Distributed Grooming, Routing, andWavelength Assignment for Dynamic

Optical Networks Using AntColony Optimization

X. Wang, M. Brandt-Pearce, and S. Subramaniam

Abstract—The physical resource assignment problem indynamic optical networks, often referred to as the routingand wavelength assignment problem, is very important forthe development of optical transport networks. Researchhas been done to optimize this operation so that the overallconnection blocking can be minimized. Traffic groomingadds another dimension to this problem by introducingopportunities for multiplexing low-bit-rate traffic into ahigh-bit-rate stream. The ant colony optimization (ACO)algorithm is a metaheuristic method that is inspired bythe foraging behavior of ants and has been widely imple-mented in solving discrete optimization problems. Thispaper proposes an ACO to solve the grooming, routing,and wavelength assignment problem. Unlike previouswork, our work includes considerations of mixed line rate,physical impairments, and traffic grooming functionality.Comprehensive simulation tests show how variations onthe ACO algorithms’ implementation affect performance.A comparison is made between this distributed algorithmand a centralized algorithm that we propose, a groomingadaptive shortest path algorithm (GASP). Although GASPshows better efficiency in terms of blocking probability,ACO shows great robustness and adaptivity to varyingnetwork and traffic conditions.

Index Terms—Ant colony optimization; Distributed andcentralized algorithms; Physical impairments; Routingand wavelength assignment; Traffic grooming; Transmis-sion reach constraint; Transport optical networks.

I. INTRODUCTION

C ompared to their electronic counterparts, fiber-opticnetworks havemany benefits, such as wide spectrum,

low electronic interference, low attenuation, and low cost.Wavelength division multiplexing (WDM) and densewavelength division multiplexing (DWDM) increase theefficiency of spectrum usage. They have therefore beenwidely deployed in long-haul core networks that often cover

the whole continent. However, the capacity of fiber-opticnetworks to carry huge amounts of traffic simultaneouslystill has not met the continuously growing traffic demandfrom the Internet, high-definition teleconferencing, re-search data transport, etc. While adding more fibers andimplementing higher-order modulation that increasesspectrum efficiency may solve the problem, a completeoverhaul of the existing structure is obviously not economi-cally practical. This implies the need for an improvedalgorithm featuring more intelligent planning and man-agement to accommodate dynamic traffic demands; yetbackward compatibility is needed for next-generationdesign. This backward compatibility goal requires mixed-line-rate (MLR) fiber-optic networks, where on each fiberthe wavelength channels can have different data rates.Furthermore, for long-haul optical networks, physicalimpairments such as noise, attenuation, dispersion, andnonlinear effects are critical and not negligible. In thispaper, we propose a real-time resource assignment algo-rithm that fits these practical requirements to improvethe performance of dynamic-access fiber-optic networksin terms of blocking probability.

Algorithms that plan and manage the assignment ofphysical resources to traffic demands in wavelength rout-ing networks are called routing and wavelength assign-ment (RWA) algorithms. With an expansion that allowslow-bit-rate substreams to be multiplexed into higher-bit-rate streams (i.e., traffic grooming), the algorithm is re-ferred to as grooming, routing, and wavelength assignment(GRWA). Traffic grooming introduces a cost-efficient bal-ance between network capacity increase and initial capitalexpenditure (CapEx). It also exhibits a dramatic improve-ment in adaptivity for heterogeneous traffic patterns.

Much research has been devoted to addressing theGRWA problem [1–4]. Solutions can be categorized fromseveral perspectives. For the design phase, a deterministictraffic matrix is assumed to reflect current and foreseen fu-ture evolving trends, and GRWA aims to minimize the totalCapEx of the networks, the so-called offline or static designproblem. For the network operation phase, in which a cer-tain existing network structure and deployment of equip-ment are assumed, GRWA aims to minimize the trafficdemand that cannot be served due to shortage of networkhttp://dx.doi.org/10.1364/JOCN.6.000578

Manuscript received January 8, 2014; revised April 25, 2014; acceptedApril 26, 2014; published May 30, 2014 (Doc. ID 204096).

X. Wang and M. Brandt-Pearce (e-mail: mb‑p@virginia.edu) are with theCharles L. Brown Department of Electrical and Computer Engineering,University of Virginia, Charlottesville, Virginia 22904, USA.

S. Subramaniam is with the Department of Electrical and ComputerEngineering, The George Washington University, Washington, DC 20052,USA.

578 J. OPT. COMMUN. NETW./VOL. 6, NO. 6/JUNE 2014 Wang et al.

1943-0620/14/060578-12$15.00/0 © 2014 Optical Society of America

resources (or maximize the total accepted traffic demand).1

The network operational algorithms are important be-cause, unlike assumptions made for static design wheretraffic arrives synchronously, in real-time networks trafficis highly dynamic, which then leads to a highly dynamicnetwork state (e.g., channel availability, optical equipmentusage, etc.). Based on the network state, dynamic GRWAoptimization needs to accommodate new and unpredictableconnection requests.

Dynamic GRWA algorithms can be categorized intocentralized control algorithms and distributed algorithms.In centralized control algorithms, either a central node col-lects global network state information and calculates theoptimal GRWA, or global information is broadcast to allnodes and each node makes its GRWA decision based onthe broadcast information. In distributed algorithms, eachnode makes its GRWA decision based on limited informa-tion that involves only neighboring nodes and a limitednumber of nodes along the lightpath. Although centralizedalgorithms often benefit from global information and yieldbetter GRWA solutions, a distributed algorithm may bepreferable when information sharing is limited (e.g., multi-domain information segregation). Because distributedalgorithms do not require a central node or control messageflooding (current popular routing algorithms require net-work state information disseminated throughout the entirenetwork whenever its state changes), they benefit fromquick connection setup and control information isolation.Also, distributed algorithms show improved scalability inthe case of network expansion or multiple domains. In thispaper, we compare a highly optimized distributed algo-rithm to a centralized algorithm and show the differencein their blocking performance.

Ant colony optimization (ACO) is a metaheuristicmethod inspired by ants’ foraging behavior in nature.“Real” ants are able to find the shortest path between theirnest and a food source. This behavior is a fundamental com-binatorial optimization problem—optimization based onvarying certain parameter(s) to maximize the goodnessof the solution. Ant colonies achieve this goal with simpleindividual agent complexity and limited indirect interac-tion. Colorni et al. first proposed the ACO algorithm forsolving the traveling salesman problem after noticingant colonies’ capability [5]. ACO has been widely appliedto solving RWA problems in optical networks. For opticalpacket-switched networks, Di Caro and Dorigo proposedan algorithm named AntNet [6]. Pedro et al. proposed anACO algorithm that solves the RWA problem for opticalburst-switched networks [7]. Garlick and Barr [8] andNgo et al. [9] implemented an ACO on the dynamic RWAproblem, in which path length and wavelength availabilityare used to measure the goodness of lightpaths. Bhaskaranet al. also solved the dynamic RWA problem using ACOwith separate ants during the RWA selection phase to test

whether the previously collected information is still up todate [10]. Kim et al. designed an ACO model to includemultiple virtual subcolonies of ants, where each subcolonyholds a different quality-of-service (QoS) requirement [11].Mapisse et al. created a variation of ACO that launches ad-ditional child ants to perform a local search based on thesolutions found at that point [12]. Wang et al. implementedan ACO to solve the routing and spectrum assignment(RSA) problem for elastic optical networks [13]. Pavaniand Waldman proposed to extend AntNet in order to solvenetwork restoration problems for WDM networks [14].

To the best of our knowledge, no ACO algorithm has beenproposed to handle traffic grooming and physical impair-ment issues before. In Li et al. [15], although they claimtheir ACO includes traffic grooming, it is not included inthe ACO mechanism but only considered when lightpathsare constructed. Physical impairments, which are not con-sidered in the previous literature, are critical in long-haul fiber-optic networks since they affect the quality oftransmission (QoT); therefore, they should be included inthe ACO as well. In this paper we expand on the techniquewe propose in [16] that shows physical impairments andtraffic grooming can be incorporated directly in ACO;dynamically varying parameters can adapt to the trafficcharacteristics, and the optimization of parameters showsthe desired balance between performance and controloverhead.

In most previous ACO work such as [6–10], shortestpath routing (SP) and adaptive shortest path routing(ASP) are used to compare with ACOs. Since a centralizedalgorithm that includes physical impairments and trafficgrooming does not seem to exist in the literature, we alsopropose an algorithm that we call the grooming adaptiveshortest path algorithm (GASP). It incorporates thenetwork state (with traffic grooming information) into adynamic logical topology and optimizes over globalinformation.

In order to deploy ACO, a comprehensive analysis of theeffect of various parameters, not considered in [16], is nec-essary. Our simulations show insight into the performanceof ACO in solving GRWA for fiber-optic networks. Althougha great amount of research has been done on how toimplement ACO in solving the RWA problem for opticalnetworks, not much work has been done on how to config-ure the ACO system to optimize the process itself. Despitethe fact that there are some general guidelines on how dif-ferent configurations affect ACO behavior, when imple-menting ACO for a particular task, such as GRWA, theproblem needs to be put into that unique perspective todetermine how the eventual solution is affected by variousconfigurations. This paper aims to investigate this rela-tionship in depth.

The paper is organized as follows: Section II discusses thenetwork on which we test our algorithm and its main char-acteristics. Section III explains the details of our ACO algo-rithm and its innovation over previous ACO algorithms. InSection IV we propose the ASP algorithm with trafficgrooming. Section V includes comprehensive simulationresults that compare the algorithm with other algorithms

1Connection blocking probability is an important measure for quality of ser-vice for network operators. Although the practical requirement of blockingprobability is quite strict, for the purpose of examining GRWA algorithms, acomparison over a relatively wider range of blocking probabilities showsperformance differences.

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and show how different system configurations affect net-work performance. Finally, Section VI concludes the paper.

II. NETWORK DESCRIPTION

In this section we introduce the network topology onwhich we apply the ACO. The scale of the network andpractical physical constraints (physical impairments,wavelength capacities) and technologies (mixed line rates,regeneration, traffic grooming) affect many aspects of theACO implementation.

For long-haul fiber-optic networks, such as NSF-24shown in Fig. 1, end-to-end connections can be as longas 6000 km. Connections are often for high throughput(from 10 to 100 Gbps). As optical signals with such highbit-rates travel through long distances, they often sufferfrom physical impairments, such as noise, attenuation,dispersion, and nonlinear effects. These impairments, bynature, accumulate along the path and therefore becomemore severe in long-haul optical networks than in regionalnetworks. They critically affect the QoT of the received sig-nal and cannot be ignored in long-haul networks [17,18]. Inorder to maintain an acceptable QoT, often measured bythe bit error rate (BER) upper bounded by 10−3 (beforefront-end error control coding), optical signals need to beregenerated along their path.

Regeneration usually includes three functions: reampli-fication, reshaping, and retiming (3R). Regeneration doneentirely in the optical domain is still in the research phaseof development; currently, regeneration requires signals tobe converted to the electrical domain, be regenerated, andthen be converted back to the optical domain after regen-eration [the optical–electrical–optical conversion (OEO)].This process involves high-speed electronic devices thatare expensive and become a major cost of the fiber-opticnetworks. Therefore, this operation should be reduced toa minimum. A network designed to minimize the numberof regenerators, called a translucent network, is equippedwith OEO regenerators only at some nodes. A network withregeneration available on all nodes is called an opaquenetwork, and the other extreme, a network with no regen-

eration capability, is called a transparent network. Fortranslucent networks, this sparse regenerator usageshould be incorporated in the GRWA algorithms, as weshow in the description of our ACO algorithm below.

Since the severity of the physical impairments dependsprimarily on the distance that the signal travels, an accept-able QoT is linked to the distance that the signal can travelwithout the need for regeneration, which is called thetransmission reach (TR). Within the TR, signals are ableto maintain acceptable QoT in optical form. Althoughthe TR depends on many factors, such as the signal launchpower, modulation schemes, and neighboring traffic, it canbe approximated based on common assumptions. In [19],the authors determined that for 10 Gbps signals, the TRis over 5000 km (which applied to the scale of the NSF net-work can be considered as unlimited), for 40 Gbps the TR isabout 2500 km, and for 100 Gbps it is about 2000 km.

As networks evolve, one important requirement is tomake networks backward compatible. The legacy 10 Gbpsfiber-optic networks are well equipped. So the process ofincreasing channel data rates therefore leads to the coex-istence of several line rates on a single fiber. Such networksare called MLR networks [20]. In MLR networks, differentchannels have different susceptibility to physical impair-ments (i.e., TR limits), so GRWA decisions differ for chan-nels with different line rates. This issue is addressed in ourACO algorithm, as discussed in Section III.

In the GRWA process, traffic grooming opportunities canoccur since the optical channel bandwidth is often muchlarger than the bit-rate of a single connection request.The technique used in traffic grooming can be one oftime-division multiplexing, frequency-division multiplex-ing [e.g., orthogonal frequency-division multiplexing(OFDM)], etc. Note that using currently developed technol-ogy traffic grooming requires signals to be in the electricaldomain, and therefore can only be performed either at thesource node of the connection or at regeneration nodeswhere signals undergo OEO conversion. By collecting infor-mation of unused capacity on channels and locations wheretraffic grooming can be performed, GRWA algorithms canincrease the spectrum usage efficiency, balance the trafficload to avoid congestion, and thereby increase the through-put and reduce the blocking probability.

III. ANT COLONY OPTIMIZATION

ACO is ametaheuristic algorithm that is inspired by antsin nature. An ant colony is seen as being able to find theshortest path between the nest and a food source in food for-aging behavior, without sophisticated individual or centralcontrol units. Such behavior also shows high adaptivity tochanges in the environment, such as a sudden obstaclealong its path. Because of the simple processing of each indi-vidual ant, no direct contact and exchange of informationbetween them is supported. Instead, ants communicatewith each other indirectly by changing the environment us-ing pheromones (such behavior is called “stigmergy”). Antssense the pheromones left by other ants and make theirmovementdecisionsbased on this information. InalgorithmFig. 1. NSF-24 network.

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design, this movement is modeled as a probabilisticbehavior [5].

In communication systems, agents mimicking the antscan be used to survey network state information, whichis then used for GRWA decisions. The simplicity of ACOagents along with their simple method of communicationreduces the complexity of the control and managementmechanism compared with centralized algorithms and istherefore preferable for designing a transport-sized net-work GRWA algorithm. Throughout network operation,ants travel through the network between neighboringnodes. At each node, the ants leave a numeric marker mim-icking the pheromone that indicates the quality of its lastmove, such as the physical length, free spectrum, andavailable regeneration resources. The pheromone thenaffects the movement of ants that arrive in the future.

The pheromone levels are represented by τ�k�i;j , where k isthe node that the ant is currently located at, i is a neigh-boring node of k, and j is the ant’s destination node. Thevalue of τ�k�i;j represents the goodness of choosing link �k; i�on its path to destination j. In Table I, a pheromone table isshown for node 8 in Fig. 1. The column indices refer to thedestination of the path from node 8, and the row indices arethe neighboring nodes of node 8. Since the ant’s movementfollows a probabilistic behavior, for each destination theprobability of choosing neighboring nodes should sum to1, which means the sum of each column in the pheromonetable is 1.

A. General ACO Approach to RWA

We begin by describing a general ACO used for RWA[10,21], which does not consider traffic grooming and physi-cal impairments, and then describe our enhanced designthat takes these factors into consideration.

In ACO, ants are sent from each node to each destinationsimultaneously. The ants follow different paths by makinga statistical decision from one node to the next. They collectnetwork state information, including wavelength usageand grooming opportunities, along the way. Using this net-work state information to calculate the “goodness” of thesolution lightpath that they find when they arrive at thedestination, they then travel back to their sources and up-date the pheromone levels according to this “goodness.”Pheromone levels at each node also evaporate after all antsfinish their round-trip. This multi-ant round-trip process isconsidered as one ACO launch cycle and is performedmanytimes before an optimal solution emerges.

At the start of the algorithm, an initial pheromone τ0 isgiven to each node as τ0 � 1∕�ND�, where N is the totalnumber of nodes and D is the diameter of the network(the length of the longest shortest path among all nodepairs). This initial pheromone is chosen because the newpheromone laid by ants is based on the physical distanceof the lightpaths. At time t an ant heading for node j thatarrives at node k makes its next move decision using

pij � τ�k�ij �t� (1)

as the probability that the ant picks node i for its nextmove. Prior research has included instantaneous wave-length usage information at node k to help the ant decideon its next move, mimicking ants’ limited visibility [5,15]:

pij � �1 − β�τ�k�ij �t� � βωk;i; (2)

where ωk;i is the fraction of wavelengths that are free onlink �k; i�, and β is a parameter used to weigh the impor-tance of wavelength usage information.

When an ant reaches its destination, it then traversesbackward following the reverse route back to its source.As the ants return home, they update the pheromone tableat each node as (subscripts representing the nodes areomitted here)

τ�t� 1�≔ ρτ�t� � �1 − ρ�Δτ; (3)

where

Δτ � 1L�1� αω� (4)

is the pheromone modification made by ants, L is the dis-tance of the route in 100 km, ω is the percentage of freewavelengths on that route, and �ρ; α� are design parame-ters that can be tuned to optimize the system performance.Equation (4) captures the main metrics of “goodness” of alightpath, which are the physical distance L of the light-path and the wavelength availability ω, and shows thata lightpath becomes preferable if it has a shorter lengthand more free wavelengths compared to others. If a uni-form link length is assumed, using L is equivalent to usingthe number of hops in the lightpath. In our study, the physi-cal distance has greater importance because we considerphysical impairments, which depend on the distance thatthe optical signal traverses. InWDMnetworks, wavelengthavailability measures the congestion level of a path.

After all ants finish their trip back to their source nodesand perform Eq. (3), the pheromones evaporate at all nodesaccording to

τ�t� 1�≔ �1 − ρ�τ�t� � ρτ0 (5)

to avoid stagnation. Equation (3) is called the global phero-mone update and is carried out at only those nodes alongthe ants’ paths. It has the effect of reinforcing the phero-mone for each successful path for future ants to follow.Equation (5) is called the local pheromone update and iscarried out on all nodes. It has the effect of lowering thepheromone toward the initial level so that ants have a

TABLE IPHEROMONES AT NODE 8 OF FIG. 1

1 2 … 24

5 τ�8�5;1 τ�8�5;2 … τ�8�5;24

7 τ�8�7;1 τ�8�7;2 … τ�8�7;24

10 τ�8�10;1 τ�8�10;2 … τ�8�10;24

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chance to explore new paths. These two pheromone updateprocesses combined with the exploration of ants composeone cycle of the ACO algorithm. It takes a number of cyclesfor the ants to cover the entire network and find the bestsolution.

In addition to updating the pheromone levels at thenodes, each surviving ant also stores its successful pathat its source node and all intermediate nodes to form acandidate route list. The order of this list is based on Δτin Eq. (4), which depends on the distance and free wave-lengths on the route. As the network state changes this listis updated continuously by the ants.

With the general structure of the ACO algorithm estab-lished, we modify the pheromone update mechanism toconsider physical impairments and traffic grooming next.The performance of ACO is also improved by modifyingthe ants’ behavior.

B. Proposed Enhancements

Based on the general ACO structure described above, weextend the algorithm to fit our problem requirements andincrease its efficiency. We make the following changes tothe general structure.

1) Mixed Line Rate: In our MLR network model, eachwavelength is assigned a different fixed line rate (10, 40,or 100 Gbps). This fact is addressed by having three sub-colonies of ants, with each subcolony representing one linerate. This also means that we have three different phero-mone tables, one for each line rate, and eventually threedifferent candidate route lists. Ants belonging to differentsubcolonies are launched separately, and they do not affectand are not affected by other subcolonies.

2) Physical Impairments: Ants representing differentline rates enforce different TR requirements. Each antkeeps a record of the distance it has traveled since its lastregeneration, and chooses only among those neighbors thatwill not exceed its TR for its next move. At intermediatenodes that are equipped with 3R regenerators, the ants bydefault consider themselves regenerated, and thereforetheir distance traveled is reset. This assumption is reason-able as OEO converters are usually available; we showed in[16] that for a network with a similar scale as in Fig. 1 thenumber of regenerators needed is reasonably low.

3) RandomWalk: To further increase the randomness ofthe ants’ movement to avoid pheromone stagnation, we al-low ants to make a uniform selection for their next hopfrom neighboring nodes with a given probability. The prob-ability that an ant chooses any neighbor node i for the nextmove at node k becomes

pij � �1 − r���1 − β�τ�k�ij �t� � βωk;i� �rNk

(6)

instead of Eq. (2), where Nk is the number of nodes neigh-boring kwithout counting the node the ant just visited, and

r is a parameter denoting the probability that an antmakesa random walk.

4) Backtracking: During its exploration, an ant mayreach a dead end such that all choices for the next movehave already been visited, there are no available wave-lengths toward any neighbor, or no next move can satisfythe TR requirement. In such situations, we can eithersimply remove the ant from the network or allow it to back-track to its previously visited node and choose a differentpath. In [7] no backtracking is allowed. In [14] a randomnext hop is selected when a dead end is formed by a loop.In our study, we consider the launching of ants as a costlyoperation, and try to make each launched ant successfullyreach its destination. Therefore we encourage ants tosearch for a viable solution by introducing backtracking,a method similar to [14] but with some critical differences.Whenever an ant encounters a dead end, it backtracks tothe previously visited node and makes a new next-hop de-cision without considering the node that it moved backfrom. This process repeats until a viable path is found orall options are exhausted. In the latter case, it then retreatsone step further to the next upstream node, until it finds aviable solution, moves back to its source node, or surpassesits time to live (TTL); in the latter two cases, the ant is re-moved. Note that pheromone values are considered evenafter backtracking, which shows an effort to use long-terminformation as much as possible. By doing this, we reducethe number of ants being wasted and improve our algo-rithm’s efficiency. It may be argued that backtrackingmay lead to “bad” solutions with unnecessarily long paths.We show that this does not happen because the pheromoneupdate depends on the goodness of the path, so long pathsdo not greatly affect pheromone tables.

5) Traffic Grooming: When ongoing traffic is beingtransmitted in the network, resource usage information,such as wavelength and routing assignment and connec-tion duration, is recorded at each node that is on the light-path. Each node keeps a list of ongoing traffic that includesconnections initiated at that node and transient traffic.Since this information is essential to traffic grooming, antscan consider this information when exploring the network.

If the ant is at a regeneration node, grooming opportu-nities can be noted and picked up by the ant through thefollowing steps:

Step 1: Before performing Eq. (6), the ant first checks fordestination grooming opportunities (i.e., an existinglightpath that has the same destination and enoughfree capacity). The segment that leads the ant directlyto its destination is always chosen for its next move,which is effectively destination grooming.

Step 2: In order to introduce randomness for explorationpurposes, ants make a random choice to either performthis step or not at each regeneration node. If step 1 fails,the ant randomly chooses a lightpath segment thatleads to a regeneration node that is not its destinationfor grooming opportunities. If the available capacity ofthe chosen segment fits the connection request’s bit-rate requirement and no nodes along that segment have

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been visited by the ant (to avoid loops, which cause awaste of physical resources by revisiting the samenode), it picks that segment as its next move.

Step 3: If no grooming opportunity is found, the ant looksfor a nongrooming move according to the probabilityassignment in Eq. (6).

Since traffic grooming does not assign new resources tothe newly groomed connection, it is highly desirable whenperforming GRWA. Therefore, the ability of grooming newtraffic with our existing connections should count towardthe goodness of a lightpath. Recall in Eq. (4) the goodnessis measured based on the lightpath length and the numberof free wavelengths on it. In order to include grooming intoour calculation of goodness, we add twomodifications to thecalculation of how much pheromone to deposit: 1) a groom-ing segment is considered as having all wavelengths free(i.e., ω � 100%), due to the capability of wavelength conver-sion, and 2) a grooming segment is considered to have zerolength, i.e., L � 0 (if the whole lightpath is a grooming op-portunity, its length isset tobethe lengthof its shortest link).Based on Eq. (4) these two modifications greatly encouragethe selection of lightpaths with grooming opportunities.

C. Algorithms

To summarize our ACO algorithm we show the pseudo-code, which consists of two parts. Algorithm 1 shows an antforaging cycle, made up of a lightpath exploration stage fol-lowed by a pheromone update stage. In the first stage, antsfollow the rules described above to explore the surroundingnetwork state; in the second stage, ants travel back to theirsource nodes, update pheromone levels along the waybased on the lightpaths’ goodness measure, and store routeinformation in the GRWA candidate lists. Foraging is per-formed repeatedly with an ant launch rate that depends onthe traffic load. Since the ant foraging process takes a shorttime compared to the interval between connection requestarrivals, during this process the network state is assumedto be unchanged.

Algorithm 2 shows what happens when a connection re-quest arrives. A GRWA decision for the connection requestis made based on the network state information providedby the ACO in the previous section. The grooming and rout-ing approach uses the candidate list provided by the ACO.The wavelength assignment employed is the first fit (FF)algorithm, where the lowest indexed wavelength availableis tried first. Lower-line-rate channels are given lowerwavelength indices, which is important because assigningan unused channel of a high-line-rate to a low-data-rateconnection both is a waste of resources and introducesunnecessary TR constraints. When a connection request ar-rives, the source node picks the route from the top (highestΔτ) of the candidate route list created by the ants and in-quires from the nodes along that path whether physical re-sources (wavelength and OEO circuits) are still available.If so the lightpath is reserved and the connection request isaccepted. If the first solution is not available at that timefor any wavelength, the next route is checked. If a route is

found to be unavailable, it is removed from the list so thatthe list can be repopulated by future ant foraging cycles.If a connection chooses a route that is marked as con-taining grooming opportunities, it tries grooming first. Ifthe grooming opportunities no longer exist, it then triesa nongrooming solution. If a nongrooming route is chosen,then wavelength assignment proceeds, favoring the lower-indexed (lower-line-rate) channels first.

Algorithm 1 Ant Foraging Cyclefor each line-rate wavelength (total of three, i.e., 10/40/100 Gbps) of each node pair in network �s; d� do

Launch one ant from s to d with probability PL

endfor each ant (in parallel) do

while current node i ≠ d and TTL > 0 doif found a next hop then

Move to next hop and decrease TTLelse

Backtrack to its previous visited node;endif TTL � 0 or i � s then

Kill ant, exit loop;endAfter i � d, travel back to s

while current node i ≠ s doFollow the same route backUpdate the pheromone at node i using Eq. (3)Store subroute information at i

endUpdate the pheromone at node s using Eq. (3) andstore route information at node s.

endfor each line-rate wavelength at each node do

Evaporate pheromone using Eq. (5);end

Algorithm 2 GRWAfor each demand request do

while no lightpath found doSelect route stored at the top of the candidate list;if resources available on chosen route then

if grooming lightpath is chosen thengroom traffic if grooming opportunitystill available

elseSelect the first available wavelength;Set up a lightpath;

endelse

Remove route from candidate list;end

if all routes have been tried thenConsider the request blocked;

endend

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IV. GROOMING ADAPTIVE SHORTEST PATH ALGORITHM

Since we have not seen a dynamic centralized algorithmthat incorporates regeneration, physical impairments, andtraffic grooming published in the literature, in this sectionwe propose one that we call the GASP. This centralizedalgorithm requires complete current network state infor-mation, so it must be computed on-line as call requestsarrive.

In the Dijkstra SP routing algorithm [22], a shortestpath tree is created for each node toward all other nodesin the network. The branches of the tree are the routes con-necting the node pairs. The SP branches are created by fol-lowing the rule that only the shortest route is kept, andthus the shortest path between all node pairs can be found.When used in a dynamically changing topology, the short-est path routing algorithm becomes the ASP algorithm.

Unlike the traditional ASP algorithms, where one short-est path is calculated for each wavelength based on the cur-rent network state and then a shortest path among allwavelengths is used, our GASP algorithm considers allwavelengths at once in order to account for wavelengthconversion functionality (a side effect of regeneration). Fordynamic systems, not all wavelengths are available, andgrooming opportunities need to be represented. We modifythe Dijkstra algorithm by introducing additional checks forwavelength continuity, as well as TR and grooming oppor-tunities. In each step of the Dijkstra algorithm, thedistance between a leaf node and the root is only updatedif all three criteria are met for the new route:

1) It has a shorter distance compared to the previous one.2) It has at least one free wavelength (including possibly a

grooming wavelength).3) It does not violate the TR constraint.

The first criterion is the same as the traditional SPexcept that the portions of the lightpath groomed ontoexisting traffic are assigned zero length; the second isimplemented by having each node keep a record of the cur-rent wavelengthmask with respect to the root. When a newroute is about to be created, the mask of the previousbranch node and mask for the link that connects to it areused to make sure there exists an available wavelength.Once a regeneration node is selected, the mask is reset.Finally the third criterion is implemented by having eachnode keep a record of the current TR distance since the lastregeneration. The TR distance is the length of the link thatconnects to this node plus the TR distance of the previousbranch node. The TR distance is the path distance over atransparent segment (no regeneration), so it is reset to zeroonce a regeneration node is traversed. Only transparentsegments with TR distance within the TR limit areselected.

After a route is selected using GASP, wavelength selec-tion for each transparent segment follows the FF rule. Notethat the wavelength could vary along the route dependingon the wavelength conversion operation at regenera-tion nodes.

The static SP and fixed-alternate (FA) algorithms [23]are often used to compare with newly proposed ACO algo-rithms [6–10]. Since no existing dynamic algorithmincludes TR constraints and traffic grooming, we also pro-vide a comparison with these two algorithms. In SP, theshortest path (in number of hops) between each node pairis always used for traffic between them; in FA, while usingthe shortest path as the first choice, a second path (usuallylink-disjoint) is used as the alternative choice if the short-est path is unavailable because it is fully occupied byexisting traffic. Although we consider regeneration andtraffic grooming in both algorithms, we show below thatthey underperform against the two proposed algorithmsdue their lack of flexibility compared to adaptive routing.

V. SIMULATION

We test our ACO algorithm using the NSF-24 networkshown in Fig. 1. There are 24 nodes; links are consideredas a pair of unidirectional fibers. Each fiber carries 32wavelengths (eight 10 Gbps, sixteen 40 Gbps, and eight100 Gbps channels). The 10 shaded nodes in the topologyare chosen as regeneration nodes following the algorithmin [24]. During our simulation, connection arrivals aremodeled as a Poisson process. The bit-rate of the requestsranges from 1 to 60 Gbps uniformly. The connection dura-tion is exponentially distributed with an average of onearbitrary time unit (h � 1). The traffic load (E, in Erlang)is then adjusted by changing the connection request arrivalrate, λ, with the formula E � λh. In this section we firstshow the dependence of the ACO performance on variousparameters to optimize it for our topology, and then com-pare it with the centralized GASP algorithm.

A. Optimizing ACO Configuration

In order to implement ACOwith a certain confidence, weshould understand its many configurations and how theyaffect the overall system performance collectively and sep-arately. We perform tests to show the impacts of severalaspects of the design on system performance.

In this paper our main goal is to include new mecha-nisms such as a TR limit and traffic grooming into the de-sign of ACO. TR limits guarantee the QoT for all node pairsand can be enforced by allowing the signal to be regener-ated along the chosen lightpath whenever necessary.However, this also requires the candidate lightpaths pro-vided by ACO to include the necessary regeneration nodes.Traffic grooming improves the physical resource usageefficiency but also requires the candidate lightpaths toinclude such opportunities.

In Fig. 2 we show the necessity of implementing newmechanisms into ACO by comparing our algorithm withpreviously proposed ACO approaches. When ACO does notcheck for TR and traffic grooming in the foraging cycle,although the system still tries to find regeneration sitesand traffic grooming opportunities along candidate light-paths in the GRWA step, without such information

584 J. OPT. COMMUN. NETW./VOL. 6, NO. 6/JUNE 2014 Wang et al.

considered in the ants’ exploration, ACO cannot providegood candidate lightpaths to the GRWA to deploy thesemechanisms. Note that the TR limit has a much greaterimpact on network performance compared to traffic groom-ing (the curves representing the cases in which ACOignores the TR and in which it ignores both the TR andgrooming are indistinguishable). Without knowledge ofthe TR, candidate lightpaths are often those with the short-est end-to-end physical distance, and many will fail the TRrequirement, thereby blocking requests. Due to this effect,certain node pairs appear to be unreachable and cause anonnegligible blocking probability even when the load islow and wavelength blocking is rare (shown as the flat re-gion of the graph when the load is less than 100 Erlangs).Even though traffic grooming opportunities are searched inall cases, candidate lightpaths with traffic grooming infor-mation tend to provide more chances for enabling trafficgrooming, as shown from the improvement achieved be-tween not checking traffic grooming and checking trafficgrooming. If grooming is not considered by the ACO, thoselightpaths often do not make the candidate list becausethey tend to be longer.

Asmentioned in Section III, backtrackingmay be consid-ered not preferable in that it can lead to poor solutions. Weargue that such poor solutions, if poor in quality at all, donot affect the system performance because the pheromoneupdate rule is based on the goodness of solutions. We alsoargue that by allowing backtracking, we can keep the num-ber of ants low, thereby reducing the control overhead(which is often measured as the ratio of control and man-agement message exchanges to real traffic) thanks to theeffort to help each ant find a solution. In Fig. 3 we showthe comparison between algorithms with backtrackingand without. In this figure we also show the effect of havingdifferent numbers of candidate routes (NR) in the solutionpool on each source node. If no backtracking is allowed, byincreasing the numbers of candidate routes, we increase

our options for connection requests, and therefore lowerthe chances of having the requests blocked. We can see thatdue to the improved efficiency of having ants backtrack, theblocking performance is improved, even with a smallersolution pool.

Algorithm 1 in Section III is carried out multiple timesevery fixed time interval, denoted as T. The number ofcycles (NC) determines the level of convergence to an opti-mal solution. The duration of T measures how frequentlythe network state information is collected and determineshow up to date the information is. Since for a given trafficload the average number of connections that arrive in T isfixed to be ET∕h, we establish this average number of con-nections as the relative launch repetition interval (TL, e.g.,when E � 100, h � 1, TL � 2 leads to T � 0.02 time units,which means on average, two connections arrive before thenext launch; given fixed traffic load, by adjusting the aver-age of number of connection arrivals, we can adjust the in-terval between two launches, therefore reflecting thelaunching frequency). The launch probability (PL) deter-mines the number of ants launched per cycle. These threeparameters together determine the number of ants in thenetwork, which is a measure of the control overhead ofACO. The average number of ants per source node iscalculated using

Average number of ants � NC × PL ×E

TLh: (7)

In Fig. 4 we show the blocking probability with differentNC for each ACO launch, TL, as well as PL, while keepingthe total number of ants launched fixed. Intuitively, if thetraffic load is high, the network state changes rapidly andrequires ants to be launched more frequently to keep theinformation up to date. When we use many cycles, we allowpheromones to converge to an optimal solution. TL and PL

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Fig. 2. Blocking probability of ACO with implementation oftraffic grooming and TR (NR � 3, NC � 1, PL � 1, TL � 30, andρ � 0.7).

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Fig. 3. Blocking probability of ACO with backtracking (NR � 3)and without backtracking (NR � 1–5).

Wang et al. VOL. 6, NO. 6/JUNE 2014/J. OPT. COMMUN. NETW. 585

show the trade-off between performance and controloverhead.

As can be seen in Fig. 4, in general, the blocking proba-bility decreases with more ants in the system. Also, if weset two of the three parameters (NC, PL, TL) as fixed(shown as connected lines in the figure), increasing thenumber of ants by changing only the third parameter, wecan lower the blocking probability. This shows that no mat-ter how one chooses to do it, increasing the number of antsdecreases the blocking probability. We also show in theinset that for a fixed number of ants, foraging can be organ-ized differently to achieve different performance. It sug-gests that ACO is more sensitive to the launch intervaland launch probability than to the number of cycles.

Since the ants’ foraging step is a process of exploring pos-sible solutions, in order to avoid the emergence of subopti-mal (i.e., locally optimal) solutions, certain randomness ispreferred. We test the ants survey with different levels ofrandomness, as measured by the probability of an antchoosing uniformly among neighboring nodes from an in-termediate node (parameter r) rather than following thepheromones. Note that this parameter only affects theants’ movement but does not affect the pheromone updateor the relationship between the pheromones and theGRWA decision. In Fig. 5 we show the blocking probabilityof ACO with different random walk probabilities. We testdifferent launch probabilities to have different numbers ofants in the system.We notice that a fairly large level of ran-domness is preferable since it reduces the blocking proba-bility. For example, for PL � 1, the blocking probability isminimized for r � 0.8. A total random movement (r � 1)leads to worse performance.

In the previous literature, there are two other differentimplementations of ACO, one assuming a single ant percycle [7–9], and the other using multiple ants per cycleper source node [5]. Both implementations can have thesame control overhead in terms of the total number of ants

in the network; for example, one cycle of ACO with threeants per cycle uses the same number of ants as three cyclesof ACO with one ant per cycle. We compare the two imple-mentations with the same number of ants in the network inFig. 6, where we show the blocking probability of the net-work. There is no discernible difference between the imple-mentations. This is because we model our ACO to have nonetwork state changes between cycles for each launch. Italso shows that NC � 1 with a single ant per cycle isenough to minimize the blocking probability, especiallyat high loads.

The performance of ACO is also affected by the rulesused for updating the pheromone levels. In Eqs. (3) and(5) we give global and local pheromone update rules, whichare both affected by the parameter ρ. Intuitively, if ρ is

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Fig. 4. Blocking probability of ACO with different ants’ behaviorparameters: number of cycles NC, launch interval TL, and launchprobability PL (E � 100 Erlangs, h � 1 time unit).

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Fig. 5. Blocking probability of ACO with different random walkprobabilities r for various ant launch probabilities PL (NR � 3,NC � 1, E � 400 Erlangs).

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Fig. 6. Blocking probability of ACO with different configurations:one ant per node pair withNC � 1 andNC � 3; three ants per cycleand NC � 1 (NR � 3, PL � 1, TL � 20, and ρ � 0.7).

586 J. OPT. COMMUN. NETW./VOL. 6, NO. 6/JUNE 2014 Wang et al.

large, the pheromone changes slowly; when ρ � 1 thepheromone does not update at all. If ρ is small, the phero-mone changes drastically, and when ρ � 0 the pheromoneis always replaced by the newly deposited amount. In Fig. 7we show the dependence of the ACO performance on theparameter ρ. Note that for different numbers of ants inthe system, as determined by the launch probability PL,the best choice for ρ is different: for PL � 1, the best ρ is0.8, and for PL � 0.1, the best ρ is 0.1. We also notice thatfor some ρ, launching more ants does not guarantee betterperformance. This is due to a rapid convergence to a sub-optimal solution.

B. Comparison to Centralized Algorithms

After optimizing our ACO over the algorithm’s parame-ters, we compare it with the proposed GASP algorithm,which is a centralized optimization algorithm. In Fig. 8we show that GASP benefits from more network state in-formation and provides better GRWA decisions, whichcauses its blocking probability to be lower than that ofACO. The ACO’s blocking probability is higher, whichshows that with limited information, the ACO providesworse blocking performance. However, the trade-off ofblocking performance and complexity of the control mecha-nism should be considered by network providers. We alsoshow the blocking probabilities of static SP routing andstatic FA routing (with one alternate route) for comparison.The paths in the SP and FA algorithms do not necessarilynaturally satisfy the TR constraints. Therefore, even whenregeneration is performed whenever possible, some nodepairs are still unreachable due to the limited routingchoices. When global state information is not available(such as in multidomain networks) when GASP cannotbe used, ACO should be used instead of SP or FA routing.

In Fig. 9, we test both algorithms with varying trafficload, which simulates the scenario of a changing traffic

pattern throughout the day. The figure shows ACO canadapt to the traffic load change quickly even without astrategy specifically defined for such a change. Again,GASP, relying on complete and accurate instantly updatedglobal information, shows larger capacity and equally fastadaptivity to traffic changes.

The robustness of ACO in case of failure is also an im-portant criterion. In Fig. 10 we show a scenario in whichlink (7, 9) in the network topology of Fig. 1 is cut duringoperation. This fiber cut affects connections in both direc-tions. The affected connections are fed back to the systemin the incoming queue and assigned possible alternativeroutes. As we can see from Fig. 10, at the moment of thefiber cut (time 50) the number of ongoing connections dropsabruptly due to the removal of the affected connections.Then the inset graph details the recovery of the network,

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Fig. 7. Blocking probability of ACO versus parameter ρ(PL � �0.1; 0.5; 1�,NR � 3,NC � 1, TL � 30, andE � 400Erlangs).

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Fig. 8. Blocking probability of ACO versus GASP and static SP,static FA (NR � 3, NC � 1, PL � 0.5, TL � 10, and ρ � 0.5).

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Fig. 9. One realization of real-time ongoing connections usingACO versus GASP (NR � 3, NC � 1, PL � 0.5, TL � 10, andρ � 0.5, averaged over 60 trials).

Wang et al. VOL. 6, NO. 6/JUNE 2014/J. OPT. COMMUN. NETW. 587

including the reassignment of affected connections andnew connections. The ACO is able to adapt to the failureimmediately without a separate restoration mechanism.Figure 10 also shows several different configurations ofACO, such as different launch probabilities and whetherto restrict candidate routes to be link-disjoint. It showsagain that with higher launch probability, the number ofongoing connections is larger and recovery is faster dueto more ants in the system. It also shows that with alink-disjoint candidate route pool, there is a better chancefor ACO to find an alternative route that is not affected bythe fiber cut, and it therefore recovers faster.

Although not shown in the simulation, ACO reduces theconnection setup delay by performing the route optimiza-tion calculation in the foraging process before a connectionrequest even arrives. When a new request arrives, the edgenode simply looks up the candidate solution table to assignthe optimized lightpath. On the other hand, GASP needs tocalculate the best lightpath based on the instantaneousnetwork state information, and this computation introdu-ces a setup delay. The complexity of implementing the twoalgorithms is discussed in [16]. We showed that the ratio ofcontrol overhead between ACO and GASP depends on therelative launch interval (TL), the number of cycles perlaunch (NC), and the launch probability (PL). By maintain-ing reasonable TL, NC, and PL, we can achieve much lowercontrol overhead in ACO compared to GASP (e.g., whenTL � 20, NC � 1, and PL � 0.5, the ratio is approximately0.71).

VI. CONCLUSION

In this paper we introduce an ACO algorithm for GRWAon a real-time dynamic-traffic fiber-optic network consider-ing features such as MLR, physical impairments, and traf-fic grooming. We show the necessity of implementing TR

and traffic grooming into the ACO foraging cycle. Wediscuss in detail how different configurations of the modelaffect the overall performance of the system. We also com-pare our ACO to a centralized heuristic method. We vali-date the robustness of our ACO by testing it on severalscenarios, such as nonstationary traffic statistics and de-vice failures. In the future, we plan to include considera-tions of limited hardware resources at nodes, such astransponders and wavelength switches, into the ACOalgorithm, implement it for elastic optical networks, andoptimize it for energy efficiency as well.

ACKNOWLEDGMENTS

Parts of this paper were published in Proc. IEEE Globecom2013 [16]. This work was supported in part by NSF grantsCNS-0915795 and CNS-0916890.

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