mpled lengths of restoraton routes [5]. The MA-SCA desgn model s as follows: Parameters: C = cost of placng a spare (or workng) channel on span. S = set of network spans. α = alpha parameter tradng off weght of two terms n the obectve functon. w = number of workng channels on span. P = set of elgble resoraton routes that can be used to dvert or restore workng channels on span. p, δ = f restoraton (or dverson) route p for falure of span crosses span, zero otherwse. Varables: s = number of spare channels requred on span, s 0. ws = max{(w s ), 0}, ws 0. p p f = number of restoraton paths assgned to the pth elgble route for falure of span, f 0. 4

5 MA-SCA: mn C s α ws () Subect to: Restoraton flow: S + S p f = w S (2) p P p, p Spare capacty: s δ f S, S, (3) p P ws metrc calculaton: ws w s ; ws 0 S (4) The obectve functon () mnmzes the total cost of spare capacty plus a penalty term ncurred when dverson of workng capacty for a mantenance acton cannot be fully contaned wthn the span tself. By ncreasng α, a planner can allow a controlled ncrease n spare capacty to mnmze the amount of externally dverted workng flow n the partally contaned roll-to-protecton type of mantenance. Constrant set (2) ensures suffcent restoraton flow to fully restore the workng wavelengths on faled span, whle constrant set (3) places enough spare capacty on each span to accommodate the maxmum restoraton flow smultaneously mposed on t for any span falure. Constrant set (4) sets ws values to be the maxmum of w s and 0 for any span, so that the obectve functon s secondary term can account for ts related cost. Results for ths approach follow n Secton MAINTENANCE IMMUNE RESTORABILITY DESIGN Let us now go a step further than smply enhancng the desgn to contan dverted mantenance flows and consder desgn of span-restorable networks that reman fully restorable for any sngle span falure n the presence of any mantenance acton. We defne a span as beng mmune to a mantenance acton on span h f span mantans ts full restorablty when workng channels on a span h are rolled to protecton under the generalzed partally contaned model. A network as a whole s sad to be mantenance mmune f all spans are mmune to all mantenance actons. Usng ths concept we develop a desgn model that wll assure complete network-wde mantenance mmunty. Prevously defned parameters and varables are re-used as needed. In addton we have: New varables: l h = number of workng channels that a mantenance dverson places on spare capacty on the mantenance span h tself, l h 0. = number of workng channels from mantenance span h that are assgned to elgble dverson m path p n the presence of falure on span, m 0. f = number of restoraton paths assgned to the pth elgble restoraton route for falure of span whle span h s undergong mantenance, f 0. MI-SCA: mn C s (5) Subect to: Mant. rest. flow: Falure rest. flow: Spare capacty: S h S, S, h (6) lh + m = w h p Ph : not n p f = w h S, S, (7) p P : s m δ f + δ p, p P p Ph h S, S, (8) S, h 5

6 p, Mant. capacty: s δ f + l h S, S, h (9) h h p P The obectve functon (5) mnmzes the total cost of spare capacty requred to make the network fully restorable to any combnaton of mantenance acton and span falure. Constrant set (6) ensures enough local roll-to-protecton flow and addtonal dverted replacement paths to fully reroute all workng channels on each mantenance span, whle constrant set (7) ensures enough restoraton flow to reroute workng wavelengths on each faled span. Constrant set (8) places suffcent spare capacty on each nonfaled and non-mantenance span to accommodate the maxmum restoraton flow smultaneously mposed on t for any combnaton of span falure and mantenance acton. Constrant set (9) places enough spare capacty on the mantenance span to accommodate flows routed over t for restoraton of any span falure plus the locally rolled capacty to protect ts own mantenance. Note that Constrant sets (8) and (9) both apply smultaneously, so that whchever consderaton s most bndng on the spare capacty requrement of a span, mantenance dverson or restoraton of other falures, wll set the fnal value of spare capacty. Keep n mnd that s and s h are not separate varables, t s ust the basc spare capacty varable beng ndexed n one nstance from a falure scenaro standpont, n the other from a mantenance scenaro standpont. 3.. Desgnng to Assert the Fully Contaned Roll-to-Protecton Model The MI-SCA formulaton as defned refers n general to the partally contaned roll-to-protecton model. To represent the fully contaned model where dverson routes cannot be placed externally from the mantenance span, we transform constrant set (6) nto (0) and transform constrant set (8) nto (). h Mant. rest. flow: l = w h S, S, h (0) Spare capacty: h s h p P δ f p, h S, S, () S, h Constrant set (0) now forces the protecton mechansm to roll all of the workng channels on the mantenance span onto spare capacty fully contaned on the span tself. And snce there are no workng channels from the mantenance span rerouted throughout the network, the last term n constrant set (8) can be dropped to create constrant set () Accomodatng the Fully Exported Roll-to-Protecton Model Desgnng a network for mmunty to fully exported mantenance dverson s equvalent to the dualfalure desgn problem. The MI-SCA model can be approprately modfed by transformng constrant set (6) nto (2), elmnatng (9), and addng new constrant sets (3) and (4) below. Mant. rest. flow: m = wh h S, S, h (2) p Ph Restrcted flow : f = 0 h S, S, h (3) p P : h n p Restrcted flow 2: m = 0 h S, S, h (4) p Ph : n p Constrant set (2) s essentally a duplcate of constrant set (7) except that t refers to the dverson of workng channels on the mantenance span whle span has subsequently faled, effectvely settng values needed n constrant set (8). Constrant sets (3) and (4) generate enough spare capacty m elsewhere n the network so that restoraton remans possble wthout assumng any spare capacty use of the mantenance span. Note that f representng the true dual-falure desgn model (DF-SCA), we would, not need separate m and f hp varables, and equatons (2) and (4) could therefore both be elmnated, snce we would now be makng no dstncton between spans h and (they would both be faled spans). 6

7 Later results n Secton 5.2 (Fgure 6) that refer to the dual-falure desgn model are generated usng ths altered model Jont Workng and Spare Mantenance Immune Capacty Desgn MI-SCA can be extended to ontly optmze the routng of workng paths and the placement of workng and spare capacty (MI-JCA). Ths wll n prncple reduce the amount of extra spare capacty requred to acheve full mantenance mmunty. New parameters and varables become nvolved, prmarly dealng wth decsons about workng path routng and capactes. Equaton (5) becomes equaton (5), and we add equatons (6) and (7) to the formulaton. New nput parameters: D = set of orgn-destnaton (O-D) demand par relatons. Q r = set of elgble workng routes for demand par r. d r = number of wavelengths on demand par r. rq, ζ = f workng route q for demand relaton r crosses span, zero otherwse. New varables: g r,q = workng flow on workng route q for demand par r, g r,q 0. w = number of workng wavelengths on span (changes from a parameter to a varable), w 0. ( ) MI-JCA: mn C s + w (5) S rq, r Workng flow: g = d D (6) r q Q rq, rq, Spare capacty: w = ζ g S, S, (7) r D r q Q New constrants (6) ensure that all channels for each O-D par are routed and new constrant set (7) places enough workng capacty on each span to accommodate all workng flows routed over t Desgnng for an Acceptable Rsk Resdual A network planner mght alternately be nterested n specfyng an acceptable rsk of partal restorablty loss, less than 00% mmunty. The mantenance mmune desgn model can be modfed to allow for such a user-controlled trade off between mantenance-related rsk to restorablty and ncreased desgn cost. We add a new parameter, replace constrant set (7) wth (8), and brng n constrant sets (2) and (3) from the MA-SCA model. New nput parameter: λ = level of restorablty requred for falure of span whle another span s n a mantenance state, 0 λ. Falure rest. flow: f = w λ h S, S, h p Ph : New constrants (8) provde enough restoraton flow for each faled span to restore a specfed percentage of that span s channels n the presence of any mantenance acton. We also need to take constrant sets (2) and (3) from the MA-SCA model and re-use them n ths model n order that we stll provde full restorablty to any sngle span falure when not concdent wth a mantenance acton. These two constrants were not requred n the basc MI-SCA model snce t s mplct n constrant set (7) that f each span s restorable n the presence of any mantenance acton, t must also be restorable n solaton. However, usng constrant set (8) wthout these two added constrants explctly provdng full snglefalure restorablty, we may only be allocatng enough capacty for the specfed level of restorablty even f the falure occurs n solaton. (8) 7

8 4. TEST CASES AND EXPERIMENTAL METHODS Several test networks were used to explore the desgn deas above. The MA-SCA tests were based on three test networks, one wth 20 nodes and 28 spans (20n28s), one wth 20 nodes and 40 spans (20n40s), and one wth 40 nodes and 70 spans (40n70s). 20n40s and 40n70s are shown n Fgure 3. 20n28s s the same test network used n [5]. MI-SCA test case networks are dvded nto two groups. The frst group s a famly of networks based on 40n70s where each subsequent member of the famly s produced by randomly removng one span from the prevous member, whle retanng b-connectvty. Ths s the same basc method used to study effects of varyng nodal degree n [6]. The second group of MI-SCA test networks s a selecton of fve networks rangng from 5 nodes up to 45 nodes (ncludng 20n40s and 40n70s already descrbed), all shown n Fgure 3. For each test network, the length of each span s the Eucldean dstance on the plane between the end nodes the span connects. Capacty costs for all test cases are taken as proportonal to the length of the span and the number of spare channels requred on the span. 5n30s 20n40s 25n50s 40n70s 45n90s Fgure 3 Test case networks. For all the test cases each O-D node par exchanges a randomly generated number of wavelength demands followng a unform random dstrbuton between and 0. All workng and spare capacty allocatons were nteger, correspondng to capacty desgn and restoraton mechansms operatng at the wavelength channel level. All lghtpath demands were frst routed along ther shortest paths (by total span-dstance, not span-count). The desgn models were mplemented n AMPL and solved wth the Parallel CPLEX 7. MIP Solver on a 4-processor Ultrasparc Sun Server at 450 MHz wth 4 GB of RAM runnng the Sun Solars 8 Operatng Envronment. Results were based on full CPLEX termnatons usng a MIPGAP of 0-4, meanng all solutons are guaranteed to be wthn 0.0% of optmal. Problems solved n seconds or a few mnutes wth the excepton of the MI-JCA models, whch took as much as several hours for the largest test cases. The run-tmes are not a concern at present because the purpose s research understandngs of the networkng concepts and phenomena. Separate work can follow to operatonalze these processes wth faster methods or heurstcs, f warranted. A pre-processng program generates the sets of elgble routes for consderaton as restoraton routes under each falure scenaro and workng routes for each O-D node par. These are generated wth the method descrbed n [6]. The same routessets represent the elgble routes for mantenance dverson. We use conventonal spare capacty allocaton (SCA), ont workng and spare capacty allocaton (JCA), and dual-falure spare capacty allocaton (DF-SCA) models as benchmarks to whch we compare our new formulatons. The SCA model s dentcal to the MA-SCA model except that equaton (5) replaces equaton () and we drop equaton (4). The JCA model adds equatons (6) and (7) to the SCA model and replaces the obectve functon wth equaton (5). The DF-SCA model s as descrbed n Secton

9 5. RESULTS AND DISCUSSION 5.. Mantenance Aware B-Crtera Desgn Results Fgure 4 llustrates how α can be vared to medate the tradeoff between addtonal spare capacty and the relatve level of exposure to restorablty loss from mantenance states. Each data pont represents a network desgned usng the MA-SCA model wth a user-defned α value. When α s zero, the desgn s optmzed for capacty cost only and so acts as the benchmark desgn. However, when we ncrease α, we observe a decrease n workng channels that are not contaned wthn ther own spans for mantenance, and a correspondng decrease n the total rsk feld. As dscussed earler, for any mantenance acton, each other span n a network may experence a loss of restorablty, and we use the methods n [3] to measure the total rsk of restorablty losses over a rsk feld such as llustrated n Fgure 2. By summng the restorablty rsk of each span over all mantenance actons, we arrve at the network s total rsk feld, whch acts as a measure of the network s ablty to deal wth mantenance actons. The x-axs of Fgure 4 normalzes the total rsk feld relatve to that at α = 0. Exactly what α value corresponds to each data pont depends on the test network (more specfcally ts unt channel costs relatve to the amount of capacty carred), but for our test networks, the α values ranged from 0 (at the far rght of each curve) through 500 (at the far left). Fgure 4(a) shows that for two of the networks represented, the average rsk feld can be reduced by about 90% at the cost of about 25% ncrease n total spare capacty. The range of tradeoff for the other test case (20n28s) was much more lmted. We hypotheszed that the extent of the tradeoff space, n terms of feasble rsk reducton depended on the network connectvty (20n28s s much more sparse than the other two test cases). To test ths, four addtonal networks (not shown) were tested, wth results shown n Fgure 4(b). The sgnfcance of the four addtonal test cases s that they are sub-networks of varous nodal degree systematcally derved from the hghly connected 45n90s network shown n Fgure 3 (usng the same method to generate the 40n70s-based famly of test cases already descrbed). Fgure 4(b) clearly shows how the scope for rsk reducton through MA desgn enhancement s greater for hghdegree networks..3 (a).6 (b).25.5 Normalzed Spare Capacty Cost n28s 20n40s 40n70s Increasng α Normalzed Spare Capacty Cost Increasng α 45n90s-Full 45n90s-80s 45n90s-70s 45n90s-60s Relatve Average Rsk Feld Relatve Average Rsk Feld Fgure 4 MA-SCA results for (a) three of the ntroduced test networks and (b) four corroboratng test cases. More generally, the capablty to trade rsk feld off wth capacty cost ncreases can be used to generate ust enough reducton of rsk felds to support a certan number of hgh-prorty paths at full mantenance mmunty. If say, under all scenaros, the rsk ntensty on any span s never more than 60% t means that up to 40% of paths over all spans could be n ths prorty class Mantenance Immune Desgn Results Next n Fgure 5, we show the relatve total capacty costs of the 40n70s-based famly of test case networks desgned usng the SCA, JCA, MI-SCA, and MI-JCA desgn models. Each data pont represents the capacty cost of the member of the famly wth the specfed average nodal degree optmally solved 9

10 usng the respectve desgn model. The relatve costs are normalzed to the MI-SCA desgn at average nodal degree of 2.2, whch has the hghest absolute cost. Fgure 5 shows that as expected, desgnng for full mantenance mmunty requres consderably more capacty than sngle-falure desgn. The MI-SCA capacty curve ranges from 29% above than the SCA curve at an average nodal degree of 3.5, up to 43% greater at average nodal degree of 2.2 for the 40n70s famly tested. These are total capactes; spare capacty dfferences range from 69% to 80%. As expected, the ont desgns were less costly but on a percentage bass they requred slghtly more ncrease above sngle-falure desgns. MI-JCA total capacty costs averaged 39% above JCA, whle MI-SCA averaged 36% more than SCA. The greater percentage ncrease s really attrbutable, however, to the fact that reference JCA desgns were already 4%-7 % lower n capacty than the SCA reference desgns. Normalzed Total Capacty Cost MI-SCA MI-JCA SCA JCA Mantenance Immune desgns Average Nodal Degree Fgure 5 Normalzed spare and total capacty costs for the 40n70s-based famly of test case networks. If we look at Fgure 5 n lght of separate work showng that desgn for complete dual-falure restorablty can requre up to three tmes as much spare capacty [], we see that whle beng somewhat smlar to dual-falure stuatons, desgn for mantenance mmunty requres consderably less extra capacty. Ths s because the mantenance span s spare capacty s not always completely wthdrawn from the network n the generalzed mesh roll-to-protecton model. Fgure 6 gves the complete comparson, showng the spare and total capacty costs of fve test case networks optmally desgned for dual-falure restorablty (DF-SCA), mantenance mmunty (MI-SCA), and sngle-falure only restorablty (SCA). Note here that DF-SCA s equvalent to the fully exported roll-to-protecton model. Capacty costs are normalzed to the sngle-falure desgns for each test network. For these test networks, an average of 62% more spare capacty (or 25% total capacty) was suffcent to render the network fully mantenance mmune. However when desgnng for full dual-falure restorablty, 65% more spare capacty was requred (66% more total capacty). Mantenance mmune desgn s thus a knd of compromse strategy between sngle-falure restorablty wth uncontrolled mantenance rsk and desgnng for full dual-falure restorablty whch s also nherently mantenance mmune. In addton to requrng less spare capacty, mantenance mmune desgn requres only bconnectvty on the network graph, whle dual-falure restorablty strctly requres a network to be trconnected, otherwse servce paths ncdent on a degree-2 node could not possbly be restored should both of the node s spans fal. However, wth the mantenance mmune desgn model, some spare capacty on the mantenance span remans ntact. So even f one span ncdent on a degree-2 node s under mantenance and the other fals, restoraton of the falure and dverson of the mantenance span s workng channels s stll possble f the spare capacty s dmensoned accordngly. 0

11 Normalzed Spare Capacty Cost Dual Falure Mantenance Immune Sngle Falure Only Normalzed Total Capacty Cost Dual Falure Mantenance Immune Sngle Falure Only 0 45n90s 40n70s 25n50s 20n40s 5n30s Test Case 0 45n90s 40n70s 25n50s 20n40s 5n30s Test Case Fgure 6 Normalzed spare and total capacty costs for fve test case networks. Fgure 6 strongly suggests that addng spare capacty for mantenance mmunty should also ncrease restorablty aganst many dual-falure scenaros as a sde effect. We can quantfy ths added protecton aganst true dual-falure stuatons of spans a and b as the dual-falure restorablty of the affected servce paths R 2 (a,b), defned n [8] as: R ( a, b) 2 N N = nr (9) aff ( ab, ) ( ab, ) In Eq. (9), N ( ab, ) s the number of non-restorable servce paths durng the falure of span a n the nr presence of falure on span b, and Naff ( ab, ) s the number of demands affected by dual falure of span a and span b. We also defne R 2 as the network average of R 2 (a,b) values over all span pars. Usng ths framework, Fgure 7 shows the network average dual-falure restorablty (R 2 ) of fve test case networks optmally desgned for dual-falure restorablty (DF-SCA), mantenance mmunty (MI-SCA), and sngle-falure only restorablty (SCA). Dual Falure Restorablty n90s 40n70s 25n50s 20n40s 5n30s Test Case Dual Falure Mantenance Immune Sngle Falure Only Fgure 7 Network average dual-falure restorablty (R 2 ) for fve test case networks. We can see that by placng the extra spare capacty requred only for mantenance mmunty we obtan nearly the same R 2 (rangng from to 0.986) as actually desgnng for full dual-falure restorablty (by defnton, R 2 =.0). In contrast, sngle-falure restorablty desgns exhbt R 2 values as low as (and only one of the test case networks desgned for sngle-falure restorablty had R 2 above 0.90). Snce mantenance actons are qute frequent, and t s much more lkely that a combnaton of mantenance acton and sngle falure wll occur than two smultaneous span falures, these fndngs suggest that mantenance mmunty mght be a more practcal goal to ncrease dual-falure restorablty

12 than explctly desgnng for R 2 =.0. Capacty requrements are consderably less but the network s most of the way to dual-falure restorablty. 6. SUMMARY Ths work has ntroduced several approaches to dealng wth the effects of mantenance actons on the restorablty of a span-restorable network. The frst s a b-crtera mathematcal model through whch one can trade an ncrease n capacty cost n exchange for a decrease n average rsk feld due to mantenance dverson that s not wholly contaned on the mantenance span tself. It was found that n hghly connected graphs ths strategy of smply enhancng the same-span contanment effect could reduce 90% of the rsk. The other man strategy s a desgn model that strctly elmnates all sngle-span mantenance rsk. Test cases showed that for a 25% ncrease n capacty one could ensure full protecton aganst span falures whle n a mantenance state on any other span n the network. In the same test cases, desgnng for complete dual-falure restorablty requred approxmately 66% more total capacty. The mantenance-mmune desgn approach also has the addtonal beneft of sgnfcantly ncreasng the dualfalure restorablty of the network as a whole and of further expandng ts protected workng capacty envelope for operatonal provsonng use. 7. ACKNOWLEDGEMENTS The authors wsh to thank Wllam Glenn of TRLabs and the Unversty of Alberta for provdng software support and assstance. 8. REFERENCES [] M. Clouqueur, W. D. Grover, Computatonal and Desgn Studes on the Unavalablty of Meshrestorable Networks, Proceedngs of the 2 nd Internatonal Workshop on the Desgn of Relable Communcaton Networks (DRCN 2000), Munch, Germany, pp. 8-86, Aprl [2] M. Clouqueur, W. D. Grover, Mesh-restorable networks wth complete dual falure restorablty and wth selectvely enhanced dual falure restorablty propertes, Optcal Networkng and Communcatons Conference (OptComm 2002), Boston, MA, n press, July-August [3] W. D. Grover, M. Clouqueur, T. Bach, Quantfyng and Managng the Influence of Mantenance Actons on the Survvablty of Mesh-Restorable Networks, Proceedngs of the 7 th Annual Natonal Fber Optc Engneers Conference (NFOEC 200), Baltmore, MD, vol. 3, pp , July 200. [4] Csco Systems, Always-On Avalablty for Multservce Carrer Networks: Prerequstes for Hgh- Avalablty Infrastructures, Csco Systems Whte Papers, 999. [5] J. Doucette, W. D. Grover, T. Bach, B-crtera studes of mesh network restoraton path-length versus capacty tradeoffs, Proceedngs of OSA Optcal Fber Communcatons Conference and Exhbt (OFC 200), Anahem, CA, pp. TuG2- TuG2-3, March 200. [6] J. Doucette, W. D. Grover, Comparson of Mesh Protecton and Restoraton Schemes and the Dependency on Graph Connectvty, Proceedngs of the 2 nd Internatonal Workshop on the Desgn of Relable Communcaton Networks (DRCN 2000), Budapest, Hungary, pp. 2-28, October 200. [7] M. Herzberg, S. J. Bye, A. Utano, The Hop-Lmt Approach for Spare-Capacty Assgnment n Survvable Networks, IEEE/ACM Transactons on Networkng, vol. 3, no. 6, pp , December 995. [8] M. Clouqueur, W. D. Grover, Avalablty Analyss of Span-Restorable Mesh Networks, IEEE Journal on Selected Areas n Communcatons (JSAC), vol. 20, no. 4, pp , May