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Physical and logical topology design of large-scale optical networks

Physical and logical topology design of large-scale optical networks
Physical and logical topology design of large-scale optical networks

On the Physical and Logical Topology Design of Large-Scale Optical Networks Yufeng Xin,George N.Rouskas,Senior Member,IEEE,and Harry G.Perros,Senior Member,IEEE

Abstract—We consider the problem of designing a network of optical cross-connects(OXCs)to provide end-to-end lightpath ser-vices to large numbers of label switched routers(LSRs).We present a set of heuristic algorithms to address the combined problem of physical topology design(i.e.,determine the number of OXCs re-quired and the fiber links among them)and logical topology de-sign(i.e.,determine the routing and wavelength assignment for the lightpaths among the LSRs).Unlike previous studies which were limited to small topologies with a handful of nodes and a few tens of lightpaths,we have applied our algorithms to networks with hun-dreds or thousands of LSRs and with a number of lightpaths that is an order of magnitude larger than the number of LSRs.In order to characterize the performance of our algorithms,we have devel-oped lower bounds which can be computed efficiently.We present numerical results for up to1000LSRs and for a wide range of system parameters such as the number of wavelengths per fiber, the number of transceivers per LSR,and the number of ports per OXC.The results indicate that it is possible to build large-scale optical networks with rich connectivity in a cost-effective manner, using relatively few but properly dimensioned OXCs.

Index Terms—Genetic algorithms,large-scale optical networks, topology design,wavelength-division multiplexing(WDM).

I.I NTRODUCTION

T HE wide deployment of point-to-point wavelength-di-vision-multiplexing(WDM)transmission systems in the Internet infrastructure has enhanced the need for faster switching at the core of the network.The corresponding mas-sive increase in network bandwidth due to WDM has occurred in conjunction with a growing effort to modify the Internet Protocol to support different levels of quality-of-service(QoS). Label switching routers(LSRs)supporting multiprotocol label switching(MPLS)[1]are being deployed to address these two issues.On one hand,LSRs simplify the forwarding function, thereby making it possible to operate at higher data rates. On the other hand,MPLS enables the Internet architecture, built upon the connectionless Internet Protocol,to behave in a connection-oriented fashion that is more conducive to supporting QoS.

The rapid advancement and evolution of optical technologies makes it possible to move beyond point-to-point WDM trans-mission systems to an all-optical backbone network that can

Manuscript received May16,2002;revised September27,2002.This work was supported by the NSF under grant ANI-9805016.

Y.Xin is with MCNC,Research Triangle Park,NC27709-2889USA.

G.N.Rouskas and H.G.Perros are with the Department of Computer Science,North Carolina State University,Raleigh,NC27695USA(e-mail: rouskas@https://www.wendangku.net/doc/4c7756127.html,;hp@https://www.wendangku.net/doc/4c7756127.html,).

Digital Object Identifier10.1109/JLT.2003.810075take full advantage of the available bandwidth by eliminating the need for per-hop packet forwarding.Such a network consists of a number of optical cross connects(OXCs),arranged in some arbitrary topology,and provides interconnection to a number of LSRs.Each OXC can switch the optical signal coming in on a wavelength of an input fiber link to the same wavelength in an output fiber link.The OXC may also be equipped with con-verters that permit it to switch the optical signal on an incoming wavelength of an input fiber to any wavelength on an output fiber link.The main mechanism of transport in such a network is the lightpath,which is a communication channel established between two OXCs or two LSRs and which may span a number of fiber links(physical hops).If no wavelength converters are used,a lightpath is associated with the same wavelength on each hop.This is the well-known wavelength continuity constraint. Using converters,a different wavelength on each hop may be used to create a lightpath.Thus,a lightpath is an end-to-end op-tical connection established between two LSRs.

Currently,there is tremendous interest within both the industry and the research community in optical networks of OXCs.The Internet Engineering Task Force(IETF)is investigating the use of generalized MPLS(GMPLS)[2]to set up and teardown lightpaths.GMPLS is an extension of MPLS that supports multiple types of switching,including switching based on wavelengths usually referred to as multiprotocol lambda

switching

lightpaths.Routing and wavelength assignment involves map-ping lightpaths onto the physical topology and assigning wave-lengths to these lightpaths.The reader is referred to[4]for a gen-eral analysis of various formulations and solution approaches to the above problems.Most of the work in the open literature fo-cuses on the configuration design and the RW A problems under the assumption of a fixed fiber physical topology.That is,given a network traffic demand and a physical network topology,an optimal network configuration,a best virtual topology,and an optimal routing and wavelength assignment are obtained.In the case in which the set of lightpaths is also given,the problem is reduced to a pure RW A problem,which can be further decom-posed into a routing sub-problem and a wavelength assignment sub-problem.

The design of virtual topologies has been studied extensively. Constrained by the limited number of available wavelengths and the available number of transceivers,it may not be pos-sible to establish a lightpath between every pair of nodes.Con-sequently,only a selected set of nodes can be connected by lightpaths,leading to a virtual topology over the given physical network.In a virtual topology,the nodes correspond to actual physical network nodes,while the links correspond to light-paths.A review of algorithms for virtual topology design can be found in[5].

Typically,the network design problem under a given phys-ical topology can be formulated as an integer programming(IP) problem with the objective of optimizing a performance metric of interest.This IP problem has been shown to be NP-hard,and several heuristic algorithms have been proposed in the literature. These algorithms differ in their assumptions regarding the traffic demands,as well as in the performance metric used.Specifi-cally,for the case of static traffic,i.e.,when all the connections are known and they are static,the objective is typically to min-imize network resource usage.In the case where the number of fibers is limited,the objective is usually to minimize the total number of wavelengths needed in the network.A linear pro-gramming relaxation technique to obtain the optimal solution for the RW A of a WDM ring network was proposed in[6],while a longest-lightpath-first heuristic was developed in[7]as an ap-proximate solution to the RW A problem for a mesh network.In the case of a limited number of wavelengths per fiber,[8]pro-vided an iterative scheme to minimize the costs associated with the working fibers for provisioning a static set of lightpaths on a given WDM network topology.A lightpath accommodation heuristic for a given set of lightpaths was developed to mini-mize the total number of OXC ports(another important network resource)in[9].A general IP model for the virtual topology de-sign was presented in[10],and a branch-and-bound algorithm to minimize the average lightpath length was described.

The design of a virtual topology was first formulated as an integer linear programming(ILP)problem in[11],where a heuristic algorithm combining simulation annealing and flow deviation was presented to minimize the delay and the maximum flow in a link.A genetic algorithm to calculate the optimal virtual topology and RW A to minimize the average signal delay was developed in[12].An upper bound on the maximum carried traffic for any routing and wavelength algorithms are adapted from Dijkstra’s shortest path algo-rithm[4],[12],[14].The wavelength assignment problem is equivalent to a graph coloring problem,and[15]adopted a known heuristic algorithm to solve it.The RW A problem for a multi-fiber network under dynamic traffic was solved in[14] using the layered-graph heuristic model.

The physical topology design problem has also received some attention.The relationship between the number of wavelengths needed and some topology parameters,such as connectivity, nodal degrees,and average hop distance,was studied in[16], [17]through simulation.A bound on the number of wavelengths given the connectivity requirements of the users and the number of switching states was derived in[18].Simple approximate equations for the scaling properties of the number of wave-lengths,the nodal degree,the total fiber lengths,and the max-imum number of transit nodes of a lightpath were given in[19]. An analytical solution of the RWA problem for some regular topologies,such as shuffle and tori was carried out in[20],[21]. In this paper we consider the problem of designing large-scale optical WDM networks of OXCs that provide end-to-end light-path services.The scale of the optical backbone network is char-acterized by the number of LSRs using its services and the number of lightpaths that it can support.We are interested in typical national or international networks,in which the number of LSRs can be in the hundreds or thousands,and the number of lightpaths that need to be established can be an order of mag-nitude greater than the number of LSRs.Given the number of LSRs,the number of wavelengths per fiber link,and a set of physical constraints(such as the number of transceivers at each LSR and the number of input–output ports at each OXC),we address both the physical topology design problem(i.e.,the number of OXCs required and their interconnectivity)and the routing and wavelength assignment.We assume no wavelength conversion in the network.Since the problem is NP-hard,we present a set of heuristic algorithms to obtain a near-optimal so-lution in terms of the number of required OXCs,including a genetic algorithm to search the space of physical topologies. While some of the problems we consider have been studied earlier,our work differs from previous studies in several impor-tant ways.To the best of our knowledge,this is the first time that the problem of designing the physical and logical topology of a wavelength-routed network is fully formulated and solved. Also,whereas previously published algorithms have been ap-plied to relatively small networks(e.g.,10–20-node topologies such as the NSFNet and the Arpanet)with few(less than100) lightpaths,we consider large-scale networks of realistic size.We provide new insight into the design of WDM backbone networks by investigating the effect of various system parameters;again, we use realistic ranges for the values of these parameters,e.g., up to128wavelengths and up to24optical interfaces per LSR. Finally,we obtain lower bounds for the optimization problem and present results which indicate that our heuristics are close to optimal.

We now summarize some of the results of our study.The most important finding is that it is possible to build cost-effec-tive optical backbone networks that provide rich connectivity among large numbers of LSRs with relatively few,but properly

creases linearly with the number of attached LSRs,but the rate of the increase is rather slow.We also find that,in order to take advantage of an increasing number of wavelengths,the number of OXC ports must increase correspondingly.Otherwise,using additional wavelengths has little effect on the number and topology of OXCs required for a given number of LSRs.This result,coupled with the fact that the number of wavelengths in a fiber is expected to continue to increase in the foreseeable future,has implications on the OXC technology and design.For instance,our results indicate that 3-D MEMS switches which can scale to large port sizes would be more appropriate than 2-D MEMS switches which are limited to small port sizes [22].Finally,we also find that it is possible to enhance the degree of connectivity among the LSRs by a large factor (through a corresponding increase of the number of optical interfaces at each LSR)with a relatively small incremental cost in terms of additional OXCs and fiber links among them.

In Section II we describe the problem we study as well as the assumptions we make,and in Section III we present an overview of our solution approach.In Section IV ,we present the heuristic algorithms for generating a 2-connected graph,routing lightpaths,and assigning wavelengths.We also describe the ge-netic algorithm used for searching the space of physical topolo-gies.We develop lower bounds for the optimization problem in Section V .We present numerical results in Section VI,and we conclude the paper in Section VII.

II.P ROBLEM D EFINITION

We consider a

number

optical

transceivers,and therefore,it may establish at

most

wavelengths,and that each

OXC has

exactly

represents the number of fiber links interconnecting

the OXCs.

Parameter

value around 0.3.

The fundamental question we address in this paper is:What is the minimum

number

:because

of (1),for a given value

of

of OXCs will also minimize the number of fiber links.

Since

of LSRs but also the traffic requirements (i.e.,the number of lightpaths between pairs of LSRs),the survivability proper-ties of the network,etc.In fact,different service providers may well have different and even conflicting requirements for their networks.Rather than trying to account for all possible design requirements,we are instead interested in providing a general framework that can help us answer the above question in a way

that can provide practical guidelines for

building

net-works.We therefore set the following requirements R1–R5that

the

network we design must satisfy.We believe that this list captures the salient features of the network and is sufficiently general to accommodate the requirements of a wide range of network providers.

R1.Each LSR accesses the backbone using two bidirec-tional fiber links,one to each of two different OXCs;both links are used for carrying traffic to and from each LSR.R2.The physical topology of the OXCs is 2-connected.R3.Each LSR

maintains

outgoing

and

III.S OLUTION A PPROACH

Our objective is to determine the optimal physical topology of OXCs for establishing the given

set

that can be supported in each fiber.This involves

determining the minimum number of OXCs required as well as the links interconnecting the OXCs.Because of the difficulty of this problem,we choose an indirect approach to obtaining a near-optimal physical topology.Specifically,we first assume that the

number

of OXCs

is given.Our objective then is to obtain

1)the set of fiber links interconnecting

the

LSRs

such that the required number of wavelengths per fiber link in the physical topology is minimized.The inputs to the problem are:the number of

OXCs,

represents the

number of lightpaths that have to be established between

OXCs

,.This traffic matrix is derived di-rectly from the lightpath

set

and

LSR .

This problem can be formulated as an integer linear program-ming problem (ILP).The formulation,which is reported in [24],is similar to the ILP formulation of the logical topology design problem developed in [25],with additional constraints that cor-respond to the physical topology design subproblem (while [25]considers the physical topology as part of the input,in our case the physical topology design is part of the problem).The solu-tion to this ILP gives an optimal topology

for

actually supported

by the fiber links of

the

network.

If .However,

if

of OXCs that was given as input

to the problem.By solving the same problem with a larger value

of

as input in the hope of finding such a

solution.

1

The above observations naturally lead to a binary search ap-proach to obtaining a solution that requires no more

than

,2)routing of lightpaths,and

3)assignment of wavelengths to lightpaths.Each of these tasks is solved using a heuristic algorithm.We then use a genetic algorithm (GA)to generate additional feasible physical topologies,and we iterate in order to obtain a near-optimal solution with a minimum total number of wavelengths.A.Generation of a Random Feasible Physical Topology Recall that a feasible OXC network is at least 2-connected.In order to get a feasible topology,we first generate a random tree,then grow a 2-connected graph from it.If we number the leaves of the tree

as

nodes,where each node represents one of

the OXCs.

We have adopted the method from [26]to generate a random tree

of

.Consider a

tree

in some manner.To obtain its Prufer

number

,we start with a null Prufer number (one with no digits)

and we repeat the following steps to

build

by appending one digit at a time to the right of the current Prufer number.Let

be the parent

of

becomes the rightmost digit

of .We remove .If ,t h e

n

the number of M of OXCs in any optimal solution that uses a larger number (less than W )of wavelengths.After extensive numerical experiments,we have

Fig.1.(a)Tree of 8nodes corresponding to the Prufer number 666585.(b)Resulting 2-connected graph.

The reverse process of obtaining a tree from a Prufer

number

with consists of these steps.First,designate all nodes whose number does not appear

in

as eligible .Let be the leftmost digit

of .Add the edge

and remove the leftmost

digit

does not occur anywhere in what remains

of

,then

designate

,still eligible.Add

and stop.

Since there are exactly

,the final

graph

edges;it is also shown in [26]

that

digits in the range

1–8).Nodes 1,2,3,4,and 7do not appear

in

and are designated as eligible for consideration.Node 1is the lowest numbered eligible node,and digit 6is the leftmost digit of the Prufer number.Consequently,we add the edge (6,1)to the tree,we make node 1ineligible,and we remove the leftmost digit 6from the Prufer number.The remaining Prufer number is thus 66585,and since digit 6appears in it,node 6is not made eligible.In the second step,node 2is the lowest numbered eligible node and digit 6is the leftmost digit in the remaining Prufer number.We add edge (6,2)to the

tree

of OXCs,randomly generate

2)Generate a

tree

OXCs,as well as a set of lightpaths between pairs

of OXCs that need to be established.We now present two algo-rithms,one to route each lightpath over a physical path of fiber links,and another to assign wavelengths to the lightpaths.Note that we treat the routing and wavelength assignment subprob-lems independently;this approach may require a larger number of wavelengths than a combined solution,but the latter is in-tractable while our approach can be applied directly to networks of realistic size.Furthermore,as we shall see,the routing algo-rithm takes into account the number of lightpaths using each link in order to minimize the number of wavelengths needed.We use Dijkstra’s shortest path algorithm to route the set of lightpaths over the given physical topology.In order to minimize the number of wavelengths used on a physical link,we use two heuristic approaches.First,the link weight used in Dijkstra’s al-gorithm is dynamically adjusted to reflect the number of wave-lengths already allocated on each link.Consider physical

link

is a tunable weight parameter.This cost function forces new lightpaths to be routed over less congested links in the physical topology,reducing the total number of wavelengths used in the network.For the next application of the algorithm,

quantities

nodes with higher degrees.This method results to a consider-

ably lower wavelength usage than when selecting the nodes ran-

domly.This is because nodes with smaller degrees have fewer

alternative links to route their lightpaths.In view of this,routing

lightpaths originating or terminating at these nodes first will in-

crease the wavelength use of their links.Because of the cost

function described above,later lightpaths will tend to avoid the

links around these nodes.On the other hand,if a node with a

small degree was considered late in the process,its lightpaths

would have to use one of its links regardless of how congested

these links were,potentially increasing the overall number of

wavelength required.We refer to this scheme as the smallest-de-

gree-first-routing(SDFR)algorithm.The following steps sum-

marize the heuristic algorithm for routing lightpaths.

1)Use the link weight function

of OXCs is given,we define our solution space as

the set of feasible physical topologies on

and the edges of the graph from0

to

and

.The solution is encoded

into a chromosome(i.e.,a bit string of length)as

follows.Each edge is represented by a bit in the bit string.If the

edge exists,the bit is set to1;otherwise it is set to0.The position

of the bit representing an edge is given by the edge index

(i.e.,

the smaller the number of wavelengths,the higher the fitness

value).This number of wavelengths is obtained by running the

routing and wavelength assignment heuristic algorithms on this

(a)(b)

Fig.2.(a)Physical topology with six nodes.(b)Its adjacency matrix.

GA parameters.The performance of a GA is determined by

the right choice of control parameters:the crossover rate

,and the population size,

,and.We use the

following operations to generate an offspring from the parent

generation until we get a new generation of the population size

.Therefore,we run the fol-

lowing four tests for each generated offspring.

1)Check the nodal degree of each node to make sure that the

constraint on the number of ports per OXC is satisfied.

2)Check if the total number of edges of the generated graph

exceeds the given number of edges determined by the

connectivity

that

is the number of LSRs,and

ning time of the algorithm as a function of the amount of traffic

storm集群的自适应调度算法

Adaptive Online Scheduling in Storm Leonardo Aniello aniello@dis.uniroma1.it Roberto Baldoni baldoni@dis.uniroma1.it Leonardo Querzoni querzoni@dis.uniroma1.it Research Center on Cyber Intelligence and Information Security and Department of Computer,Control,and Management Engineering Antonio Ruberti Sapienza University of Rome ABSTRACT Today we are witnessing a dramatic shift toward a data-driven economy,where the ability to e?ciently and timely analyze huge amounts of data marks the di?erence between industrial success stories and catastrophic failures.In this scenario Storm,an open source distributed realtime com-putation system,represents a disruptive technology that is quickly gaining the favor of big players like Twitter and Groupon.A Storm application is modeled as a topology,i.e. a graph where nodes are operators and edges represent data ?ows among such operators.A key aspect in tuning Storm performance lies in the strategy used to deploy a topology, i.e.how Storm schedules the execution of each topology component on the available computing infrastructure.In this paper we propose two advanced generic schedulers for Storm that provide improved performance for a wide range of application topologies.The?rst scheduler works o?ine by analyzing the topology structure and adapting the de-ployment to it;the second scheduler enhance the previous approach by continuously monitoring system performance and rescheduling the deployment at run-time to improve overall performance.Experimental results show that these algorithms can produce schedules that achieve signi?cantly better performances compared to those produced by Storm’s default scheduler. Categories and Subject Descriptors D.4.7[Organization and Design]:Distributed systems Keywords distributed event processing,CEP,scheduling,Storm 1.INTRODUCTION In the last few years we are witnessing a huge growth in information production.IBM claims that“every day,we create2.5quintillion bytes of data-so much that90%of the data in the world today has been created in the last two Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for pro?t or commercial advantage and that copies bear this notice and the full citation on the?rst page.To copy otherwise,to republish,to post on servers or to redistribute to lists,requires prior speci?c permission and/or a fee. DEBS’13,June29–July3,2013,Arlington,Texas,USA. Copyright2013ACM978-1-4503-1758-0/13/06...$15.00.years alone”[15].Domo,a business intelligence company, has recently reported some?gures[4]that give a perspective on the sheer amount of data that is injected on the internet every minute,and its heterogeneity as well:3125photos are added on Flickr,34722likes are expressed on Facebook, more than100000tweets are done on Twitter,etc.This apparently unrelenting growth is a consequence of several factors including the pervasiveness of social networks,the smartphone market success,the shift toward an“Internet of things”and the consequent widespread deployment of sensor networks.This phenomenon,know with the popular name of Big Data,is expected to bring a strong growth in economy with a direct impact on available job positions;Gartner says that the business behind Big Data will globally create4.4 million IT jobs by2015[1]. Big Data applications are typically characterized by the three V s:large volumes(up to petabytes)at a high veloc-ity(intense data streams that must be analyzed in quasi real-time)with extreme variety(mix of structured and un-structured data).Classic data mining and analysis solutions quickly showed their limits when faced with such loads.Big Data applications,therefore,imposed a paradigm shift in the area of data management that brought us several novel approaches to the problem represented mostly by NoSQL databases,batch data analysis tools based on Map-Reduce, and complex event processing engines.This latter approach focussed on representing data as a real-time?ow of events proved to be particularly advantageous for all those appli-cations where data is continuously produced and must be analyzed on the?https://www.wendangku.net/doc/4c7756127.html,plex event processing engines are used to apply complex detection and aggregation rules on intense data streams and output,as a result,new events.A crucial performance index in this case is represented by the average time needed for an event to be fully analyzed,as this represents a good?gure of how much the application is quick to react to incoming events. Storm[2]is a complex event processing engine that,thanks to its distributed architecture,is able to perform analytics on high throughput data streams.Thanks to these character-istics,Storm is rapidly conquering reputation among large companies like Twitter,Groupon or The Weather Chan-nel.A Storm cluster can run topologies(Storm’s jargon for an application)made up of several processing components. Components of a topology can be either spouts,that act as event producers,or bolts that implement the processing logic.Events emitted by a spout constitute a stream that can be transformed by passing through one or multiple bolts where its events are processed.Therefore,a topology repre-

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