Recently, the hardly predictable and permanently increasing data traffic of IP services andbroadband applications has become the largest traffic component in transport networks.Major market changes, e.g., the pay-as-you-grow preference of providers, and the layeredstructure of the players on the service market (content providers, network service providers,and transport service providers) led to significant difficulties in modeling and forecast-ing services and traffic growth. This evolution disabled the traditional approach based onforecast-driven off-line design and preconfiguration of network resources. The implemen-tation of the next-generation network concept [1], i.e., the realization of a unified all-IPservice platform will strengthen these trends in the foreseeable future.
Transport networking under uncertain capacity demands requires either inefficientoverdimensioning of network resources or intelligent configuration flexibility to follow un-expected changes in the traffic pattern. Both strategies are capable of preventing early sat-urations of some transport systems that would lead to network bottlenecks and, ultimately,blocking of transport capacity requests. Reduction of the effect of demand uncertainty hasbeen studied in the context of many network technologies, such as in the case of leasedline service networks [2], asynchronous transfer mode (ATM) networks [3], and survivablemesh-based transport networks [4–6].
Provisioning-oriented optical networks are optical networks with enough intelligentflexibility to automatically serve optical channel requests arriving at the network spreadout over time and space. The intelligent control and management functions are based onthe automatically switched optical network (ASON) or the generalized multiprotocol labelswitching (GMPLS) concept. The strategies, presented in this paper, can be realized byapplying either the GMPLS or the ASON concept with centralized or distributed user-to-network interface (UNI) implementation [7, 8].
In recent years numerous research and development projects, such as InformationSociety Technologies (IST) Next Generation Optical Network for Broadband EuropeanLeadership (NOBEL) [9] and Multi-Partner European Testbeds for Research Networking(MUPBED) [10]; standardization activities, e.g., the UNI specification of the Optical In-ternetworking Forum (OIF) [8]; and a large number of publications have been devoted tofast-provisioning-enabled optical networks. However, in the related research activities lessattention has been paid to network state evolution during the provisioning processes.
The reoptimization phase has already been part of the life cycle of traditional time divi-sion multiplexing (TDM) networks, where the amount of reserved capacities was optimizedby periodically regrooming the traffic [11].
The reoptimization of optical networks has been studied widely in research works.These works differ in the applied measures of the reconfiguration, in the algorithms, inhow the reconfigured network state can be achieved, and in the relation between the currentand the reconfigured network state. The applied measures can be divided into two basicclasses. The first class contains measures that consider the reoptimization of occupied net-work resources, e.g., minimizing average hop numbers of connections [12], the number ofoccupied wavelengths [13], the number of occupied physical links [13], the average prop-agation delay over a light path [14], or the maximum link load [14]. At the same time thesecond class of measures describes the number of changes necessary to reach the optimalnetwork state from the current state. Various types of changes may be considered accordingto the network model, e.g., the number of wavelength changes [13], the number of wave-length path changes [12], the mean number of disrupted transceivers, or the maximuminstantaneous number of disrupted transceivers [15].
The algorithms can be assorted into methods giving exact results, e.g., linear [4, 12–14, 16, 17] or nonlinear programming methods, and methods giving approximate results,e.g., genetic algorithms [14, 18] or Lagrange decomposition [19].
Finally, in terms of the relation between the current and the reconfigured network state,one can distinguished direct approaches, where the new network configuration is indepen-dent from the current one; partial reconfiguration approaches; and local search approaches.A detailed summary of measures and algorithms can be found in Ref. [20].
Reference [21] was among the first publications that raised the light path reoptimizationissue in mesh optical networks. The authors published a more comprehensive descriptionof the problem and their related achievements recently in Ref. [22]. In these studies [21, 22]the reoptimization was carried out in a live Optical Electrical Optical (OEO) network. Thework presented covers the reoptimization of optical mesh networks where shared (backup)path protection is used. The main focus of the paper is on the algorithmic considerations oflight path reoptimization. The savings yielded by optimal rearrangement are also demon-strated by numerical examples in both networks with static infrastructure and traffic churnand networks with growing infrastructure. Rearrangement strategies and algorithms aregiven both for backup path reoptimization and complete reoptimization, which involvesworking and backup paths, as well.
The main motivations for rerouting and reconfiguration in optical networks mentionedin Ref. [23] are resilience, i.e., rerouting in failure cases, and easing congestion, i.e., rerout-ing of already accommodated requests to make room for new ones. This work studies thererouting and reconfiguration process itself and puts emphasis on finding the proper se-quence of rerouting and resolving the dependencies that block a potential rerouting se-quence.
In Ref. [24] the author shows some situations, related to the size of the modules, whenthe reoptimization of the network is unnecessary and only the incremental design can givenearly the same good result.
The next research paper that must be mentioned is Ref. [25]. In this work the authors
compare four reoptimization strategies for span-restorable mesh survivable networks. Thedefined strategies differ in their objective functions and they are given both for backup pathand complete reoptimization. The applied network model was an Optical Optical Optical(OOO) network with wavelength conversion and static demands.
The focus of the present paper is different from that of the listed works. The adaptedapproach here is closer to that of Ref. [26], where some practical preferences of a networkoperator are taken into account, as well. In a previous paper [27] we already identified anddemonstrated the inherent lack of capacity efficiency of provisioning processes by numeri-cal examples. This justified the insertion of consolidation into the life cycle of provisioning-oriented optical networks. The introduced papers [21, 22, 25] deal with the measure of thereoptimization of the network, i.e., what must be reconfigured; the complete network; oronly the protection paths, besides different objective functions. The present paper definessome new reoptimization strategies, which also take into consideration the frequency ofreoptimization. To make it easier to understand, a general formulation is given to the de-scription of consolidation strategies. The introduction of the new strategies is connected tosuch real network situations where the application of these strategies can guarantee betterefficiency. These contributions can provide new information to the research area.
Section 2 gives a brief overview of the efficiency issues of the network configurationsinvolved in real-time provisioning processes and discusses an approach to operate andmaintain provisioning-oriented optical networks with improved efficiency. Section 3 in-troduces a formulation that is suitable to the general description of consolidation strategies.Then Section 4 shows some useful strategies for the consolidation of a highly saturated net-work and a network that serves optical channel requests with high reliability requirements.Finally, the work presented is summarized and concluded in Section 5.
2. Life Cycle of Provisioning-Oriented Optical Networks
Fast provisioning of permanent optical channels, that is, soft permanent optical channel ser-vices [28], can be interpreted as follows. Because of traffic changes in client services, theclients generate optical channel requests spread out in time and space. Based on the distrib-uted signaling and switching intelligence of optical network nodes, routing and wavelengthallocation (RWA) is solved on-line, and the appropriate network elements are configured toaccommodate the optical channel requests. After an optical channel is set up to accommo-date a request, it remains unchanged, assuming a simple incremental traffic model.
2.A. Traditional Life Cycle
During the lifetime of a provisioning-oriented network, basically, there are two repetitivephases:
• Provisioning phase: Arriving requests are served sequentially. This process may leadto the saturation of some network resources; in that case, extension of network ca-pacity is needed.
• Network capacity extension phase: Additional resources are designed and installedto remove or prevent network bottlenecks.
The aim of the provisioning process is to set up optical light paths by performing on-linedecisions and configuration actions while minimizing blocking probability on the givenlimited network resources. The decisions cover both path selection and wavelength assign-ment.
The basic two-phase cycle leaves the configuration and setup of network resources un-changed; thus the capacity efficiency of the network is determined by the applied provision-
ing process; i.e., it may strongly depend on the random arrival sequence of optical channelrequests.
In the case of on-line provisioning, the capacity demands are not known in advance;therefore, because of the sequential service of the arriving optical channel requests, thedecisions made during the provisioning process are suboptimal. In other words, the accom-modation of the current request is optimal in the given network state, but not for the wholeprovisioning process.
2.B. Life Cycle with Consolidation
With the extension of the life cycle the overall network performance can be improved.When network saturation requires actions from the operator, before or even instead of in-stalling new resources, a consolidation process can be activated. During the consolidationprocess limited rearrangement and reconfiguration of the network is performed to improvecapacity efficiency. This may free some network resources. If the consolidation does notresult in enough idle resources the network capacity should still be extended by installingnew network elements.
The consolidation phase should be repetitive since the requests arriving after a consoli-dation phase are served according to suboptimal decisions, again.
This extension of network phases results in a three-phase life cycle (see Fig. 1) includ-ing
• provisioning phase,
• consolidation phase,
• network capacity extension phase.
The basic idea behind consolidation is that configuration decisions based on the knowl-edge of a certain group of optical channel requests (already in the network) is definitelymore efficient than those that result from a given realization (sequence) of the provisioningprocess.
Extension of the network
Provisioning Network configuration
to serve dynamic requests
Consolidation Rearrangements to achieve the optimal configuration
Optional
Fig. 1. Major networking processes in a provisioning-oriented optical network.
A more optimal resource allocation may be obtained by performing a traditional net-work design including all demands currently being served. A sequence of reconfigurationactions is then needed to set up the obtained optimal network state. But the trade-off be-tween the increase of capacity efficiency and the extent of rearrangements should be con-sidered in the process.
The extent of rearrangements can be restricted according to the types and amount ofchanges, as well. For example, having a network configuration with predefined routes, therouting can be left unchanged, and only the wavelength assignment is modified.
An important problem is to identify when the consolidation process needs to be trig-gered. The simplest approach is that consolidation is executed after fixed time intervals.Another approach can be to trigger consolidation by the change of some network parame-ters, e.g., the amount of the free capacities in the whole network.
The frequency of reconfiguration is likely to have an effect on the amount of changesand the computational complexity of the optimized solution. Thus one must find a trade-offbetween the frequency of the reconfigurations and the amount of required changes. Theseproblems will be explained in detail in Section 4.
The gain in efficiency due to consolidation can also be considered as the suboptimalityof the provisioning process. The measure of this kind of suboptimality can be evaluatedaccording to a simple theoretical upper bound, if the operation of the provisioning mecha-nism is known. Assuming that the set of sequential demands is known in advance, an upperbound concerning the achievable capacity efficiency can be obtained by means of applyingtraditional off-line design (see Fig. 2).
In Ref. [27] a more detailed description of the traditional and the three-phase life cycleis given.
Network EfficiencyLow High
Optical channel requestsarriving spread in time and space are served one by one by a distributed and flexible network intelligence applying on-line provisioning algorithms.
Optical channel demandsassumed to be known in advance (based on a proper forecast) and an optimal network configuration is designed to meet the demands.
Practical Case Theoretical Lower Bound
Consolidation:rearrangement of already arrived and served requests
Network EfficiencyLow High
Optical channel requestsarriving spread in time and space are served one by one by a distributed and flexible network intelligence applying on-line provisioning algorithms.
Optical channel demandsassumed to be known in advance (based on a proper forecast) and an optimal network configuration is designed to meet the demands.
Practical Case Theoretical Lower Bound
Consolidation:rearrangement of already arrived and served requests
Fig. 2. Inefficiency of on-line provisioning.
3. Formalization of the Consolidation Phase
This section presents a formulation of the general description of consolidation strategies.In the provisioning phase, each optical channel request that can be served gets a path anda wavelength. Based on this concept the consolidation can be realized as the transforma-tion of the path and wavelength allocation. The result of this transformation is the optimalallocation. However, the input cannot be described so simply because it contains multipleparameters. The first parameter is the suboptimal allocation of the paths and wavelengthscoming from the provisioning phase.
The second parameter of the transformation is the objective function, which determineswhat the optimal solution of the reconfiguration is. The objective function may requiremore parameters, as well. These parameters can belong to three groups:
• parameters controlling the paths of the demands (e.g., to minimize the amount ofreserved capacities),
• parameters controlling the wavelength allocation (e.g., to minimize the number ofused wavelengths),
• special parameters that depend on the applied provisioning strategy (e.g., the serveddemands must not overachieve their reliability requirements significantly).
The effect of the different parameters can be weighted in the objective function.The further parameters of the transformation concern the strategy of the consolidation.
The two main questions in relation to consolidation are when the consolidation should takeplace and what should be reconfigured. More precisely, what kind of network attributetriggers the consolidation process and what the measure of the consolidation is. Based onthis approach, two new parameters are needed, one to describe the triggering attribute andanother to define the measure of the reconfiguration.
Besides, a last parameter must still be introduced to describe the restrictive conditionscoming from the applied provisioning strategy, e.g., an optical channel demand with a highreliability requirement must not be interrupted for a long time.
Thus the consolidation can be interpreted as the following transformation:Consolidation(Allcurr,Obj,Tri,Mea,Re s) → Allopt, where Allcurr is the current path andwavelength allocation before the consolidation, Allopt is the optimal path and wavelengthallocation, Obj is the objective function, Tri is the network attribute that triggers the consol-idation process (the simplest case is when the interval between the consolidation processesis fixed), Mea is the reconfiguration measures allowed, and Re s is the parameter to describethe restrictive conditions. Section 4 shows how some different consolidation strategies canbe interpreted by this formulation and what these parameters of the transformation mean inpractice.
4. Consolidation Strategies
In this section some basic strategies are introduced to the consolidation of two networkshaving different features. In the first case the network is highly saturated and in the secondthe demands have high reliability requirements. In both cases an unavailability-threshold-based provisioning strategy [29] is used. This provisioning strategy is a kind of sharedprotection. This means that protection paths can share capacity to decrease the amount ofrequired resources if their working paths are disjoint. This provisioning strategy completesthe shared protection with end-to-end reliability guarantees for the connections in the pres-ence of multiple simultaneous failures. The complexity of the computations of this problemis eliminated by introducing the concept of sharing unavailability, defined as the probabilitythat a shared backup resource is activated and thus becomes unavailable to a demand. Theextent of allowed sharing is determined by introducing a threshold on sharing unavailabil-ity. Shared (backup) path protection is combined with this threshold to propose an on-lineprovisioning strategy.
In the experiment of the current study a layer 1 virtual private network [30] (L1VPN)with 9 nodes, 16 links, and 9 wavelengths/link was used over a theoretical Hungarian op-tical network topology for accommodating a certain random demand sequence. The ninewavelengths belong to one VPN; the consolidation is applied only to this network segment.In this case the extension of the network capacities can be made easily by adding one or twowavelengths to the VPN. To implement the on-line provisioning a simulator has been devel-oped. After each 10 demand arrivals until 40 demands, a snapshot is taken of the networkstate and the resource consumption yielded by the proposed provisioning-oriented networkdevelopment life cycle is compared against the output of the integer linear programming(ILP) design process performed with the data of the respective snapshot. The ILP formu-lation of the consolidation phase can be found in Appendix A. This is the formulation ofthe strategy, when all of the arrived demands are consolidated. For a specific consolidationstrategy the formulation must be completed with further constraints. These constraints areintroduced next to the definition of the strategies. To support the observations, all of the
cases are simulated with six random sequences of demands and confidence intervals arecalculated, which can be found in Appendix B.
4.A. Consolidation of Highly Saturated Networks
The first network example is a highly saturated network. In this case the problem is thatthere are only a few free capacities for the reconfiguration of the demands. The solution ofthe problem is that only some reconfiguration actions can be made during a consolidationphase. The obvious way is that only a few demands are reoptimized during a consolidationphase. On the other hand, it can also be reached if the network is not allowed to movefar from the optimal ILP solution. Based on the first approach, one reconfigures only thosedemands that arrived after the previous consolidation process. Although after the consolida-tion the allocation of paths and wavelengths will not be optimal, the number of reconfigureddemands in a consolidation process will be lower, and this number can be decreased evenmore with more frequent consolidation.
The description of strategies termed consolidate recent arrived demands and consolidateall arrived demands with the introduced formulation can be found in the first and secondcolumn of Table 1. When applying the consolidate all arrived demands strategy one mustuse the formulation introduced in Appendix A. In the consolidate recent arrived demandsstrategy the ωλ
pw(x) and the ρλ
pp[pw(x)] variables of the demands, which arrived before the lastconsolidation phase, must be bounded.
Table 1. Obj, Tri, and Mea Parameters of the Different Consolidation Strategies
Consolidate Recent Arrived Demands
Consolidate All Arrived Demands
Permanent Working Path and Wavelength
Permanent Working Path
Obj Minimize the amount of reserved capacities Tri Consolidation after 10 new demands arrived
Mea
Reconfiguration of the demands,
arrived after the last consolidation phase
Reconfiguration of all arrived demands
Reconfiguration of the protection path and wavelength of
all arrived demands
Reconfiguration of the working
wavelength and the protection path and wavelength of all arrived demands
The difference between the consolidate recent arrived demands and the consolidate allarrived demands strategies can be seen in Fig. 3. The observation is that the difference be-tween the amount of reserved capacity of the two different consolidation strategies is notso significant, although it increases with the number of arrived demands. After 40 demandarrivals the average difference is 10% before the consolidation and 5% after the consol-idation. However, the number of reconfigured demands is significantly lower in the caseof the consolidate recent arrived demands strategy. Figure 4(b) demonstrates the total pathand wavelength changes in the case of the two different strategies. As is expected, the con-solidate recent arrived demands strategy requires fewer path and wavelength changes toachieve the optimal solution.
The second solution is that the network is not allowed to move far from the optimalconfiguration, and therefore fewer reconfiguration actions are needed to reach the optimalallocation. This approach can be realized if the network is consolidated more frequently. Inthis case the strategy can be defined as the consolidate all arrived demands strategy, but thevalue of the Tri parameter is changed.
Fig. 3. Amount of reserved capacities when in the snapshot points all of the arrived de-mands or only the demands arrived after the last consolidation phase are reoptimized.
Fig. 4. Amount of reserved capacities in the optimal case and the provisioning case withdifferent consolidation frequencies.
Figure 4 shows the amount of reserved capacities in the optimal case and during theprovisioning phase with consolidation activated with different frequencies. The observationis that the deviation of the provisioning process from the optimal solution increases overtime, and so does the potential resource utilization gain due to consolidation. But afterreconfiguration the network state gets close to the optimal configuration. In the case of afrequent consolidation strategy the amount of the used resources is closer to the optimalILP solution, as can be seen in the case of the CONS(10) curve. In the case of a rareconsolidation strategy, as in the case of CONS(40) curve, where consolidation is run only atthe end of the provisioning process, the resource efficiency gap is larger. This phenomenoncan also be observed in Fig. 5(a), which illustrates the dependence of deviation from theoptimal resource usage as a function of the frequency of the consolidation. The CONS(x)refers to the provisioning process with consolidation, where x is the number of demandarrivals between successive reoptimization attempts.
A) Maximal and average deviation from the optimal B) Total number of path and wavelengths changes in case solution in the reconfiguration points of different consolidation strategies
Fig. 5.
Fig. 5. (a) Maximal and average deviation from the optimal case solution in the reconfig-uration points. (b) Total number of path and wavelength changes in different consolidationstrategies.
Even though every consolidation frequency gives nearly the same result after the ar-rival of the last demand, the amount of necessary configuration changes are not the same.A frequent consolidation strategy results in a higher number of total path and wavelengthchanges executed during the consolidation, as demonstrated by Fig. 4(b). At the same timethe average number of configuration changes required per reconfiguration is lower. Intu-itively, fewer changes also means that during the reconfiguration phase less extra capacity(buffer capacity temporarily used in a given reconfiguration sequence) is needed to reachthe consolidated network state. As a consequence, in a nearly saturated network, consoli-dation should be triggered more frequently. The opposite of the described phenomenon canbe observed if the frequency of consolidation is decreased.
Based on the observations, it can be claimed that the best strategy for the consolidationof a highly saturated network is that only the most recently arrived demands are reoptimizedand/or the consolidation process is applied frequently. In this case the network may movefarther from the optimal solution, but the number of reconfiguration actions remains fewer.
4.B. Reoptimization of Demands with High Reliability Requirements
The problem with the reoptimization of these demands is that the demands must not beinterrupted for a long time because their reliability requirements may be violated. Thereforethe demands can be reconfigured only a few times. The solution for this problem can be theconsolidate recent arrived demands strategy or a rare consolidation strategy because, in thecase of these strategies, the consolidation phase is activated in less time, as can be seen inSubsection 4.A.
Another solution is that only the protection path and wavelength of a demand can bereconfigured. The description of this permanent working path and wavelength strategy can
be found in the third column of Table 1. In this case the demand is not interrupted andthe reliability requirement is not violated. In the permanent working path and wavelengthstrategy the ωλ
pw(x) variables for each demand must be bounded. As can be seen in Fig. 6,the amount of reserved capacities is far from the optimal ILP solution and the deviationincreases with the number of arrived demands.
Fig. 6. Amount of reserved capacities if both the working paths and wavelengths or only the working paths of the demands are permanent
Fig. 6. Amount of reserved capacities if both the working paths and wavelengths or onlythe working paths of the demands are permanent.
To decrease this deviation, we may also allow the reoptimization of working wave-lengths beside the protection paths and wavelengths. Thus only the working paths stayfixed under the consolidation phases. The definition of this permanent working path strat-egy is in the fourth column of Table 1. The basis of this approach is that the change ofa wavelength requires less management complexity than the reconfiguration of the wholepath. The reason is that the change of a wavelength, besides wavelength continuity, meansonly freeing a wavelength and reserving another along a fixed path, whereas the reconfigu-ration of a path is a path search in the space of continuous wavelengths, and the solution ofthis problem involves more nodes.
When applying the permanent working path strategy the ∑λωλ
pw(x) ≤ 1 constraint mustbe used for each working path. As expected, the amount of reserved capacities is lowerwhen applying this strategy (see Fig. 6).
Figure 7(a) demonstrates the average and maximum deviance from the optimal solution,and Fig. 7(b) shows the total number of path and wavelength changes. On both figures theresults are compared to the results of the rare consolidation strategy and the consolidaterecent arrived demands strategy.
The observation is that the two strategies last introduced approximate the optimal solu-tion much better than other strategies [see Fig. 7(a)]. However, to reach the configuration,which is close to optimal, significantly more reconfiguration actions must be made thanin applying the other two strategies [Fig. 7(b)]. The conclusion is that if there are enoughfree capacities in the network, the application of the permanent working path and wave-length or the permanent working path strategy is recommended. Otherwise, if the networkis saturated, then the rare consolidation strategy or the consolidate recent arrived demandsstrategy is proposed. Another potential solution can be a mixed strategy; e.g., only theprotection path and wavelength of the most recently arrived demands can be reoptimized.Research into these mixed strategies will take place in the future.
5. Summary and Conclusions
This paper has proposed a potential approach to designing provisioning-oriented opticalnetworks. The limited resource efficiency of provisioning strategies due to the on-line na-ture of the problem was identified, and a consolidation stage was introduced in the life cycle
A) Maximal and average deviation from the optimal B) Total number of path and wavelengths changes in
solution at the reconfiguration points case of different consolidation strategies Fig. 7.
Fig. 7. (a) Maximal and average deviation from the optimal solution at the reconfigurationpoints. (b) Total number of path and wavelength changes in the case of different consolida-tion strategies.
to improve capacity efficiency. Then, a general formulation was given that can describe thedifferent consolidation strategies as a transformation whose input parameters are the pathand wavelength allocation before the consolidation, the objective function, the triggeringattributes, the reconfiguration measures allowed, and a parameter that can describe the re-strictive conditions that derive from the applied provisioning strategy.
Finally, some useful consolidation strategies were introduced for the consolidation ofa highly saturated network and for the reoptimization of demands with high reliabilityrequirements, and their advantages and disadvantages were analyzed by means of simu-lations. Based on the results obtained, it is determined that different network situationsrequire different consolidation strategies (e.g., consolidate recent arrived demands or fre-quent consolidation strategies in the case of a highly saturated network; rare consolidation,consolidate recent arrived demands, permanent working path and wavelength, or perma-nent working path strategies in the case of a network that serves optical channel requestswith high reliability requirements) to achieve the best efficiency.
A. Appendix A: Mixed-Integer Linear Program Formulation of the OptimizationProblem
To determine the solution with the least amount of capacity usage for the consolidationof the unavailability-threshold-based provisioning strategy we solve this problem formallyas a mixed-integer linear program. The following formulation is based on the notationsintroduced in Ref. [29].
In the formulation the network topology is represented as a directed graph G(V,E),where V is the set of nodes and E is the set of links. Links can have two states—they areeither operating or failed. Link failures are assumed to be statistically independent, and thelink failure probability FP(e) is known for all links e ∈ E.
Each link e ∈ E corresponds to a pair of fibers, one for each direction of propagation.Without loss of generality, links are assumed to have W wavelength channels on each fiber.
Each Optical Channel (OCh) demand x∈ X requires one wavelength channel between asource node s ∈V and a destination node d ∈V and has a reliability requirement parameter0 ≤ r < 1; i.e., the maximum accepted probability that demand x is disrupted by a failureof any multiplicity in the network. Demands are served from a predefined set of routesthat contains the working paths and the link disjoint backup paths. (Note that the pathsare wavelength continuous; therefore we do not have a specific constraint for wavelengthcontinuity in the formulation).
• e(i, j) Link originating in i ∈V and terminating in j ∈V
• L(e) Length of link e ∈ E
• W = {λ} Number of wavelengths on each fiber
• X = {x} Set of demands
• r (x) Reliability requirement parameter of demand x ∈ X
• Pw (x) = [pw (x)] Set of working paths of demand x ∈ X
• Pp [Pw (x)] ={
pp [pw (x)]}
Set of protection paths of demand x ∈ X
• e ∈ pw (x) Means that pw (x) contains link e ∈ E
• e ∈ pp [pw (x)] Means that pp [pw (x)] contains link e ∈ E
• Pr [pw (x)] Probability that working path pw (x) is disrupted
• Pr{
pp [pw (x)]}
Probability that protection path pp [pw (x)] is disrupted
• Pr(e) Failure probability of link e ∈ E
• qs Unavailability threshold
Variables:
• αλ
e(i, j) Link indicator that equals one if the λ wavelength of the link e(i, j) isused by any working path; zero otherwise (binary variable)
• βλ
e(i, j) Link indicator that equals one if the λ wavelength of the link e(i, j) is usedby any protection path; zero otherwise (binary variable)
• ωλ
pw(x) Working path indicator that equals one if the λ wavelength is used bypw (x); zero otherwise (binary variable)
• ρλ
pp[pw(x)] Protection path indicator that equals one if the λ wavelength is used bypp [pw (x)]; zero otherwise (binary variable).
Objective:Minimize ∑
λ,e(i, j)α
λ
e(i, j) + ∑λ,e(i, j)
βλ
e(i, j).
The objective function minimizes the amount of reserved capacities (wavelength ∗ link).Constraints:
• Topology constraints:
Equation (A1) ensures that only one working path is assigned to a demand. If the reli-ability requirement of a demand is higher than what the working path can guarantee,a protection path must also be reserved for the demand. Equation (A2) ensures thatonly one working path is assigned to a demand. The constraint that one working pathcan be realized on a wavelength of a link is guaranteed by Eq. (A3). Equation (A4)ensures the sharing of protection paths and prevents protection paths from sharinga wavelength with any working path. Equation (A5) guarantees that the protection
path of the demand will be chosen from that protection path set that belongs to theworking path of the demand:
∀x ∑pw(x)
∑λ
ωλ
pw(x) = 1 (A1)
∀x ∑pp[pw(x)]
∑λ
ρλ
pp[pw(x)] ≤ 1 (A2)
∀e,λ ∑x
∑pw(x)|e∈pw(x)
ωλ
pw(x) ≤ 1 (A3)
∀pp [pw (x)] ,λ ρλ
pp[pw(x)] + ∑pw(x)|pw(x)∩pp[pw(x)]6={ }
ωλ
pw(x) ≤ 1 (A4)
∀pw (x) ∑λ
ωλ
pw1(x) + ∑λ,pp[pw2(x)]|pw1(x)6=pw2(x)
ρλ
pp[pw2(x)] ≤ 1 (A5)
• Constraints on traffic variables:
Equations (A6) and (A7) set the value of the variables that show the usage of awavelength on a link:
∀e,λ αλ
e(i, j)− ∑pw(x)|e∈pw(x)
ωλ
pw(x) ≥ 0, (A6)
∀e,λ K∗β
λ
e(i, j)− ∑pp[pw(x)]|e∈pp[pw(x)]
ρλ
pp[pw(x)] ≥ 0. (A7)
In Eq. (A7) the value of K must be higher than the number of protection paths.
• Reliability constraints:
The reliability requirements of each demand are guaranteed by Eq. (A8), whereUBPr
{pp [pw (x)]
}is an upper bound of Pr
{pp [pw (x)]
}:
∀x ∏∀pw(x)
Pr[pw (x)]∗ ∏∀pp[pw(x)]
UBPr{pp[pw(x)]} ≤ r (x) . (A8)
The failure probability of working paths and the upper bounds can be calculated in advance;thus the ILP formulation of the constraint is as follows:
∑∀pw(x),λ
(ln{Pr [pw (x)]}∗ωλ
pw(x)
)+ ∑∀pp[pw(x)],λ
[ln
(UBPr{pp[pw(x)]}
)∗ρ
λ
pp[pw(x)]
]≤ r (x) ∀x.
In this equation, ILP variables are multiplied by one another, which is not feasible inan ILP formulation. For this reason the natural logarithm of the probability values must betaken, where the multiplication is transformed into addition:
UBu(e,λ,yi) ≤ qs (e,λ,yi) (A9)
for each shared resource (e,λ) used by the protection path pp [pw (x)] of connection demandx and each demand yi ∈Q(e,λ,x). The detailed description of the criterion and the variablescan be found in Ref. [29].
Equation (A9) checks that the unavailability threshold is not violated anywhere.The ILP formulation of the constraint seems as follows:
∀pp [pw (x)] ,λ
∑pp[pw(x)],2|e∈pw(x),2
{ln[1−Pr(e)]∗ρλ
pp[pw(x)],2
}+[−ln(1−qs)]
∗ρ
λ
pp(pw(x)),1
−L∗ρλ
pp[pw(x)],1 ≥−L,
where{
pp [pw (x)] ,1∩ pp [pw (x)] ,2}6= {}, i.e., protection paths are not link indepen-
dent, and pw (x) ,2 is the working path of pp [pw (x)] ,2. Here 1 and 2 represent two differentdemands.
pw (x)∩L(e,λ) 6= 0 (A10)
for each e∈ pw (x) and the assigned protection wavelength λ. This criterion enforces that noshared resource might be used by two different demands for protection against the failureof the same component.
The ILP formulation of the constraint is as follows:
∀e,λ ∑pp[pw(x)]|e∈pw(x)
ρλ
pp[pw(x)] ≤ 1.
The above formulation gives the solution with the lowest capacity usage for the consol-idation of the unavailability-threshold-based provisioning strategy. Numerical results arepresented in the paper.
B. Appendix B
In this Appendix you can find the confidence intervals of the numerical results presented inthe paper. The significance level is α = 0.05 and the sample size is 6 in each calculation.The term no cons. means that the demands are not reoptimized in that case.
CONS(5) CONS(10) CONS(20) CONS(40) # of working path change [44.93, 54.06] [31.99, 41.51] [23.07, 26.42] [18.78, 21.72] # of working wl. change [135.07, 138.42] [69.96, 77.53] [46.23, 48.77] [34.23, 36.77] # of protection path change [72.11, 77.88] [45.70, 53.30] [35.01, 37.48] [23.88, 28.12] # of protection wl. change [109.05, 116.45] [64.62, 68.38] [41.07, 44.42] [22.16, 26.83]
Table 6. Confidence intervals of Fig. 5(b)
Last Arrived Demands
Consolidation # of working path change [16.34, 22.14] # of working wl. change [29.88, 38.42] # of protection path change [25.17, 30.56] # of protection wl. change [27.03, 33.69]
The author thanks the anonymous reviewers for their helpful comments and sugges-tions. The research presented in this paper was initiated within the framework of Italian–Hungarian Intergovernmental Project 17/04 titled Planning and Implementing Reliable IPover a WDM Optical Network and partially funded by OTKA 048985 Project titled Dimen-sioning and Reliability Analysis of Fault-Tolerant Networks in a Differentiated Reliability(DiR) environment.
References and Links[1] International Packet Communication Consortium (IPCC), Reference Architecture v1.2,
June 2002, http://www.imsforum.org/documents_wg/IPCC_Reference_Architecture.pdf.
[2] S. Sen, R. D. Doverspike, and S. Cosares, “Network planning with random demands,” in SelectProceedings of the 2nd International Conference on Telecommunication Systems (1994), pp.11–30.
[3] A. Gaivoronski, “Stochastic programming approach to the network planning under uncertainty,”in Optimization in Industry 3 (Wiley, 1995), pp. 145–163.
[4] A. Gencata and B. Mukherjee, “Virtual-topology adaptation for WDM mesh networks underdynamic traffic,” IEEE/ACM Trans. Netw. 11, 236–247 (2003).
[5] J. Kennington, E. Olinick, K. Lewis, A. Ortinsky, and G. Spiride, “Robust solutions for theDWDM routing and provisioning problem: models and algorithms,” Opt. Netw. Mag. 4(2), 74–84 (2003).
[6] D. Leung and W. D. Grover, “Capacity planning of survivable mesh-based transport networksunder demand uncertainty,” Photon. Netw. Commun. 10, 123–140 (2005).
[7] P. Szegedi, Zs. Lakatos, and J. Spath, “Signaling architectures and recovery time scaling forgrid applications in IST project MUPBED,” IEEE Commun. Mag. 44, 74–82 (2006).
[8] Optical Internetworking Forum: User Network Interface (UNI) 1.0 Signalling Specification,Release 2: Common Part, February 2004, http://www.oiforum.com.
[9] IST Next Generation Optical Network for Broadband in Europe (NOBEL), http://www.ist-nobel.org.
[10] IST Multi-Partner European Testbeds for Research Networking (MUPBED), http://www.ist-mupbed.org.
[11] G. Bernstein, E. Mannie, and V. Sharma, “Framework for MPLS-based control of opticalSDH/SONET networks,” IEEE Netw. 15(4), 20–26 (2001).
[12] D. Banerjee and B. Mukherjee, “Wavelength-routed optical networks: linear formulation, re-source budgeting tradeoffs, and a reconfiguration study,” IEEE/ACM Trans. Netw. 8, 598–607(2000).
[13] B. Ramamurthy and A. Ramakrishnan, “Virtual topology reconfiguration of wavelength routedoptical WDM networks,” in IEEE Gobal Telecommunications Conference (IEEE, 2000), pp.1269–1275.
[14] B. Zhou, J. Zheng, and H. T. Mouftah, “Dynamic reconfiguration based on balanced alternaterouting algorithm (BARA) for all-optical wavelength-routed WDM networks,” in IEEE GlobalTelecommunications Conference (IEEE, 2002), pp. 2713–2717.
[15] H. Takagi, Y. Zhang, and X. Jia, “Virtual topology reconfiguration for wide-area WDM net-works,” in IEEE 2002 International Conference on Communications, Circuits and Systems andWest Sino Expositions (IEEE, 2002), pp. 835–839.
[16] M. Tornatore, G. Maier, and A. Pattavina, “WDM network optimization by ILP based on sourceformulation,” in Proceedings of the Twenty-First Annual Joint Conference of the IEEE Com-puter and Communications Societies (IEEE, 2002), pp. 1813–1821.
[17] R. Dutta and G. N. Rouskas, “Design of Logical Topologies for Wavelength Routed Networks”inOptical WDM networks: principles and practice in design of logical topologies for wavelengthrouted networks,” K. Sivalingam and S. Subramanian, eds. (Kluwer, 2000), pp. 79–102.
[18] Y. Xin, G. N. Rouskas, and H. G. Perros, “On the physical and logical topology design of large-scale optical networks,” J. Lightwave Technol. 21, 904–915 (2003).
[19] M. E. M. Saad and Z.-Q. Luo, “Reconfiguration with no service disruption in multifiber WDMnetworks based on Lagrangean decomposition,” in IEEE International Conference on Commu-nications (IEEE, 2003), 1509–1513.
[20] W. Golab and R. Boutaba, “Policy-driven automated reconfiguration for performance manage-ment in WDM optical networks,” IEEE Commun. Mag., Special Issue on Management of Op-tical Networks 42, 44–51 (2004).
[21] E. Bouillet, P. Mishra, J. F. Labourdette, K. Perlove, and S. French, “Lightpath re-optimizationin mesh optical networks,” in 7th European Conference on Networks and Communications(2002), pp. 235–242.
[22] E. Bouillet, J. F. Labourdette, R. Ramamurthy, and S. Chaudhuri, “Lightpath re-optimization inmesh optical networks,” IEEE/ACM Trans. Netw. 13, 437–447 (2005).
[23] N. Jose and A. K. Somani, “Connection rerouting/network reconfiguration,” in Proceeding ofthe Fourth International Workshop on the Design of Reliable Communication Networks (IEEE,2003), pp. 23–30.
[24] W. D. Grover, “Mesh-based survivable networks: options and strategies for optical, MPLS,SONET and ATM networking,” (Prentice-Hall, 2003), Section 5.10.
[25] D. Leung, S. Arakawa, M. Murata, and W. D. Grover, “Re-optimization strategies to maximizetraffic-carrying readiness in WDM survivable mesh networks,” in Optical Fiber Communica-tion Conference and National Fiber Optic Engineers Conference (Optical Society of America,2005), p. 3.
[26] N. Geary, N. Parnis, A. Antonopoulos, E. Drakopoulos, and J. O’Reilly, “The benefits of re-configuration in optical networks,” in Proceedings of 10th International TelecommunicationNetwork Strategy and Planning Symposium (NETWORKS 2002) (2002), pp. 373–378.
[27] T. Kárász, Zs. Pándi, and T. Jakab, “Network consolidation—how to improve the efficiency ofprovisioning oriented optical networks,” in Proceedings of the Fifth International Workshop onthe Design of Reliable Communication Networks (IEEE, 2005), pp. 151–158.
[28] S. Ramamurthy, L. Sahasrabuddhe, and B. Mukherjee, “Survivable WDM mesh networks,” J.Lightwave Technol. 21, 870–883 (2003).
[29] Zs. Pándi, M. Tacca, and A. Fumagalli, “A threshold based on-line RWA algorithm with reli-ability guarantees,” in Proceedings of the Optical Network Design and Modeling Conference(IEEE, 2005), pp. 447–453.
[30] T. Takeda, I. Inoue, R. Aubin, and M. Carugi, “Layer 1 virtual private networks: service con-cepts, architecture requirements, and related advances in standardization,” IEEE Commun. Mag.42, 132–138 (2004).
