SURVIVABLE IP OVER WDM: GUARANTEEEING MINIMUM NETWORK BANDWIDTH

Transcription

1 SURVIVABLE IP OVER WDM: GUARANTEEEING MINIMUM NETWORK BANDWIDTH Galen H Sasaki Dept Elec Engg, U Hawaii 2540 Dole Street Honolul HI USA Ching-Fong Su Fuitsu Laboratories of America 595 Lawrence Expressway Sunnyvale, CA USA ABSTRACT A novel survivable IP over WDM network esign problem is propose The IP network uses lightpath services of the WDM network to implement its IP links The WDM network can provie unprotecte an protecte lightpaths, as well as a new lightpath service referre to as survivable pair The IP network must support two traffic matrices, one uner normal conitions an the other whenever there is a failure A mixe integer linear programming (MILP) formulation of the problem is presente An example is given where the survivable pair service can lea to significantly lower costs, sometimes by at least 30% KEY WORDS Optical networks, survivable networks, IP over WDM, overlay networks, network esign, mixe integer linear programming 1 Introuction We consiere esigning a survivable IP network where the IP links are realize by subscribing to lightpath services from a WDM network as shown in Figure 1 The IP network is part of some organization, perhaps a commercial Internet Service Provier (ISP) or government entity We refer to the organization as Company X The WDM network is part of another organization, which we refer to as Company Y We refer to Company Y as an optical transport service provier (OT-SP) Company Y provies ifferent graes of lightpath services, where each grae is a type of protection from faults Two services we consier are unprotecte an protecte Unprotecte service means that the lightpath can fail, while protecte service means that the lightpath cannot, ie, it has back-ups that it can switch to in case of faults Note that protecte service will cost more than unprotecte Lightpath Fiber-Link Router for Company X Optical Cross- Connect (OXC) Company Y (OT-SP) Figure 1 An IP network overlaye over a WDM network We assume that Company Y oes not reveal its resources such as its fiber-link layout Thus, the view of the OT-SP by Company X is more like Figure 2 rather than Figure 1 This is realistic because telecommunication companies typically keep their resources secret from competitors an customers However, they will reveal the type an price of their lightpath services We consier the following questions: What is an appropriate efinition of survivable IP networks over WDM networks? We assume there are two traffic matrices T an R that the IP network must support The IP network is require to carry T uner normal conitions, ie, no faults It is require to carry R whenever a fault occurs Thus, R is a survivable (guarantee) network capacity Note that R will be chosen to balance network costs with survivable performance Presumably R will be significantly smaller than T since IP network users are cost sensitive What kins of lightpath services will support survivable IP networks over WDM networks? We

2 consier unprotecte an protecte lightpath services These services are for iniviual lightpaths We also consier protection for pairs of lightpaths that have the same en routers We refer to such a pair as a survivable pair An example is shown in Figure 3 They are two unprotecte lightpaths that are route so that one of them is guarantee to survive a fault, ie, their routes o not have a common point of failure Note that survivable pair service only makes sense when there can be multiple IP links between routers, ie, when link bunling can be applie IP Link Figure 2 Company X's view of the OT-SP Router Lightpath Lightpath Figure 3 A survivable pair Company Y (OT-SP) Router In Section 2, we present a mixe integer linear programming (MILP) problem formulation of esigning an IP network that can support the traffic matrix T uner normal conitions, an support traffic matrix R whenever a fault occurs The problem assumes that unprotecte, protecte, an survivable pair lightpath services are available Note that esigning a survivable IP network over a WDM network has been consiere before in [1][2][3] However, in these works the esign problem is ifferent in a number of ways First, the input to the problem is an IP topology rather than traffic matrices Secon, only unprotecte lightpath service is available rather than a variety of protection types Thir, part of their esign problem is to route the unprotecte lightpaths, while we o not consier lightpath routing Finally, their iea of a survivable IP network is ifferent They only require that the IP network remain connecte after a fault Thus, they have very minimal surviving network banwith requirements This may be insufficient for networks with many users that nee quality of service On the other han, our problem requires that a prescribe network traffic R be supporte by the network even after a fault In Section 3, we show that the survivable pair lightpath service can reuce costs consierably by giving an example The costs can be reuce by as much as 30% for a 50 noe network Our final remarks are given in Section 4 2 Network Design Problem The following is the IP network esign problem we consier The network esigner is given a collection of IP routers, where we enote their number by n The IP routers are labele 1, 2,, n The esigner is given a traffic matrix T, where for each pair of routers {}, T( enotes the rate of traffic from i to The esigner is also given another traffic matrix R We assume that R is no greater than T, ie, for all pairs of routers {}, R( T ( Note that the traffic matrices may be asymmetric The IP network esigner must set up IP links between the routers to create an IP network, that in turn supports traffic matrix T The traffic may be route over multiple hops an bifurcate This can be accomplishe by MPLS traffic engineering In aition, the network is survivable in the following sense For any fault, the surviving IP network must support traffic matrix R, where rerouting of traffic is allowe The esigner leases lightpaths from Company Y (ie, the OT-SP) an uses them as the IP links The lightpaths are assume to be full uplex an have unit capacity Company Y is able to provie any number of lightpaths to connect any pair of routers In aition, Company Y provies ifferent types of lightpaths which correspons to ifferent protection The protection types are as follows: Unprotecte: An unprotecte lightpath is an orinary one If a failure occurs along its path then it goes own We enote the cost of leasing an unprotecte lightpath between routers {} by ucost( Note that since the IP network esigner oes not know how the lightpaths are route in the WDM network, she must assume that a single fault may bring own all unprotecte lightpaths Protecte: A protecte lightpath has back-ups When the lightpath fails, its signal is switche over to a back-up Thus, the IP network esigner may assume that a protecte lightpath will never fail We enote the cost of leasing a protecte lightpath between routers {} by pcost( Survivable Pair: Survivable pairs service is for a pair of IP links between the same routers The lightpaths

3 are unprotecte, ie, they may fail iniviually However, at least one lightpath will survive any failure We enote the cost of leasing a survivable pair between routers {} by scost( The esign problem for the IP network esigner is to choose the number of lightpaths between the routers an their protection types to support T an R In aition, there may be IP router port constraints at each router which is enote by D(u) This is an upper boun on the number of IP links that may terminate at the router u The esign problem can be formulate as an MILP problem as follows: Input Parameters: Matrix T: the traffic that the network must support uner normal conitions We refer to this as the nominal traffic Matrix R: the traffic that the network must support whenever there is a failure We refer to this as the surviving traffic Vector D: port constraints at each router Costs: for each router pair {}, ucost(, the cost of an unprotecte lightpath between {} pcost(, the cost of a protecte lightpath between {} scost(, the cost of a survivable pair between {} Integer Variables: Matrix C: for each pair of routers {}, C( is the number of unprotecte lightpaths (that are not part of survivable pairs) between them Matrix P: for each pair of routers {}, P( is the number of protecte lightpaths between them Matrix S: for each pair of routers {}, S( is the number of survivable pairs between them Continuous Variables: For all orere pairs of routers {} an estination router, t is the amount of nominal traffic that is carrie on some IP link between {}, from i to, an that is estine for For all orere pairs of routers {} an estination router, r is the amount of surviving traffic that is carrie on some IP link between {}, from i to, an that is estine for Constraints: All variables are nonnegative Lightpaths are full uplex: Since the lightpaths are full uplex, the matrices C, P, an S are symmetric Thus, for each pair of routers { }, C ( = C (, i), P ( = P(, i), S ( = S (, i) Port constraints: for each router v ( + P( + 2S( ) C ( D( u) The summation is the number of IP links that are incient to router u Thus, the inequality insures that there are at most D(u) incient IP links Link capacity constraints fort : for each router pair { }, ( C( + P( 2S( ) t + The summation is the amount of nominal traffic carrie on links between routers { } from i to This cannot excee the total capacity of the IP links between the routers Link capacity constraints for r : for each router pair { }, r S( + P( The summation is the amount of surviving traffic carrie on links between routers { } from i to This cannot excee the total capacity of the surviving IP links between the routers It is assume that only protecte lightpaths an one of every survivable pair will survive failures This assumption is necessary because the exact routes of the lightpaths are unknown, an so it is unclear which lightpaths will fail together when a physical fault occurs In aition, the surviving traffic must be supporte Flow conservation constraints fort : for each router i an estination router, t t i T( ) = T(, ) if if i i = Note that the left han sie of the equality is the "net flow" of nominal traffic that is estine for that comes out of router i The right han sie is what the net flow shoul be for router i If i is not then the net flow shoul be T(), which is the require amount of traffic that router i sources that is estine for If i is equal to then the net flow shoul be the total amount of traffic that must sink

4 Flow conservation constraints for r : for each router i an estination router, R( ) if i r ri = = R(, ) if i This constraint is for surviving traffic, an is similar to the flow conservation constraints for t escribe above Obective: the obective is to minimize ( ( : u< v ucost( C( + pcost( P( + scost( S( v Thus, the obective is to minimize the total cost of leasing lightpaths 3 Cost Efficiency of Survivable Pairs In this section, we will iscuss whether survivable pairs can reuce cost A natural approach to illustrate the cost effectiveness is to create instances of traffic matrices T an R an lightpath costs, an then esign IP networks with an without the survivable pair lightpath service For the case when survivable pair service is available, the esign woul be accomplishe by solving the MILP of Section 2 For the case when survivable pair service is unavailable, the esign is accomplishe by first moifying the MILP so that the service is unavailable (which is straightforwar), an then solving it The resulting network costs can be compare to etermine the effectiveness of the survivable pair service However, we foun that solving the MILP of Section 2 can be time consuming for even small networks For example, we solve the MILP for a case of six routers an uniform traffic matrices T an R using the AMPL an CPLEX software package on a SUN Blae 100 workstation The run time ("elapse time") to solve the MILP took approximately 5 minutes an 43 secons We also trie an example of seven routers but the run time exceee a couple of hours, an so we terminate it before completion Therefore, we will use another approach to illustrate the cost efficiency of survivable pairs We will erive two formulas for the cost of IP networks The first formula will be a lower boun on network cost without survivable pair lightpath service, an the secon formula will be an upper boun on cost with the service Then the formulas will be compare We will make the following simplifying assumptions Traffic matrices T an R are uniform: We assume that there are values τ an ρ such that for all pairs of )) routers {}, T( = τ an R( = ρ Note that uniform traffic matrices are commonly use in the research community for performance evaluation Also note that R is a fraction ρ/τ of T No port constraints: For all routers the value D(u) is essentially infinite, ie, it is ignore Cost of a lightpath is inepenent of the pair of routers it connects We assume the values of ucost(, pcost(, an scost( are inepenent of the pair of routers {} This assumption may be false for long-haul lightpath service Then lightpath costs may epen on istance, which can vary consierably However, the assumption may be reasonable for metro networks, where lightpath lengths are less variable Without loss of generality, we may further assume that for all router pairs {}, ucost( = 1 In aition, without loss of generality, we may assume that there are constants σ an π such that for all router pairs {}, scost( = 2 + σ an pcost( = 1 + π Note that the value of σ shoul be nonnegative (ie, 2 + σ shoul be at least 2) because a survivable pair is compose of two lightpaths In aition, σ can be significant To illustrate this, consier the following example Suppose the WDM network is a large ring network Suppose unprotecte lightpaths follow shortest hop paths Note that, on average, a shortest hop path traverses approximately 1/4 of the fiberlinks However, the lightpaths of a survivable pair must traverse all fiber-links of the ring because the lightpaths must be isoint Thus, on average, a survivable pair uses about four times as many fiberlinks as an unprotecte lightpath This suggests σ = 2 Note that the value of π epens on the type of protecte lightpaths The two types of protecte lightpaths are eicate an share Deicate protection means that the back-up lightpath has eicate, reserve banwith, eg, 1+1 an 1:1 protection The avantage of eicate protection is simpler an faster switching to the back-up Typically, a lightpath has only one back-up Then the lightpath must be isoint from its back-up to avoi a common point of failure Therefore, a protecte lightpath an its back-up consumes as much banwith as a survivable pair Hence, for eicate protection, 1 + π = 2 + σ, or equivalently, π = 1 + σ Share protection means that the back-ups of lightpaths may share banwith The avantage of share protection is smaller banwith use an lower

5 cost Note that if π < σ then survivable pairs are not cost effective because there will be a cheaper alternative The alternative to a survivable pair is another pair of lightpaths, one protecte an the other unprotecte It has cost 2+π, which is less than the 2+σ cost of a survivable pair It also supports the same traffic (2 units of capacity uner normal conitions an 1 unit of capacity if there is a failure) The following is an example of when π < σ Suppose the WDM network is a ring network Then σ = 2, as we have shown earlier Suppose that the scheme to share protection banwith is the same as in a biirectional line switche ring (BLSR) BLSR requires twice as much banwith as an unprotecte network because half of its banwith is for protection Hence, if cost is epenent on banwith then a protecte lightpath has twice the cost of an unprotecte one Then π = 1, an so π < σ Now we will erive the lower boun formula for IP network cost without survivable pair lightpath service We will use the following proposition Proposition 1 Consier a network with n noes, fulluplex links with capacity 1, an a traffic matrix T' such that for all pairs of noes {}, T'( = t Let L enote the total number of links Then ( ) nt L 1 + t Proof Let a enote the amount of traffic that is route along one-hop paths, an b the amount of traffic that is route on multi-hop paths Since one-hop traffic traverses one link, it consumes a unit amount of link banwith per unit of traffic Since multi-hop traffic traverses two or more links, it consumes at least 2 units of link banwith per unit of traffic Also note that each link is full uplex an can carry a unit of banwith in both irections Therefore, 2 L a + 2b Next, note that the total amount of traffic is n 2 t 2 Thus, n b = 2 t a, which implies 2 n n 2 L a + 2 t a 2 = 4 t a Finally, note 2 2 that if there are L links then at most 2L orere pairs of noes will have their traffic route along one-hop paths n Hence, a 2Lt This implies 2L 4 t 2Lt 2 After some algebra, we get the inequality of the proposition QED The proposition implies that we nee at least ( ) nτ 1 + τ lightpaths to support T If survivable pair lightpaths are unavailable, we woul nee ( ) nρ 1 + ρ protecte lightpaths to support R Thus, to insure we have enough lightpaths to support T, we nee least ( ) nt ( ) nρ 1 + t 1 + ρ unprotecte lightpaths Hence, the cost is at least ( ) nρ ( ) nτ ( ) nρ (1 + π ) ρ 1 + τ 1 + ρ This is our lower boun for the cost of an IP network that can support T an R without survivable pair lightpath service We enote this lower boun by LB Next we will erive an upper boun on IP network cost when survivable pair lightpaths are available We accomplish this by efining an IP network that can carry traffic matrices T an R, an then evaluate its cost Since the network can carry the require traffic, its cost is an upper boun The network has the star topology shown in Figure 4 It has one router esignate as the center, an all other routers are referre to as peripheral The peripheral routers are irectly connecte to the center by unprotecte an survivable pair lightpaths The number of survivable pairs between a peripheral router an the center is ( )ρ because ( ) ρ is the amount of traffic that the peripheral router must source/sink even when there is a failure The number unprotecte lightpaths between a peripheral router an the center is max { 0, ( 1) τ 2 ( )ρ } n Then the total number of lightpaths between the peripheral router an the center is at least ( )τ This insures that the lightpaths can carry ( n 1) τ amount of traffic, which is the amount that the peripheral router must source/sink uner normal conitions Thus, the cost of the lightpaths between the peripheral router an the center is K, where ( 2 + σ ) ( n 1) ρ + max{ 0, ( n 1) τ 2 ( 1) ρ } K = n Since there are n 1 peripheral routers, the total network cost is ( n 1)K This is our upper boun on the IP network cost if survivable pairs are available, an we enote it by Star

6 Next, we numerically compare the lower boun LB with the upper boun Star For parameter values, we choose τ an ρ so that ρ = τ/2, ie, the surviving matrix R is half of T We choose π = 1 + σ, ie, the case when protecte lightpaths use eicate protection We consier σ = 0 (the minimum value for σ), σ = 1, an σ = 2 (the case when the WDM network is a ring) 5 Acknowlegements The authors woul like to thank the reviewers who provie valuable comments This research was supporte in part by Fuitsu Laboratories of America an the National Science Founation uner grant NCR Peripheral Routers Figure 4 Star topology for an IP network Figure 5 shows δ, which is efine to be 100 % LB Star LB, for n = 50 The value δ inicates the percent ecrease in cost of using survivable pairs It is plotte as a function of τ, which ranges from 2 to 8 Note that for positive values c, if c τ = then each peripheral router must have at least c lightpaths Since LB an Star are bouns, the actual ecrease in cost coul be greater than δ This is why δ is sometimes negative The figure shows that the ecrease in cost can excee 30% This occurs when σ = 0 an 2 τ = = 0041 Also note that survivable pairs are more cost effective for smaller values of σ, which suggests that they will be more effective in WDM networks with mesh topologies 4 Conclusions Center We have efine a survivable IP over WDM network esign problem an formulate it into an MILP The resulting network guarantees a survivable network throughput We introuce survivable pairs as a lightpath service an emonstrate that in certain cases, it can achieve a ecrease in cost of at least 30% A future irection for research is to investigate other lightpath services that support survivable network throughput at lower cost δ Figure 5 Percentage ecrease in cost δ as a function of τ for n = 50 References σ = 0 σ = 1 σ = 2 [1] O Crochat, J-Y Le Bouec, Design protection for WDM networks, IEEE J Selecte Areas on Communications, 16(7), 1998, [2] E Moiano an A Narula-Tam, Designing survivable networks using effective routing an wavelength assignment (RWA), Proc OFC 2001, Anaheim, CA [3] E Moiano an A Narula-Tam, Survivable routing in logical topologies in WDM networks, ProcIEEE Infocom 2001, Anchorage, AK, τ