The Effects of Multi-Layer Traffic on the Survivability of IP-over-WDM Networks

Transcription

1 The Effecs of Muli-Layer Traffic on he Survivabiliy of IP-over-WDM Neworks Peera Pacharinanakul and David Tipper Graduae Telecommunicaions and Neworking Program, Universiy of Pisburgh, Pisburgh, PA 15260, Unied Saes {peerap, Absrac The survivabiliy of backbone neworks o failures is an on-going concern. This paper invesigaes survivabiliy sraegies for IP-over-WDM neworks in a muli-layer framework where raffic originaes a each layer. We presen an opimizaionbased formulaion of performing recovery mechanisms a he boom layer for boh layers of raffic in wo cases: Wih capaciy sharing beween backup pahs of he raffic in wo layers and wihou. We hen sudy and compare spare capaciy requiremens under muli-layer raffic raios and he impac of nework conneciviy. Numerical resuls indicae ha, in such a wavelengh-based opical nework, implemening survivabiliy of all raffic a he boom layer can be a viable soluion wih significan advanages. Index Terms survivabiliy, mulilayer nework design, spare capaciy allocaion I. INTRODUCTION Revenue-generaing IP and opical-swiching WDM neworks are moving oward an inegraed high-speed backbone archiecure wih GMPLS as a common conrol plane. The abiliy of he nework o survive link or node failures will be a required feaure in fuure nework infrasrucure. However, mulilayer planning is necessary o guaranee he survivabiliy of raffic in a wo-layer nework. Survivabiliy of he raffic a boh layers is essenial as bandwidh a he lighpah level is becoming more in demand [1]; however, providing survivabiliy o boh IP flows and lighpahs is challenging. In mos cases, hese wo-layer neworks are under he same adminisraive ownership, bu since he layers are formed by differen echnologies, ineroperabiliy beween wo layers of differen echnologies has become increasingly imporan. Layers render a number of problems. Firs, failures a he boom may ear down services a he op layer. This effec is called failure propagaion and is a he forefron of problems in mulilayer survivabiliy. Survivable mapping, a map of a op-layer over a boom-layer opology such ha link failures a he boom do no disconnec he op-layer opology, is a way o avoid such problem. Link mapping is almos always developed in anicipaion of a single link failure [2]; however, ref. [3] has recenly developed a mapping for muliple link failures. A second problem is, for a given mapping funcion, an IP op-layer pah may require more or less bandwidh from P. Pacharinanakul is suppored by a TOT Graduae Fellowship, Thailand. Fig. 1. A sample wo-layer nework he perspecive of he op layer han ha of he boom, depending on which layer deermines capaciy allocaion and rouing assignmen. For example, consider he op-layer pah (1,2) in Fig. 1 when i is mapped o boom-layer links (1,8) and (8,2). From a op-layer perspecive, his IP pah requires 2 capaciy unis a he boom. However, from he boomlayer perspecive, i can be roued on a boom-layer pah (1,2), requiring only 1 capaciy uni. Failure propagaion also imposes difficuly in he nework design phase as o deciding, for each IP op-layer pah, which layer is responsible for failure recovery and under wha condiions. This is because for an IP primary pah, a backup pah can be provided in eiher layer. Recovery mechanisms may also be redundan beween wo layers; however, his does no auomaically imply ha all of he mechanisms are used a boh layers [4]. In addiion, since capaciy of a boom link can simulaneously be shared by many op pahs, allocaing capaciy among heir corresponding backup pahs in wo layers becomes a concern; he services provided by he op-layer nework mus be survivable under failures a he boom. Capaciy allocaion ensures sufficien link capaciy for rerouing pahs in he face of failures. Rouing assignmen guaranees ha he end-o-end requiremens are me, e.g., availabiliy, ec. In pracice, dynamic and efficien mulilayer rouing algorihms [5] may be needed. Similar o much of he work in his area, we joinly consider capaciy allocaion and rouing assignmen problems, in a core nework, as a spare capaciy allocaion (SCA) problem. Bu, in addiion, we examine several sraegies for survivabiliy in wo-layer neworks when raffic originaes a boh layers and grooming of he raffic, in each layer, is available a he edge. These sraegies require raffic flows in boh layers o be survivable under single link failure a he boom. In paricular,

2 he following four survivabiliy sraegies are considered: 1) Sraegy A: Backup pahs are provided a he layer where raffic originaes. Le BP be a se of op-layer backup pahs o proec op-layer raffic, and BPb b be a se of boom-layer backup pahs o proec boom-layer raffic. Sharing spare capaciy beween he wo backup pah ses is no allowed. 2) Sraegy B: Similar o Sraegy A bu capaciy beween he wo backup pah ses BP and BPb b can be shared. 3) Sraegy C: Backup pahs of raffic a boh layers are provided a he boom layer. Le BPb be a se of boom-layer backup pahs o proec op-layer raffic and BPb b as previously defined. Sharing capaciy beween he wo backup pah ses BPb and BP b b is no allowed. 4) Sraegy D: Similar o Sraegy C bu he capaciy beween he wo backup pah ses BPb and BP b b can be shared. For all sraegies, spare capaciy may be shared wihin a backup pah se, e.g., sharing capaciy among backup pahs in BPb b is allowed. Sharing is also allowed in BP as well as in BPb. This paper is organized in he following manner. In he nex secion, we provide background on mulilayer survivabiliy in wo-layer neworks. A mahemaical formulaion of he wo survivabiliy sraegies a he boom, C and D, is hen presened in Secion III. Performance evaluaion of all sraegies and numerical resuls are given in Secion IV. Finally, our conclusions are summarized in Secion V. II. BACKGROUND In he conex of survivabiliy in wo-layer neworks, several sraegies have been proposed bu hey all share he same principle. Wheher recovery can be iniiaed a eiher layer, boh, or only a he boom will be based on he originaing raffic layer. When he raffic originaes a he op, recovery can be performed a eiher layer or boh, bu when he raffic originaes a he boom, i can only be recovered a he boom layer. Survivabiliy a he op provides backup pahs o op-layer raffic a he op layer. Survivabiliy sraegy a his layer can be used o give muliple availabiliy guaranees o raffic wih prioriies. This sraegy can also resolve failures a boh layers, i.e., IP node, opical link, and WDM node failures. However, recovery ime and rerouing saes may be high due o he fac ha each raffic flow needs o be recovered individually. Survivabiliy a he boom provides backup pahs o wolayer raffic a he boom layer. Owning o fas failure deecion and pre-reserved resources in WDM neworks, recovery a his layer is usually faser [6]; however, i may no be able o provide survivabiliy when failures happen a he op layer. In some cases, his sraegy is no aware of he IP op-layer node failures unless here is an appropriae signalling coordinaion like GMPLS. In mos cases, recovery a he opical boom layer has o be performed on an aggregae basis, meaning ha all IP flows ha share he same failed opical link are reroued o he same backup opical link. In he case of lighpah (re-)esablishmens in WDM neworks, he siuaion is a lile differen: The IP flows ha share ha failed link can be reroued o differen lighpahs in opical links, giving more flexibiliy and beer spare capaciy uilizaion. Survivabiliy a boh layers provides backup pahs o oplayer raffic a boh layers. By providing each op flow wih wo backup pahs, one pah a each layer, his sraegy guaranees full recovery upon failures a any layer. In such a case, proecion seleciviy [7] or spare unproeced [8] refer o he sraegy where sharing space capaciy of he wo backup pahs is no allowed. When he capaciy can be shared, i is known as common pool survivabiliy [4], [8]. Alernaively, he backup pah a he op layer can also be provided wih a backup pah a he boom. In such a case, spare capaciy is used wice, resuling in over-allocaion of capaciy. Survivabiliy can also be provided o raffic wih muliple availabiliy guaranees. In many cases, combinaions of he above sraegies are considered. For example, in raffic wih wo prioriy classes, survivabiliy a he boom and a he op can be provided o high-prioriy and low-prioriy raffic, respecively. Iner-level sharing beween he wo classes [9] can also be allowed. Inegraed shared pool [10] considers 3 raffic classes: Gold, Silver, and Bronze. Survivabiliy a he boom is provided o Gold whereas survivabiliy a he op is provided o Silver while here is no survivabiliy guaranee for Bronze classes of raffic. In his sraegy, sharing capaciy among Gold backup pahs, Silver backup pahs, and Bronze primary pahs is allowed. As here is no backup pah for Bronze raffic, some capaciy savings can be achieved by allocaing spare capaciy only o he wo mos imporan raffic classes. Idle proecion capaciy reuse [11] reains he same boom-layer sraegy for all 3 classes of raffic bu chooses o explore possibiliies in capaciy-limied neworks, i.e., wheher some pahs can be preemped by ohers wih higher prioriy upon failures and wheher backup pahs are preplanned or compued upon failures. Alernaively, a noion of shared risk link groups (SRLGs) can also be used o provide muliple guaranees o differen raffic classes [12]. Implemening a survivabiliy sraegy in pracice may depend on wheher a wo-layer nework is under a single adminisraive managemen. Under he overlay model [13], neiher layer nework has a complee view of he oher. In his case, from a global view, some care needs o be aken when allocaing capaciy or minimizing capaciy coss because his can someimes lead o differen soluions from differen perspecives of he op- and boom-layer nework providers; however, his siuaion is beyond he scope of his paper. III. SURVIVABILITY OF TWO-LAYER TRAFFIC AT THE BOTTOM LAYER In his secion, we exend he SCA model in [14] o include survivabiliy sraegies when op-layer raffic is proeced a he boom layer. In his case, spare capaciy due o he op BPb and boom BP b b layer raffic can eiher be unshared or shared. In addiion, we consider a disjoin backup pah from is primary pah. The noaion used is summarized in Table I.

3 Symbol N {,b} L {,b} B {,b} F {,b} M {,b} D {,b} P {,b} Q {,b} B b M b D b P b Q b G b S b G b S b H e TABLE I NOTATION Definiion from a {op, boom}-layer perspecive {Top, Boom}-layer node se {Top, Boom}-layer link se {Top, Boom}-layer incidence marix w/ dimension N {,b} L {,b} {Top, Boom}-layer flow vecor Diagonal marix of bandwidh of {op, boom}-layer flow f {,b} w/ dimension F {,b} F {,b} {Top, Boom}-layer flow-node incidence marix w/ dimension F {,b} N {,b} Primary {op, boom}-layer pah marix w/ dimension F {,b} L {,b} Backup {op, boom}-layer pah marix w/ dimension F {,b} L {,b} from a boom-layer perspecive Top-layer incidence marix w/ dimension N b L b Diagonal marix of bandwidh of op-layer flow f w/ dimension F F Top-layer flow-node incidence marix w/ dimension F N b Primary op-layer pah marix w/ dimension F L b Backup op-layer pah marix w/ dimension F L b Top-layer spare capaciy marix w/ dimension L b L b Backup op-layer link capaciy vecor w/ dimension L b 1 Boom-layer spare capaciy marix w/ dimension L b L b Backup boom-layer link capaciy vecor w/ dimension L b 1 Survivable mapping marix Column vecor of ones Our nework of ineres is defined as follows: Given a boom-layer undireced nework wih node se N b, link se L b, and incidence marix B b [15], a op-layer undireced nework wih similar quaniies in superscrip is consruced as follows: A node n k N, where 1 k N, exiss only if is associaive node n b k Nb a he boom layer exiss. Tha is, N N b. No more han one op-layer node is allowed o associae wih a node a he boom. Moreover, he presence of uncapaciaed links a each layer is independen from one anoher. Le H be a binary survivable mapping marix, where h ij =1if a op-layer link i is mapped ono a boom-layer link j, and 0 oherwise. A survivable mapping marix H can be derived from a necessary condiion of a wo-conneced nework, as presened in [2]. Now we have a opology consrucion including nodes, links, and link mapping. In he nex wo subsecions, we will provide formulaions of he SCA problem due o wo-layer raffic. A. Providing backup pahs o op-layer raffic a he boom A he op layer, primary and backup pahs of flows f, where 1 f F are represened by wo 1 L binary row vecors p f l and q f l, respecively. The l -h elemen in one of he vecors equals one if and only if he corresponding pah uses link l. The pah marices [16] P and Q are formed by a collecion of p f l and q f l, respecively. The primary pahs: P, can be obained from Dijksra s algorihm. Le M = diag({m f } F 1) be a marix of op-layer inegral flow bandwidh. The op-layer raffic flows are represened by amarixd. An elemen d f n of he marix D equals 1 if he flow f originaes from node n and 1 if i erminaes a node n. Flows having idenical end poins, if exis, are reaed as a single flow wih flow bandwidh from hose flow bandwidhs combined. In order o provide backup pahs o op-layer raffic a he boom, we need o map op-layer informaion o he boom. Because he incidence marix is opology dependen, a op-layer incidence marix, when mapped o he boom, is equivalen o ha of he boom. This is shown in (1). In (2), bandwidh of he mapped op-layer flow sill holds he same value, i.e., m f, as ha of he op-layer flow as i depends on flows only. Since a op-layer nework may no have he same number of nodes as he boom, he flow-node incidence marix in (3) is mapped o he boom layer by padding columns of zeros as necessary o D. In (4), he link-mapping informaion in H is used o derive op-layer primary pahs P from he perspecive of he boom layer, as P b.the symbol is a marix muliplicaion operaor, realizing he inclusive OR and AND operaion, e.g., 1+1=1. Using his operaor, he logical relaions among flows and links in an undireced nework can be simplified ino one marix operaion. Since binary flows are considered, we do no include a single-pah rouing consrain in our ILP formulaion as i would be redundan. A mapping funcion f : b can be described for each op-layer marix as: B b = B b (1) M b = M (2) D b =[D 0] (3) P b = P H (4) Using he noaion and definiions given previously, he SCA problem of he op-layer raffic can be formulaed as: Q b B bt = D b (5) P b + Q b 1 (6) G b = Q bt M b P b (7) S b Z Lb + (8) Q b : binary marix (9) Consrains (5) and (6) guaranee ha a backup pah marix Q b is feasible via flow conservaion consrains and disjoin from he primary pahs. A marix Q b has he same dimension as P b, which is F L b. Consrain (7) deermines he amoun of spare capaciy unis needed in order o proec mapped op-layer primary pahs which fail as he resul of a single link failure a he boom layer. This informaion is

4 given in G b, which is a ( L b, L b ) marix. An elemen gij b defines he spare capaciy needed by boom link i o reroue failed pahs in he face of failure a boom link j. Equaion (8) defines ineger variables, where Z Lb + is he se of nonnegaive inegral L b -dimensional vecors; equaion (9) defines a (0,1)-marix variable, which will be explained furher in he nex secion. B. Providing backup pahs o boom-layer raffic a he boom Since providing backup pahs o boom-layer raffic a he boom layer requires no mapping, we now have all necessary informaion o find he backup pahs of raffic in boh layers. I is equivalen o finding a se of disjoin primary-backup pah pairs in single-layer neworks. A mahemaical formulaion for survivabiliy of wo-layer raffic a he boom layer can be wrien as: Q b B bt = D b (10) P b + Q b 1 (11) G b = Q bt M b P b (12) S b Z Lb + (13) Q b : binary marix (14) Similar o backup pahs of op-layer raffic, a consrain se (10)-(14) defines backup pahs Q b = {q b } F b L b and he spare capaciy G b = {g b } Lb L b required o proec primary pahs P b of he boom-layer raffic. As in Secion III-A, he primary pahs P b can be obained from Dijksra s algorihm. The objecives of he wo sraegies C and D are defined as follows: Sraegy C has an objecive o minimize he spare capaciy requiremens of he wo-layer raffic independenly, and so can be described as: min (S bt + S bt )e, (15) where S b = row-max G b, S b = row-max G b, and e is a column vecor of ones. The row-max (x) operaion deermines he maximum elemen in each row of he marix x. This min-max opimizaion of spare capaciy requiremens ensures he minimum capaciy ha mus be allocaed for each boom-layer link under single link failure a any oher links. The objecive funcion of Sraegy D is expressed as: min (S b,bt )e, (16) where S b,b = row-max (G b + G b ). This sraegy merges he wo spare capaciy marices and joinly consider hem, allowing heir spare capaciy o be exchanged. The wo survivabiliy sraegies a he boom: C and D, and wo sraegies where raffic originaes: A and B, from [14, Secion III.B(B) and Secion III.D] consruc a basis for our sudy in his paper. IV. NUMERICAL RESULTS In his secion, we sudy he effecs of he survivabiliy sraegies on spare capaciy requiremens of mulilayer raffic in wo-layer neworks. Firs, we look a he impac of raffic raios beween op- and boom-layer in fixed nework opologies as well as he impac of capaciy sharing beween he wo-layer raffic. Then, we look a he impac of oplayer nework conneciviy in erms of average node degrees. We use AMPL/CPLEX 9.1 on a Sun Fire V240, 2x1.2GHz UlraSPARC IIIi, 2GB o solve our models and he resuls are based on a 0% inegraliy gap, meaning ha hey are opimal. A wo-layer nework opology wih a number of nework scenarios is considered o deermine he effecs. The considered wo-layer opology is Fig. 1 where he op has 6 nodes, 9 links and he boom has 10 nodes, 22 links. Primary pahs in boh layers, when needed, are precompued and unchanged over he course of simulaions. A primary pah is manually adjused if he corresponding backup pah canno possibly be obained, called a rap pah. This is a counerexample o he exisence of wo disjoin pahs in wo-conneced neworks, when here are no parallel links. We are also aware ha join opimizaion of primary and backup pahs ofen leads o beer capaciy uilizaion [17]; bu since we wan o focus on he spare capaciy requiremens of he survivabiliy sraegies, we le he primary pahs be fixed. In addiion, a number of wavelenghs and wavelengh converers are assumed o be available and uni-capaciy flows are assumed. A. Impacs of Traffic Raios In his secion, he impacs of raffic raios are discussed for he wo possible seings: When he number of boomlayer flows is fixed while varying he number of op-layer flows, and vice versa. Wih varying number of flows, f flows are chosen from he firs f-h lexicographical elemen of he combinaions of wo elemens ou of he node se, e.g., for 8 op-layer flows in Fig. 1, he considered flows are ({1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 3}, {2, 4}, {2, 5}). Spare capaciy requiremens are measured in erms of redundancy, or resource overbuild, which is defined as a capaciy raio of backup pahs o primary pahs. 1) varying op-layer flows: Over a fixed 45-flow boomlayer nework, Fig. 2(a) shows by varying a number of oplayer flows ha Sraegy A and Sraegy D perform wors and bes, respecively. The reasoning can be given as follows: Le us pu aside boom-layer raffic o consider op-layer raffic only. There are wo survivabiliy sraegies for he op-layer raffic: Providing backup pahs a he op layer and a he boom. We claim ha he firs sraegy never requires fewer spare capaciy unis han he laer. The reasons are as follows: Firs, a survivable marix limis he number of feasible backup pahs of op-layer raffic a he boom. This is because he marix ies a op-layer link o boom-layer links, and his link mapping is no allowed o change. Second, spare capaciy is provided by he boom layer; regardless of where backup pahs are compued, heir capaciy requiremens are consrained by boom-layer opology. This is also rue even if he survivable marix can be changed because consrains will be a he boom-layer insead. In oher words, if he number of oplayer links are significanly fewer han ha of he boom hen he backup pahs are limied by he op opology. Bu when he

5 Sraegy A Sraegy B Sraegy C Sraegy D Sraegy A Sraegy B Sraegy C Sraegy D Sraegy B: degree 3 op nework Sraegy B: degree 4 op nework Sraegy B: degree 5 op nework Redundancy Redundancy Redundancy Numbers of op layer raffic flows (a) Top-layer flows vs. redundancy ( F b =45) Numbers of boom layer raffic flows (b) Boom-layer flows vs. redundancy ( F =8) Numbers of op layer raffic flows (c) Redundancy of neworks wih op-layer conneciviies ( F b =45) Fig. 2. Graphical resuls of Table II number of op-layer links are significanly more han ha of he boom, a boom opology iself limis improvemens on capaciy sharing by is own opology. An example when hese wo sraegies are equivalen is when he wo-layer opologies are idenical and a survivable mapping is link-o-link. Now le us pu boom-layer raffic back ino consideraion. We have shown ha, for op-layer raffic, boom-layer backup pahs require no more capaciy han he op-layer counerpar. This is also rue when here is boom-layer raffic and sharing spare capaciy beween BPb b and BP or BPb is no allowed. Since capaciy sharing usually reduces spare capaciy requiremens, Sraegy D always ouperforms or a leas performs as well as Sraegy A. This analysis suppors oher opologies as well. The oher wo sraegies, however, are compeing. When a op-layer nework has few raffic flows, Sraegy B ouperforms Sraegy C. This is because hese few flows may well be able o share capaciy wih he boom flows. Bu when here are more flows a he op layer, he siuaion is reversed. Consider a scenario of 1 primary op-layer flow and 45 primary boom-layer flows in Fig. 2(a). In his scenario, he boom flows require 23 spare capaciy unis. Because of capaciy sharing, Sraegy B requires only 1 more capaciy uni o provide a backup pah o he op-layer flow. The oal spare capaciy required is now 24 unis. However, in Sraegy C, when sharing is no allowed, he backup pah requires 2 capaciy unis. The spare capaciy requiremen of boom-layer flows is never changed in Sraegy C regardless of he number of op-layer flows because hey do no allow capaciy sharing wih he op flows. In his scenario, primary pahs require 1 and 71 capaciy unis for op- and boom-layer flows, respecively. When here are more flows, i.e., more han 12 flows, in he op nework, a higher number of flows in boh layers are subjec o failures. In his scenario, Sraegy C reduces spare capaciy requiremens by giving more rerouing choices o he op flows. These choices offer an advanage over Sraegy B. A similar rend is also observed for differen numbers of oplayer flows, when boom-layer flows are fixed, in Table II. 2) varying boom-layer flows: In his secion, we coninue o evaluae Sraegy B and C, bu insead, he number of oplayer flows is fixed, and we vary he number of flows a he boom layer. Consider a scenario of 8 op-layer flows when he number of boom flows ranges from 0 o 45, in muliples of 3. Unlike he above seing, his ime Sraegy C requires fewer capaciy unis han Sraegy B when he number of boom-layer flows is small. Fig. 2(b) shows ha Sraegy B sars o ouperform Sraegy C when here are 15 flows in he boom-layer nework. These resuls conform wih our previous discussions in Secion IV-A1 in erms of raffic raios. Observaions in his secion and Secion IV-A1 sugges ha here should be a characerisic of he compeing wo survivabiliy sraegies which could enable us o deermine which sraegy o implemen o ensure beer capaciy uilizaion according o each nework scenario. Due o space consrains, we decide o omi he discussion on he operaing characerisics of he wo survivabiliy sraegies. B. Impacs of Nework Conneciviy In his sudy, capaciy requiremens of op-layer neworks wih varying node degrees, 3, 4, and 5, over a boom-layer nework are compared. Neworks in a family are relaed by link removals from a maser nework, while keeping nodes and demand flows fixed. The use of nework families in simulaions can resemble he resuls from many random neworks while requiring much less simulaion ime. A more horough analysis on he use of nework families is provided in [18]. For a degree-3 op-layer nework, we use he nework shown in Fig. 1. A degree-4 op nework can be accomplished by adding links (1, 5), (2, 6), and (3, 6) o he degree-3 nework. A degree-5 op-layer nework is se hrough is full mesh, i.e., adding links (1, 6), (2, 5), and (3, 4) o he degree-4 nework. Since op-layer opologies have effec on he spare capaciy requiremens of neiher Sraegy C nor D, we focus only on Sraegy A and B. Fig. 2(c) shows ha reducion of spare capaciy comes a an expense of a higher number of op-layer link insallmens in which a significan difference in capaciy savings is observed when he number of op-layer flows is high. A 15 flows, which are he maximum number of disinc flows a he op, we observe a capaciy saving of 9 unis from a degree-3 o degree-5 nework, compared o 2 when here are 8 flows a he op. One possible explanaion is ha an adding link can help reduce he capaciy requiremens by giving more rouing choices o he backup pahs. This link has lile effec when here are few flows in he nework, i.e., 1-3 flows.

6 TABLE II REDUNDANCY PERCENTAGE OF OPTIMAL SPARE CAPACITY Numbers of boom-layer raffic flows Numbers of op-layer raffic flows ,300,100, ,133,67,67 100,100,60,60 78,78,67,67 92,92,50,50 85,85,46,46 80,80,47, ,100,100, ,100,100, ,88,88,88 100,80,80,80 86,79,79,79 94,76,65,65 89,72,61,61 85,70,60, ,91,91,91 108,100,92, ,86,86,86 94,88,81,81 85,75,80,70 91,83,70,70 88,79,67,67 85,77,65, ,88,88,88 100,88,88,88 95,84,84,84 90,81,81,76 84,76,80,72 89,75,71,68 86,72,69,66 84,71,68, ,71,71,71 82,73,77,73 79,71,79,71 77,65,77,65 73,67,73,63 79,67,73,61 76,65,71,62 75,92,67, ,59,59,59 68,61,64,61 67,60,67,60 66,56,66,56 64,58,64,56 69,59,64,54 68,58,63,53 67,57,60, ,55,55,55 63,59,59,59 62,56,62,56 61,56,61,53 60,55,60,53 65,53,60,51 64,52,59,50 63,52,57, ,46,46,46 53,50,50,50 53,48,53,48 52,48,52,45 52,48,52,52 57,47,53,45 56,46,52,44 56,46,50, ,43,43,43 49,46,46,46 49,44,49,44 49,44,49,42 49,47,49,45 54,44,50,42 53,43,49,42 53,44,47, ,41,41,41 47,44,44,42 47,43,47,43 47,41,47,41 47,43,47,42 52,41,48,39 51,40,47,39 51,41,46, ,38,38,38 43,41,41,39 43,39,43,39 43,38,43,38 44,40,44,39 48,40,45,38 48,39,44,38 48,40,43, ,36,36,36 41,37,39,37 41,36,41,36 41,34,41,34 42,37,42,35 46,37,43,35 45,36,42,35 46,37,41, ,36,36,36 40,37,39,37 41,36,41,36 41,34,41,34 42,37,42,35 46,37,43,35 45,36,42,35 45,37,41, ,34,34,34 39,35,37,35 39,34,39,34 39,33,39,33 40,36,40,34 44,36,41,34 43,35,41,34 43,36,39, ,33,33,33 37,34,35,34 37,33,37,33 38,33,38,33 38,34,38,33 42,34,39,33 41,34,39,33 41,34,38, ,32,32,32 36,33,35,33 36,32,36,32 37,32,37,32 38,33,38,31 41,33,39,31 40,32,38,31 41,33,37,30 Numbers of boom-layer raffic flows Numbers of op-layer raffic flows ,94,44,44 100,100,48,48 88,88,40,40 89,89,41,41 87,87,37,37 88,88,38,38 94,94,36,36 91,91,35, ,83,57,57 100,88,58,50 90,80,50,47 91,81,50,50 89,77,46,49 89,76,46,46 95,82,45,45 92,79,44, ,79,62,62 97,84,63,59 89,78,56,56 89,76,55,55 88,76,51,54 88,77,51,51 93,80,50,50 91,78,49, ,71,65,59 95,76,65,54 88,71,59,51 88,70,58,51 87,67,54,50 88,69,54,48 92,71,53,47 90,70,52, ,67,67,56 86,69,64,52 80,65,61,48 81,67,63,50 80,67,59,49 81,66,58,47 85,69,57,46 84,67,56, ,60,60,51 77,63,58,48 73,60,56,44 74,61,57,46 74,63,54,46 75,63,54,44 78,65,53,43 77,64,52, ,55,57,47 73,58,56,44 70,55,54,43 71,57,55,43 70,59,52,43 71,59,52,41 75,61,52,41 74,60,51, ,49,51,42 66,52,50,40 63,50,48,39 64,52,50,41 64,54,48,39 65,54,48,38 69,56,47,37 68,55,46, ,47,48,40 62,49,48,38 60,48,46,37 61,49,48,39 61,51,46,39 63,51,46,38 66,53,45,37 65,53,45, ,44,47,37 60,46,46,35 58,45,45,35 59,46,46,37 59,49,45,36 61,49,45,36 64,51,44,35 63,50,44, ,41,44,36 57,43,43,35 55,42,42,34 56,44,44,35 56,46,42,35 58,46,43,34 60,48,42,33 60,48,41, ,38,42,34 54,41,42,32 53,40,41,32 54,41,43,33 54,43,41,33 55,44,41,32 58,45,41,31 57,45,40, ,38,42,34 53,42,42,32 52,41,41,32 53,42,42,34 53,43,41,34 55,44,41,33 57,46,40,33 57,46,40, ,38,41,33 51,41,40,33 50,40,40,33 51,41,41,33 52,43,40,34 53,44,40,33 55,46,39,33 55,45,39, ,35,39,33 49,39,36,32 48,38,38,32 49,39,39,32 49,40,38,32 51,41,38,31 53,43,38,31 52,43,38, ,34,38,31 48,37,38,30 47,36,38,30 48,38,39,31 49,38,38,31 50,40,38,30 52,41,38,30 51,41,37,30 forma: Sraegies A, B, C, D V. CONCLUSIONS This paper examines he four possible survivabiliy sraegies in wo-layer neworks, where raffic presens a boh layers. An opimizaion-based formulaion is proposed o invesigae he spare capaciy requiremens under various raffic raios and nework conneciviies in he role of lighpah rouing. Numerical resuls show ha he survivabiliy of wo-layer raffic a he boom, when sharing spare capaciy among all backup pahs is allowed, performs bes. However, wo of he sudied sraegies are compeing. Moreover, neworks wih higher average node degree can provide more capaciy savings, bu his comes a he expense of link insallmens. Our analysis and resuls provide imporan guidelines for he design of survivabiliy sraegies in neworks and for undersanding heir radeoffs. Fuure work may include differeniaed survivabiliy. REFERENCES [1] C. Cavdar, A. G. Yayimli, and B. Mukherjee, Muli-layer resilien design for layer-1 VPNs, in OFC/NFOEC 2008., Feb [2] E. Modiano and A. Narula-Tam, Survivable rouing of logical opologies in WDM neworks, in IEEE INFOCOM 2001., vol. 1, Anchorage, AK, Apr. 2001, pp [3] K. Lee and E. Modiano, Cross-layer survivabiliy in WDM-based neworks, in IEEE INFOCOM 2009., Rio de Janeiro, Brazil. o appear. [4] M. Pickave e al., Recovery in mulilayer opical neworks, Journal of Lighwave Technology, vol. 24, no. 1, pp , Jan [5] E. Oki e al., Dynamic mulilayer rouing schemes in GMPLS-based IP+Opical neworks, IEEE Communicaions Magazine, vol. 43, no. 1, pp , Jan [6] A. Urra, E. Calle, and J. L. Marzo, Enhanced muli-layer proecion in muli-service GMPLS neworks, in Global Telecommunicaions Conference, GLOBECOM 05. IEEE, vol. 1, Nov./Dec [7] P. Demeeser e al., Nework resilience sraegies in SDH/WDM mulilayer neworks, in Opical Communicaion, h European Conference on, vol. 1, Madrid, Spain, Sep [8] W. Bigos, S. Gosselin, B. Cousin, M. Le Foll, and H. Nakajima, Opimized design of survivable MPLS over opical ranspor neworks, Opical Swiching and Neworking, vol. 3, pp , Dec [9] Q. Zheng and G. Mohan, Muli-layer proecion in IP-over-WDM neworks wih and wih no backup lighpah sharing, Compu. Neworks, vol. 50, no. 3, pp , [10] W. Wei, Q. Zeng, and Y. Wang, Muli-layer differeniaed inegraed survivabiliy for opical inerne, Phoonic Nework Communicaions, vol. 8, pp (18), November [11] N. Andriolli, A. Giorgei, L. Valcarenghi, and P. Casoldi, Idle proecion capaciy reuse in muliclass opical neworks, in Lighwave Technology, Journal of, vol. 25, no. 5, Houson, TX, USA,, May [12] X. Wang, L. Guo, and C. Yu, RLDP: A novel risk-level disjoin proecion rouing algorihm wih shared backup resources for survivable backbone opical ranspor neworks, Compu. Commun., vol. 31, [13] B. Rajagopalan, J. Luciani, and D. Awduche, IP over Opical Neworks: A Framework, RFC 3717 (Informaional), Mar [14] Y. Liu, D. Tipper, and K. Vajanapoom, Spare capaciy allocaion in wo-layer neworks, IEEE JSAC, vol. 25, pp , Jun [15] R. K. Ahuja, T. L. Magnani, and J. B. Orlin, Nework Flows: Theory, Algorihms, and Applicaions. Prenice Hall, [16] O. Wing and W. Kim, The pah marix and is realizabiliy, IRE Transacions on Circui Theory, vol. 6, no. 3, pp , Sep [17] S. Orlowski and R. Wessäly, Comparing resoraion conceps using opimal nework configuraions wih inegraed hardware and rouing decisions, J. New. Sys. Manage., vol. 13, no. 1, pp , [18] B. Todd and J. Doucee, Use of nework families in survivable nework design and opimizaion, in IEEE ICC 08., May 2008, pp