A Vectored Fragmentation Metric for Elastic Optical Networks
11 A Vectored Fragmentation Metric for ElasticOptical Networks
Anjali Sharma, Varsha Lohani and Yatindra Nath Singh
Department of Electrical Engineering,Indian Institute of Technology Kanpur
Abstract —When circuits are set up and dismantled dynam-ically in elastic optical networks, spectrum tends to becomefragmented in the fiber links. The fragmentation limits theavailable path choices and may lead to significant blocking ofconnection requests. There are two types of fragmentation in thenetwork spectrum- in the links due to contiguity constraints andover the paths due to continuity. Study of fragmentation and itsmanagement is essential to operate the networks efficiently. Thispaper proposes a vectored fragmentation metric for characterizingthe fragmentation, which covers both types of fragmentation.We discuss the characteristics of this metric in both transientand steady-state of the dynamic network. We also test theproposed metric for connection requests’ granularity range,arrival rates and holding times, to establish functionality of thismetric. We also compare the link-based fragmentation metricwith our Vectored Fragmentation Metric to understand the betterrepresentation.
I. INTRODUCTIONOver last few decades, optical fiber communications haveemerged as the core of communication infrastructure acrossthe globe. The reason for this is capability of long distancetransmission using optical fiber due to its inherently largebandwidth distance product. Further, availability of huge band-width has fuelled innovation and development of applicationswhich use this bandwidth and consequently further fuel thebandwidth demand. According to the Cisco Annual Internetreport (2018-2023), nearly two-thirds of the global populationwill have access to the internet and mobile connectivity by2023 [1].This growing demand has led to intense research in wave-length routed networks, optical circuit, packet and burstswitching. Elastic optical networks (EONs) have also beenposed as a possible way of moving ahead from WDM(Wavelength Division Multiplexed) networks leading to moreefficient and hence possibly more economical networks.WDM networks allocate fixed bandwidth channels to anydemand received. Typically 25 GHz or 50 GHz channelsare used in WDM networks. In a network with 50 GHzchannels, if a bandwidth request of 5 GHz arrives at aningress node, the network has no option except to allocatea 50 GHz channel. Elastic optical networks are conceived toresolve this limitation. In EONs, the lowest bandwidth that canbe fulfilled by a single channel with 100 percent efficiency is12.5 GHz [2]. Thus, if received by an Elastic Optical Network,the same 5 GHz request will get only 12.5 GHz allocated and in terms of spectral grid requirement not 50 GHz. Finer bandwidth allocation granularity allowsmore efficient use of resources. Thus we expect better andefficient use of the existing optical networks and thus increasedeffective capacity catering to more bandwidth demand. Thetutorial paper [3] and [4] cover the enabling technologies forEON at hardware (transceivers and switches) and networklevel (resource allocation schemes).Instead of defining a fixed bandwidth channel of 50 GHzas in WDM, EON defines a bandwidth slice as a basic unit.In order to cater to large bandwidth, multiple adjacent slicesin the spectrum can be allocated together. Thus, bandwidthdemands can be accommodated in a given spectrum by allo-cating bandwidth in integral multiples of the basic slice unit,or Frequency Slot Unit [5]. As a consequence, the wastageof spectrum is reduced drastically as compared to WDM net-works. However, this strategy of elastically allocating severaladjacent slices depending on demand also leads to anotherproblem, i.e., fragmentation. Sometimes bandwidth, despitebeing available, cannot be allocated as it is not contiguous.This paper is investigating elastic optical networks in refer-ence to improving the methods for maintaining the efficiency,and hence possibly improving the economics of using them.The organization of the paper is as follows. In Section II,we discuss the basic concept of resource provisioning andissues related to it in EONs. Section III discusses the conceptof the vectored fragmentation metric. In the subsections, wediscuss the metric’s formulation along with an example offragmentation level calculation. We also evaluate the prop-erties of the metric and its application. Section IV presentsthe assessment of the proposed fragmentation metric usingsimulation results. Section V closes the paper with a generalconclusion, and future challenges in the study of vectoredfragmentation metric.II. B ASIC C ONCEPTS IN E LASTIC O PTICAL N ETWORKS
A. Routing and Spectrum Assignment
In WDM networks, the connection requests on their arrival,are set up through the nodes and the links using a wavelengthchannel. Routing and Wavelength Assignment problem en-sures that the connection request is set up on a selected path,and its bandwidth requirement from the source (also calledingress) to the destination (also called egress) is satisfied. Theallocated wavelength channel may be selected using First-fit a group of slices is considered as a bandwidth slot in this paper. a r X i v : . [ c s . N I] F e b Fig. 1: RSA Constraints example. (a) A connection requestbetween N1 and N4 with two spectrum slices requirement,(b) given a network spectrum scenario at T1, and the slots ona path complying with the constraints, (c) Non- availability ofslices for the same connection request at T2.or Last-fit assignment rules. In case conversion of wavelengthis not feasible in the path, then the path has to be on thesame wavelength. If it cannot be done, path setup is declaredinfeasible. Commonly, we should set up the connection requeston a shortest path using the shortest path algorithm. If we donot enforce the shortest path constraint, it will still be possibleto set up the connection request on the same wavelength (whenno converters are there) through a longer route.Routing and wavelength assignment problem need to besolved in a reasonable time to set up paths if feasible. Foran operating network, the problem becomes an incrementaloptimization problem. When the requests arrive, the bestpossible path is set up while trying to reduce the blockingprobability.The same problem gets extended to Elastic Optical NetworkScenario with another constraint of contiguity in addition tocontinuity [6]. Spectral continuity constraint sets the rule thatthe same part of the spectrum is allocated all through the path unless there are waveband shifters at some intermediate nodeswhere there is an option to shift the allocated spectral band.Spectral contiguity constraint dictates that the slices allocatedto the path are together forming a continuous band in thenetwork spectrum. Due to these constraints, the routing andwavelength assignment problem now becomes an RSA (rout-ing and spectral assignment) problem. An example of how aconnection request is provisioned under the RSA constraints ina linear network is shown in fig. 1(a)-(b). If the slot satisfyingthe constraints are available, then the connection request isprovisioned and set up fig. 1(b). If sufficient resources arenot available or not complying the RSA constraints, for aconnection request, then that connection request is blockedfig. 1(c). In this paper, we first discuss this problem and thelimitations associated with it.An EON can deploy RSA strategies for both static traffic aswell as dynamic traffic scenarios. In static traffic, paths of allthe connection requests are known a priori. Hence, the light-path allocation and configuration of switches are computed andconfigured beforehand. In a dynamic traffic scenario, connec-tion requests arrive as well as depart randomly. Appropriatestochastic models can characterize the arrival and departure.The RSA decides the allocation of the spectrum slices andpath after the arrival of connection. At this step, there mayarise a situation where the resources are not available. In thatcase, connection request is rejected (blocked). In a real-lifesituation, most connection requests arrive dynamically; thus,we characterize the network performance in terms of blockingprobability for given arrival rates and connection durationstatistics.Ideally, in both static or dynamic traffic scenarios, all thepaths that satisfy the constraints are identified, and then thebest path (which can be a shortest path) is chosen. Weare assuming that connections are arriving one at a timesequentially. If path requests contend for the same link, therequest arriving earlier gets precedence, and the second one iseither setup through an alternate path or gets blocked. Next, wediscuss spectrum fragmentation issue and related inefficienciesin EON.
B. Spectrum Fragmentation
In dynamic traffic scenarios, the connection requests withdifferent bandwidth requirements keep coming and leaving.As the RSA constraints of contiguity and continuity are tobe satisfied while setting up a connection, the situations arisewhen the required number of slices are available, but still, thepath cannot be set up. The path is not available there becauseeither the continuity or the contiguity constraint is not satis-fied. Though if all the existing connections could have beenreorganized, then some of the refused connections could havebeen set up. Such situations depict the network’s fragmentedstate, and the reorganization is the desirable defragmentationprocess in the network.Fragmentation can be understood to be happening due toa lack of continuity or contiguity fulfillment of spectrumslices. The fragmentation brings spectrum inefficiency anddegrades network performance. To address this fragmentation
Fig. 2: (a) Connection requests occupying spectrum resourcesat a time t , then (b) two connection requests depart at t ,two spectrum slices become available. (c) A new connectionrequest with 2 spectrum slice requirement arrives at t , butcannot be accommodated as available resources are not con-tiguous.issue, we identify two types of fragmentation- the one due tothe non-continuity of available resources on a path and thesecond one due to the non-contiguity of available resourceson a link. Consider the scenario as shown in fig. 1(c). Herea connection request for two slices from node N1 to nodeN4 cannot be setup. In each of the individual links, i.e., A,B, and C, more than two slices are available, and still, dueto continuity constraint, the request cannot be satisfied. Theconnections with shorter hops and lesser slice requests willhave higher chances of getting through, i.e., will have lesserblocking probability.Fragmentation also leads to unfair treatment to connectionsrequesting higher bandwidth, as in a fragmented situation, thelow bandwidth connection has a higher probability of gettingthrough (fig. 2). A few works with Markov Chain (MC) modeltried to characterize the fragmentation in network by usinga single channel and a super-channel services, [7],[8]. Theblocking probability plot of individual services shows howthe single channel requests rob off the resources from super-channel requests. The fragmentation management approachesare of utmost importance to deal with the inefficiencies andunfairness in the system.There are two approaches to manage the fragmentation:one with no reorganizations (non-defragmentation) and theother with periodic reorganization (i.e., a defragmentationprocedure). In the first approach, i.e. non-defragmentation, theobjective is to operate the network to minimize fragmentation.In the periodic defragmentation approach, whenever the frag-mentation increases, reorganization of existing connections isdone to allow for setting up of new connections.The non-defragmentation approach cannot guarantee the fragmentation less operation of the network. While thedefragmentation approach requires some interruption in theexisting connections when their reorganization occurs. But thedefragmentation approach is expected to give better utilizationof resources.Both the management strategies can reduce the consumptionnetwork resources. But for the second strategy, it is importantto defragment the network at right instants. We need to definea methodology to quantify the fragmentation level and use itto identify the time instants to defragment the network. Themethodology should also help decipher the causes behind thefragmentation.There have been several attempts to quantify the frag- mentation. These are either based on fragmentation in links’spectrum, or fragmentation through paths, or throughout thenetwork.Some of the link-based fragmentation metrics which exploitthe spectrum status in links have been discussed in [9], [10],[11]. Some of the link-based fragmentation measures are -the external fragmentation [9], the Shannon entropy-basedmeasure [9], the Access Blocking probability-based measure[9], the utilization entropy [10], the high-slot mark [10] andthe spectrum compactness [11]. The metrics discussed in thecited works give an abstract treatment to the fragmentationmeasure. They tend to ignore some of the crucial aspects ofspectrum status, e.g., small fragments, and cannot differentiatebetween different spectrum scenarios.Some of the proposed fragmentation measures are depen-dent on connection requests and paths requested by them.Pederzolli et al. [12] have proposed a path-based fragmen-tation metric. It accounts for both wasted and unusable slots(equivalent to slices in this paper) in a path, capturing the onsetof fragmentation for a specific connection request. The authorsuse this metric in the RSA, to find path-slots combinationfor a connection request. The selected path-slots combina-tion should result in lower overall fragmentation value. So,appropriate path selection is precursor to fragmentation, ifany. While this metric captures fragmentation due to bothcontinuity and contiguity both, but it is path/connection requestspecific. In [13], authors used two network-level metrics, oneassociated with the contiguity aspect and the other associatedwith network utilization. The first metric uses the link con-secutiveness aspect in all links at specific observation periods(time-weighted) to decide on a network’s fragmentation level.The second metric is also a time-weighted network utilizationmetric. It accounts for the unavailability of links due to highload, which should not be a reason for fragmentation. Theauthors in this work also gave a perception of unfairness i.e.,high bandwidth requests are more likely to get blocked due tofragmentation.There have also been attempts to devise the fragmentation-aware routing and spectrum allocation techniques [14], [15].The metric can provide information about the onset of frag-mentation shortly after the fragmentation has set in. In bothscenarios, one can update routing or spectrum assignmentstrategy one the onset of fragmentation is detected. For thefragmentation awareness part, various spectrum parametersin the links of the network, are monitored. Though, theseparameters may not have a direct link to the fragmentation. Inthe given schemes, different spectrum allocation strategies areupdated to achieve maximum request acceptance even in thepresence of fragmentation. The authors in [16] made anotherinteresting attempt where they accommodate the connectionrequests only if they do not lead to fragmentation in thefuture. However, it lead to selective acceptance and, in turn,unfairness in the system. The common aspect in all of theabove fragmentation management approaches is the use offragmentation metric to either routing (deadlock-avoidance) orspectrum allocation (to achieve lowest contiguity ratio). Thecontiguity ratio is the ratio of maximum contiguously availableslices to total available slices in a link. Fig. 3: Types of fragmentation cases.This paper presents a two-dimensional fragmentation met-ric, which gives an absolute value for the fragmentation statusfor the whole network. We call it a vectored fragmentationmetric (VFM). It has two fragmentation components, onecovering the fragmentation due to continuity constraint over anumber of links, and the other, covering the fragmentation dueto contiguity constraint within the links. These are calculatedindependently of each other.III. A V
ECTORED F RAGMENTATION M ETRIC
A fragmentation metric quantifies the level of fragmentationin the spectrum. The fragmentation level can be high orlow, depending on the vacant bandwidth slice positioning inthe spectrum on the links and its continuity over the linksforming a continuous path. The standard performance metricsfor the network, e.g., blocking performance for new arrivingconnections, are expected to reduce for the lesser value offragmentation metric for the same spectrum utilization.We would like to have a single metric that can be entrustedwith representing the fragmentation level, considering bothcontiguity and continuity aspects. Several metrics have beenproposed in the literature using different network spectrumcharacteristics (e.g., link spectrum status). However, they failto quantify the fragmentation satisfactorily, e.g., the inabilityto identify smaller fragments. Based on earlier studies, weenumerate a few cases which a useful fragmentation metricshould be able to identify (fig. 3).1) Case (a)- Where all slices are free (No fragmentation)2) Case (b)- Where all slices are busy (Case of no frag-mentation; blocking due to resource unavailability)3) Case (c)- Where free slices are contiguous (No fragmen-tation)4) Case (d)- Where free slices are lost/unusable (absolutefragmentation)5) Case (e)- Higher the fragmentation in the spectrum,larger is the metric value (relative fragmentation).Blocking of a connection can happen due to unavailabilityof contiguous bandwidth slices in one or more links formingthe path over which connection is to be setup. Thus, thefragmentation due to both continuity and contiguity are amajor contributors to the blocking of connection requests. Itwill happen due to improperly managed RSA.We formulate a vectored fragmentation metric which pro-vides an absolute single value for the fragmentation level whileconsidering both continuity as well as contiguity. The proposedmetric takes into account the fragmentation in individual links (by considering largest number of contiguous slices) andfragmentation over multiple links forming a path, by findingthe maximum number of continuously free links for eachspectrum slice.Operationally, We can assume a centralized network con-troller (like SDN controller) which interacts with all therouters to gather all the status, and setup the paths for thearriving connection demands. It will have extensive status ofcomponents and can help in making better decisions [20]. Thecentral controller can determine the vectored fragmentationmetric using the individual links’ status and continuity ofavailable slices across the specified paths. Though the specifiedpath will have impact on the computed metric.VFM consists of α - and β -components. • α -component : which covers the fragmentation due tonon-contiguity of available spectrum slices in individuallinks across the whole network. • β -component : which covers the fragmentation due tonon-continuity of available spectrum slices over thelongest paths in the network covering all the links. A. Formulation of metric
The ν is the fragmentation indicator also called VectorFragmentation Metric (VFM). It is resultant of α and β components. For the α - component, the maximum contiguousslices in a link are taken up against total available slices in thatlink. Ideally, if all the available slices form a single contiguousslot, then there is no fragmentation. An important assumptionis that at least one spectrum slice is available in the networkspectrum. More than one spectrum slices scattered is the maincause of fragmentation. For the β -component, continuity ofa single slice over a path is taken into account. If possiblea single longest path (a cycle), or otherwise, multiple pathsare used to check continuity of each slice index over all thelinks in each path. When single path is not feasible, minimumpath(s) are chosen in such a way that no link is repeated andstatus of all the links are covered. Then, the continuity ofall the spectrum slice indices (which are available at least inone of the links on the path) is used. The maximum numberof continuous hops where slices (of a particular index) areavailable, is taken against the total available (unused) hops forthat spectrum slice over the whole path. The calculation ofthe components and the fragmentation indicator is done as inequations 1 - 3. α = 1 | EL | . EL (cid:88) i =1 CG i SS i (1) β = 1 | P | . P (cid:88) i =1 E i E i (cid:88) j =1 CN ij AS ij (2) V F M = ν = (cid:112) α + β (3)where EL = set of links with at least one empty (or available)spectrum slice, SS i = total number of available spectrum slices in the i th link, CG i = Maximum number of contiguous spectrum slicesavailable on i th link in the network spectrum, P = set of multiple paths in the network specified for thepath continuity aspect, covering all the links E i = total spectrum slice indices in the network spectrumwith at least one empty spectrum slice anywhere on thepath in the i th path, AS ij = Number of hops where slices on j th index is freein the i th path, CN ij = Maximum number of continuous hops withavailable j th spectrum slices in i th multihop path, T SS = total number of spectrum slices in all the links(includes both available and occupied), H p = Number of hops on p th path, L = set of links in the network.This formulation calculates the fragmentation level in thenetwork spectrum using the available spectrum slices. If thereare no available spectrum slices, then no fragmentation exists.We emphasize on longest path selection (or a Hamiltonianpath) for β − component as it ensures that we get a network-wide beta-component and its value is not independent of path-specific continuity aspect. As the β - component checks con-tinuity of all spectrum slices individually, i.e., the componentdecides on non-continuity fragmentation from a single slice in-dex’s point of view. Therefore, even if several single spectrumslices (at high spectrum utilization) are available on multipleindices along the path, which is a case of fragmentation, it getsignored in β -component calculation. Later, we also intend touse different path combinations in both Hamiltonian and non-Hamiltonian network to see if the choice of paths has anyimpact on the defragmentation trigger and hence the blockingperformance. Another important question is, if using a singlelongest or multiple paths with no or minimum repetition oflinks has any impact on the β − component’s contribution inthe fragmentation level? As per our understanding, we wouldlike to surmise here that if one considers static routing, thenusing multiple paths could be a better for β calculation. Wehypothesize so because in static routing case the paths arefixed and hence easy to rely on. However, in dynamic routingscenario, the paths are not fixed and the controller looks for thebest possible path available. So in place of using large multiplepaths we try to use a a single longest path or multiple longestpaths which can preserve the flow information and contributeto β -component at an abstract level.The ranges of α and β are (considering T SS as evennumber): T SS ≤ α ≤ , (4) H p ≤ β ≤ , if H p is even, and H p H p − ≤ β ≤ , if H p is odd . (5)For the minimum value of β for odd value of H p , we canconsider the chequered patterns as shown in Fig.4. In that case, β = 12 (cid:18) H p − H p + 1 (cid:19) = 2 H p H p − . Fig. 4: Worst case fragmentation scenario in a network with
T SS number of spectrum slices, and continuity over a singlepath (an Euler path- covering all links of network withoutrepetition, where number of visited nodes may repeat).The lower limit of the range is calculated by consideringa worst case scenario. In the worst case scenario each linkin the network exhibits fig. 3 case (d)’s spectrum status, withslices available alternatively in a link as well as in a path. Asshown in the fig. 4, a single available slice is the maximumcontiguous slot size in each of the links and also in the path(s).This scenario is further worsened by half of the availableresources. We also get a highly fragmented scenario over apath, if maximum continuous slice over a single path is 1 fora spectrum index ’i’ and half of the resources on that pathare available. If such a case exists for all the spectrum sliceindices, we get a worse case scenario for α as well as for the β .The best case scenario is when all the available slices/resourcesare available continuously and contiguously. Equations (4) and(5) present the range of α and β respectively. The resultant ofthese components give ν - or the vectored fragmentation metric(VFM) value in worst and best case scenarios. B. An example of fragmentation level calculation
In fig. 5, we have a 4-nodes 5-links network, with itsnetwork spectrum status. All the white blocks represent emptyor available spectrum slices. In this spectrum scenario theoccupancy level is 50 % .In the example, for the calculation of α -component theaverage ratio of maximum contiguous slot size to total avail-able spectrum slices is taken into account. In β -componentcalculation, a single longest path is taken into account whichcovers most of the source-destination pair routes. A single pathtraversing all of the links in 3-1-4-5-2 direction is consideredfor continuity calculation, hence P = 1. The routes of nearlyall the source-destination pairs are covered in this path. All thespectrum slice indices are having at least one available slice,in the given path, so E i = 8. In the example we calculate frag-mentation level using Vectored fragmentation metric (AVFM),and compare the level with a link-based external fragmentationmetric (L-EFM).The L-EFM considers the largest contiguous slot’s size ( CG i )in links, i ∈ L , to decide the fragmentation level. It is themost basic metric with the least complexity. It also tends toignore fragmentation due to smaller fragments present in thespectrum. The L-EFM formulation is given in equation 6. L − EF M = 1 − (cid:80) Li =1 CG i totalavailable (6) Fig. 5: An example for calculation of vectored- fragmentationmetric with 50 % occupancyThe α and β components for the above scenario are calcu-lated as follows. α = 15 . ( 23 + 23 + 35 + 23 + 46 ) = 0 . β = 18 ( 12 + 12 + 44 + 11 + 11 + 44 + 55 ) = 0 . ν = (cid:112) . + 0 . = 0 . V F M min = ν min = 0 . Normalized Vectored Fragmentation Metric (NVFM),
N V F M = ν norm = ν − ν min ν max − ν min = 0 . − . . − .
486 = 0 . AV F M = 1 − ν norm = 0 . L − EF M = 1 − − . In this particular example, the network spectrum utilizationis 50 % , that is half of the total wavebands are currentlyused. The corresponding normalized vectored fragmentationmetric (NVFM) value is around 0.547844. This means that amoderate fragmentation is present in the spectrum. If the ν (VFM) value is closer to √ (or ν norm (NVFM) is closerto 1), then fragmentation in the network spectrum is notsignificant. While comparing the VFM with other link-basedfragmentation metrics, we use the adapted form of VFM(AVFM), i.e., (1 − ν norm ) . This ensures that same meaningis conveyed effectively, that is low metric value means lowerlevel of fragmentation and vice versa. A direct relationshipbetween the network spectrum utilization and the fragmenta-tion level as vectored fragmentation metric is very unlikely,as the way in which the spectrum is occupied also plays apart. The fragmentation is lowest when there is small spectrumutilization and large spectrum utilization. For the midwayscenario, the metric essentially depends on the state of networkspectrum, and the relation between adjacent slices, not on thetotal number of slices. In the real time traffic scenario, thefragmentation level can vary for the same network spectrumutilization, when observed in steady state condition.We compare theoretical aspects of the vectored fragmenta-tion metric and the other metrics reported in the literature.The comparison allows us to put vectored fragmentation metric in perspective. The comparison is based on some ofthe essential characteristics as well as the complexity of themetrics. Table I compares link-based metric, path-based metricand the vectored metric using some key features such asthe ability to identify fragmentation scenario and the timecomplexity. The vectored fragmentation metric can outperformlink-based fragmentation metrics for fragmentation estimationat the network level with an additional computation cost whichis still less than that of any path-based fragmentation metric.In the simulation study of fragmentation indicator AVFM,we compare it with only link based metric, L-EFM. The L-EFM is the simplest representation of fragmentation level anddoes not have any pre-conditions. The L-EFM covers onlythe contiguity aspect, and thus, comparison with a continuitybased metric is pertinent in fragmentation study. C. Evaluation of the vectored fragmentation metric α -component presents the consolidated fragmentationof individual links, covering the fragmentation due tocontiguity constraint.2) β -component presents the consolidated fragmentation ona single slice index over a multi-hop path, covering thefragmentation due to continuity constraint.3) Both α and β -component can be accepted as a measureof fragmentation individually.4) The connectivity of multiple slices over a path in β -component is ignored here. We take the continuity andcontiguity as independent entities here.5) Higher is the value of the vectored fragmentation metric( ν or ν norm ), lower is the fragmentation in the networkspectrum.6) This metric is independent of any particular connectionrequest type.7) This is st level metric, as it takes into account only sin-gle slice index for the evaluation of continuity constraintfragmentation.8) When β -component is individually taken as a fragmenta-tion indicator, and we check continuity of n contiguousslices over a path, it becomes a n th -level metric.9) The computational complexity in finding fragmentationlevel in a network with N nodes, L links and S spectrumslices on each link, using Vectored fragmentation metricis O (2 .S.L ) .IV. R ESULTS AND D ISCUSSIONS
The table I presents a qualitative comparison between thelink-based, path-based, and vectored fragmentation metric. Tostudy the metrics quantitatively, we use the link-based andvectored fragmentation metric in a real-time traffic scenarioin some example networks. We consider three networks: Net-A with 7-nodes 12-bidirectional links, NSF network with 14-nodes 21-bidirectional links, and German network with 17-nodes 26-bidirectional links (table II). We generate connectionrequests, also called demands, on every node using Pois-son distributed arrival process and exponentially distributedholding time. At each node, the arrived connection requests’destinations are selected with equal probability from the
TABLE I: Comparison of fragmentation metrics
Characteristics
Link- based Path- based Vectored
Identifiesfully fragmented scenario No No Yes(Fig.3(d))Identifieszero fragmentation scenario Yes Yes Yes(Fig.3(a,b,c))Differentiates betweenfragmentation scenarios Some of them Yes Yes(Fig. 3(e)) Lowest among others High ModerateTime Complexity O ( S.L ) [17] O ( S.L ) - O ( S.L.G ) [17] O (2 .S.L ) General Observations 1. Ignores small fragments2. Can be relative orabsolute3. Covers only contiguityaspect 1. Specific to path of theconnection request2. Relative3. Covers contiguity andcontinuity aspect specific toconnection request 1. Covers all availablespectrum slices2. Absolute3. Covers both contiguityand continuity aspectindependently.
S is total number of spectrum slices, L is total number of Links and G is total number of permissible granularity of connection requests.
TABLE II: Network Scenarios for Evaluation of FragmentationMetrics in EONs
Properties
NET-A NSFNET GERMAN NET
Nodes 7 14 17Links 24 42 56Average Nodaldegree 3.42 3 3.05Paths, P ineqn.(2) 2 10 6 other nodes. We consider a randomly distributed bandwidthrequirement (in terms of spectrum slices) ranging from oneto some maximum permissible slices for each connectionrequest (including guard band). In the networks, each linkis considered to have 320 spectrum slices. We assume nowaveband conversion scheme at any intermediate node. Di-jkstra’s shortest path algorithm is used to find a route betweeneach source-destination pair. Thereafter, the spectrum sliceassignment is done according to the first-fit (FF) strategy. Incase, a connection request cannot be satisfied, it is dropped.We obtain all the results with a 99 % confidence interval byaveraging over multiple simulation runs.We analyze our fragmentation metric for steady-state andtransient-state scenarios for constant load condition. Thetransient-state starts from the initial empty network spectrumstate. The spectrum state changes with the arrivals and de-partures of connection requests and eventually settles to asteady-state. There is not much variation with time in thecharacteristics of the network spectrum in steady-state. Thesteady-state observations indicate normal operating status. Itdoes not give any insight into how the fragmentation shapesup in the spectrum with time. To analyze how fragmentationlevel changes with changing network state dynamics, we needto evaluate the fragmentation metric and other parameters inthe transient state. A. Simulation Results1) Transient-State Scenario:
We observed the transientstate parameters to understand their time evolution for three (a) (b)
Fig. 6: Evolution of fragmentation level with time for trafficloads (a) 50 E, and (b) 100 E in Net-A Network topology (a) (b)
Fig. 7: Evolution of fragmentation level with time for trafficloads (a) 50 E, and (b) 100 E in NSF Network topology (a) (b)
Fig. 8: Evolution of fragmentation level with time for trafficloads (a) 50 E, and (b) 100 E in German Network topology networks and two traffic load conditions of 50 Erlangs (lowload) and 100 Erlangs (high load). The maximum permissibleslice requirement by a connection request is sixteen. We startedfrom a completely available/ empty network. The connectionrequests arrive, set up, and finally released dynamically on thecompletion of their holding time. Some of them are blockedif set up is not feasible. We observed the evolution of averagenetwork spectrum utilization (Utilization in figs. 6, 7, 8), theaverage link-based external fragmentation metric (L-EFM), theaverage blocked requests to total requests ratio (BR/TR), andthe average adapted vectored-fragmentation metric (AVFM),i.e., (1- ν norm ), till the arrival of initial 5000 connectionrequests. We also observed average adapted- α (A-alpha) andadapted- β (A-beta) components as individual fragmentationindicators as defined by relations in eq.(1) and eq.(2)’s adaptedform. All the observed parameters increase initially with theincoming connection requests and then attain a steady-statevalue without any oscillatory behaviour, in all the graphs.For Net-A, at low load condition (fig.6(a)), A-beta (con-tinuity fragmentation) increases faster and remains slightlyhigher than A-alpha (contiguity fragmentation). For higherload conditions (fig.6(b)) also, A-beta increases faster andattains a steady state value. A-alpha increases relatively slowerbut exceeds the A-beta. This indicates at high load conditions,contiguity fragmentation is dominant factor. AVFM valuesalways lie in between A-alpha and A-beta. L-EFM value islower than AVFM but follows the same pattern. It can be alsoseen that L-EFM is lower than AVFM initially, but it becomesnearly equal to AVFM in steady-state. The network utilizationand BR/TR ratio also increases with time to attain a steady-state.For NSFNET and German network, we observed that A-alpha parameter changes at a faster rate and is the majorcontributor to fragmentation level (fig.7(a) and (b), fig.8(a)and (b)) for both the loading conditions. Here, in fig.7(a) and(b) for NSFNET, the L-EFM is greater than AVFM valueand it follows A-alpha (both being contiguity component)instead of AVFM. In fig.8(a) and (b), for German networkalso, L-EFM follows same pattern as A-alpha. L-EFM is lowerthan AVFM for some initial time and then crosses over theAVFM value. The reason could be contribution of A-betaand number of paths in AVFM. A-beta increases and attainssteady-state value quickly. In NSFNET and German networktopology, we consider multiple paths for A-beta calculation.The fragmentation on these paths is relatively low as thespectrum slices’ unavailability on a path is considered nofragmentation. A-beta increases initially and then is seen toslightly fall. The reason could be busy network resourcesthemselves on the selected paths.In the time evolution plots for the three network topologies,fragmentation level indicators, AVFM and L-EFM developgradually as expected. The transient state evolution of theAVFM allows us to reach a conclusion that A-alpha and A-beta together can be used to check the fragmentation level,considering some pre-defined parameters (like number of load or average load means traffic load at every node of the network,wherever mentioned paths and number of spectrum slices). Next, We observe theproposed AVFM’s performance for varying network loadingconditions, starting with A-alpha and A-beta dominance study.A-alpha dominates A-beta throughout the observation time forboth load conditions in NSFNET and German network. So,the network conditions affecting dominance of A-alpha andA-beta are also important.In A-beta, if the number of considered paths is large, thenthe fragmentation due to continuity is not significant, and theoutput is merely the availability of spectrum resources on apath. So, the A-beta may not be of significance dependingon whether the static or dynamic routing conditions areconsidered as discussed in section III A.The A-alpha and L-EFM are same in pattern, only theirvalues are different. L-EFM can be replaced by A-alpha aslink fragmentation indicator for smaller networks or networkswith multiple paths of shorter lengths. The smaller networkswill have paths with shorter length.
2) Steady-State Scenario:
In a transient-state, we estab-lished that AVFM in the network could follow fragmentationlevel development, just like L-EFM. But, there may be moreawareness of the two contributors, A-alpha and A-beta, inAVFM. Next, we studied AVFM elaborately in the steady-state. We first studied performance measures of A-alpha andA-beta over varying load conditions. We also studied the per-formance measure of AVFM for different connection requests’arrival rates, holding times, and the maximum permissiblegranularity range .In fig.9(a)-(c), we observe how the influence of A-alpha andthe A-beta as fragmentation level indicator vary for differentnetwork topologies. In Net-A, at low load traffic, A-beta isdominant than the A-alpha (A-alpha/A-beta <
1) for trafficload of 1 Erlang to 50 Erlangs. As already discussed, the A-beta influences the Net-A more due to fewer path and longerpath length consideration. The crossover point is when A-alphabecomes more than A-beta. For Net-A, the crossover pointoccurs at around 52 Erlangs. This crossover point arrives atlow load ( ≤ Erlangs ) in NSFNET and German networkbecause there are many paths for continuity test, and themajor contributor in them is contiguity fragmentation onindividual links. It can be seen in fig.9(b)-(c) that A-alphais the dominant component for a wide range of the averageload at nodes. It again implies that the A-alpha is sufficient totrack fragmentation for larger networks, where a more numberof the paths are needed for A-beta.There is one inconsistency in A-beta’s contribution also.Here, we check the continuity of the individual spectrumindex, and there may be a single slice available on each linkof the path but at the different indices. Then this type offragmentation goes unnoticed by the metric. However, thereis very little likelihood of this event, as it requires a veryhigh network utilization value (almost full use of networkspectrum). This situation can only arise when there may benon-uniform/irregular traffic distribution, creating a crunch ofavailable capacity. Also, there is no requirement of A-beta in afull mesh network topology with fixed routing. There will be labeled MaxDemand in related plots (a) (b) (c) Fig. 9: Ratio of A-alpha and A-beta vs traffic load in steady-state for (a) Net-A, (b) NSFNet, and (c) German topology fordifferent average holding times. (a) (b) (c)
Fig. 10: AVFM vs traffic load in steady-state for (a) Net-A, (b) NSFNET, and (c) German topology for different arrival rates(lambda).single link paths between all source-destination pairs, and theA-alpha component is sufficient to evaluate the fragmentationlevel.Fragmentation level depends on the network spectrum statuswhich in turn depends on the network traffic dynamics. Thevarying traffic dynamics could be the average arrival rate, theaverage holding time, or the MaxDemand (acceptable granu-larity) of connection requests. In fig.10(a)-(c), we consideredfour different arrival rates (lambda 1, lambda 10, lambda25, and lambda 50), each one with increasing holding timesto create varying load conditions. We observed that AVFMincreases with the traffic load. The maximum steady-statefragmentation level in Net-A is around 0.6, i.e., 60 percentfragmentation, for traffic load up to 100 Erlangs. In NSFNETand German network (fig.10(b)-(c)), the steady-state AVFMvalue varies from 0.55 to 0.6 for an average load of 40 Erlangstill 100 Erlangs. We observe that the steady-state AVFM valuedoes not change for a fixed load. So, varying the arrival rateand holding time for a fixed load will result in the samefragmentation level.We also observe that the maximum permissible slot sizeor granularity range of the incoming connection requests(MaxDemand) also affect the fragmentation level (fig.11(a)-(c)). The higher granularity range (MaxDemand 8 and 16)indicates more fragmentation as the arriving connection re-quests are more diverse and leave the spectrum disorganized.We observe this behavior in all the three network topologies.However, at very high loads, the fragmentation level for such range may fall due to the unavailability of network slicesfig.11(b)-(c).In fig. 12, we also record the correlation between frag-mentation level indicators and the normalized network spec-trum utilization. We start with a completely vacant networkspectrum (network utilization = 0.0) till the network spec-trum is fully or almost fully occupied (network utilization ≥ (a) (b) (c) Fig. 11: AVFM vs traffic load in steady-state for (a) Net-A, (b) NSFNet, and (c) German topology for different maximumdemand. (a) (b) (c)
Fig. 12: Fragmentation level indicators with network utilization for (a) NET-A, (b) NSFNET and (c) German Networkbeta-component is significant in a true fragmentation indicator.The beta-component affects the network fragmentation levelsignificantly; hence, it is better to consider the continuityfragmentation component in the overall analysis.V. C
ONCLUSION
There has not been any metric using both continuity andcontiguity aspect for network-level fragmentation in elasticoptical network spectrum to the best of our knowledge. Inthis work, we used the vectored fragmentation metric toquantify the fragmentation level in a network at some instant.This work has assessed a vectored fragmentation metric’s(AVFM) ability to capture continuity as well as contiguityfragmentation level in real-time network scenarios. We for-mulate the VFM to include st -level continuity fragmentationmetric for applications with a single slice requirement. Ifthere is significant fragmentation for low-bandwidth (singleslice) connection requests, it also represents a worst-casescenario for applications with large bandwidth requirements.We observed that fragmentation level evolves with time andnetwork spectrum status. We observed the AVFM, the L-EFM,the A-alpha, and the A-beta over time. The continuity (A-beta)and contiguity (A-alpha) aspects contribute significantly to theoverall fragmentation level. We also observe how the A-betalevel is more at low traffic load, and the A-alpha surpassesit at some cross over point as load increases. The othernetwork characteristics like arrival rate and the connectionrequests’ granularity range also contribute to fragmentationmetric (AVFM). We have also studied the correlation betweenthe network spectrum utilization and fragmentation level. It is worth noting that AVFM captures the essence of fragmentationin empty as well as in fully utilized network spectrum moreaccurately than L-EFM.In future work, we plan to investigate the effectiveness ofthis metric in triggering the defragmentation procedure. Wealso plan to utilize the proposed vectored fragmentation metricin the joint Routing and Spectrum Provisioning (RSA). It canbe used in optimizing routing decisions and slot selectionsto efficiently use the spectral resources. The work can be ex-tended to include the number of paths in continuity assessmentand the multiple slices based continuity fragmentation. Theindividual components (multi-level fragmentation indicators)of the vectored fragmentation metric can be moulded to act asthe application-specific indicators.R Journal of Lightwave Technology , vol. 35, no.5, pp. 1116-1124, March, 2017.[4] Masahiko Jinno, Hidehiko Takara, Bartlomiej Kozicki, Yukio Tsuk-ishima, Yoshiaki Sone, and Shinji Matsuoka, ”Spectrum-efficient andscalable elastic optical path network: Architecture, benefits and enablingtechnologies”,
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