On ant routing algorithms in ad hoc networks with critical … MEE/EE... · 2008. 7. 7. · On ant...

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Ad Hoc Networks 6 (2008) 827–859

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On ant routing algorithms in ad hoc networks withcritical connectivity

Laura Rosati a,*, Matteo Berioli b, Gianluca Reali a

a University of Perugia, Department of Electronic and Information Engineering, via G. Duranti 93, 06125 Perugia, Italyb German Aerospace Center (DLR), Institute of Communications and Navigation, P.O. Box 1116, Oberpfaffenhofen, Germany

Received 31 August 2006; received in revised form 23 May 2007; accepted 16 July 2007Available online 24 July 2007

Abstract

This paper shows a novel self-organizing approach for routing datagrams in ad hoc networks, called Distributed AntRouting (DAR). This approach belongs to the class of routing algorithms inspired by the behavior of the ant colonies inlocating and storing food. The effectiveness of the heuristic algorithm is supported by mathematical proofs and demon-strated by a comparison with the well-known Ad hoc On Demand Distance Vector (AODV) algorithm. The differencesand the similarities of the two algorithms have been highlighted. Results obtained by a theoretical analysis and a simula-tion campaign show that DAR allows obtaining some important advantages that makes it a valuable candidate to operatein ad hoc networks and the same method helps in the selection of the algorithm parameters. Since the approach aims atminimizing complexity in the nodes at the expenses of the optimality of the solution, it results to be particularly suitable inenvironments where fast communication establishment and minimum signalling overhead are requested. These require-ments are typical of ad hoc networks with critical connectivity, as described in the paper. Thus the performance of theproposed algorithm are shown in ad hoc networks with critical connectivity and compared to some existing ad hoc routingalgorithms.� 2007 Elsevier B.V. All rights reserved.

Keywords: Ad hoc networks; Routing protocol; Ant routing; Critical connectivity

1. Introduction

Routing protocols for ad hoc networks may bedescribed in terms of the state information charac-terizing each node and/or in terms of the informa-tion exchanged among nodes. Topology-based

1570-8705/$ - see front matter � 2007 Elsevier B.V. All rights reserved

doi:10.1016/j.adhoc.2007.07.003

* Corresponding author. Tel.: +39 075 5853918.E-mail addresses: [email protected] (L. Rosati),

[email protected] (M. Berioli), [email protected](G. Reali).

protocols use the principle that each node in a net-work maintains large-scale topology information.This principle is just the same as what link-state pro-tocols use. Destination-based protocols do not main-tain large-scale topology information, but onlytopology information needed to know the nearestneighbors. The best known are distance-vector pro-tocols, which maintain a vector of distances to eachdestination (hop count or other metrics) for all pos-sible next hops, based on the classical Bellman–Ford routing mechanism.

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828 L. Rosati et al. / Ad Hoc Networks 6 (2008) 827–859

Another traditional classification is to divide pro-tocols in proactive (table-driven) and in reactive(on-demand). Proactive routing protocols maintaintables that store routing information; for anychange in network topology, they trigger propagat-ing updates throughout the network in order tomaintain a consistent network view. Reactive rout-ing protocols are characterized by a path discoverymechanism that is initiated when an informationunit needs to get to a given destination. Some ofthe most known MANET routing protocols arementioned below.

Destination-Sequenced Distance Vector (DSDV)[1] routing protocol is a proactive destination-based algorithm. The modifications to the Bell-man–Ford algorithm include loop avoidance. AlsoAd hoc On Demand Distance Vector (AODV)routing protocol [2] is destination-based, it mini-mizes the number of required broadcast messagesby creating routes on an on-demand basis.Dynamic Source Routing (DSR) [3] is reactiveand topology based. It uses source routing ratherthan hop-by-hop routing; each packet is routedaccording to the routing information carried inits header, which includes the complete, orderedlist of mobile nodes through which the packet mustpass. Temporally-Ordered Routing Algorithm(TORA) [4] is neither a distance-vector nor alink-state; it belongs to a family of algorithmsreferred to as ‘‘link-reversal’’ algorithms. It pro-vides multiple routes for any desired source/desti-nation pair and reacts only when all routes tothe destination are lost. TORA is reactive in thesense that route creation is initiated on demand.However, route maintenance is done on a proac-tive basis such that multiple routing options areavailable in case of link failures.

In this paper we focus on MANETs where theQuality of Service (QoS) requirements consist of afast communication establishment and a minimumsignalling overhead. Such scenarios are referred toas ad hoc networks with critical connectivity. Animportant instance is represented by ad hoc net-works featuring randomly changing topology andpotentially sparse and intermittent connectivity withlong outages, and thus the unfeasibility to rely onany static or pre-calculated routing information.In such scenarios traditional MANETs routingprotocols could work not effectively, since the routediscovery process intrinsically relies on the‘‘reachability’’ of the destination node at the timeof route discovery. The objectives in designing an

efficient routing protocol for ad hoc networks withcritical connectivity should be:

• low convergence time: to build routes quickly sothat they can be used before the topologychanges;

• robustness: to react quickly, re-establishing rout-ing when topological changes destroy existingroutes;

• minimum routing signaling overhead.

There are many scenarios characterized by criti-cal connectivity, for example military and disasterrecovery operations. Another instance is given byAd hoc Space Networks (ASNs), which have beenrecently designed for scientific space explorationmissions, where the space-borne nodes of the net-work typically consist of multiple spacecrafts withmultiple sensors [5–7]. Space-borne nodes in thefuture should be self-organizing and able to estab-lish communications with heterogeneous nodesand with pre-existing constellations. Space commu-nication links can be intermittent, with very longpropagation delays, and consequently the networkmay not be connected. In this framework, as wellas in other areas (see, e.g., the Saami Network Con-nectivity (SNC) project [8]), the new paradigm ofDelay Tolerant Network (DTN) [9] was proposed.The DTN architecture provides a common methodfor interconnecting heterogeneous gateways orproxies that employ store-and-forward messagerouting to overcome communication disruptions.An end-to-end message-oriented overlay called the‘‘bundle layer’’ is placed on top of the transportlayer, it enables the interconnection of different por-tions of the network where different routing algo-rithms operate. Thus different routing protocolsmight be used in this context. The applicability ofsome of them is constrained by precise assumptions.Another proposed approach is epidemic routing[10]: nodes forward each received datagram to eachnode in their transmitting range until the datagramreaches the destination. Thus this approach is effec-tive only in very sparse networks.

On the other hand it would be desirable forMANETs with critical connectivity to have one sin-gle routing algorithm which could leave aside theseassumptions, and that can adapt to the environ-ment, performing better in case of good connectivityand worse in case of very intermittent links. In par-ticular hop-by-hop and ad hoc routing is expectedto be the solution, using incomplete topology infor-

L. Rosati et al. / Ad Hoc Networks 6 (2008) 827–859 829

mation and probabilistic estimations. Some recentpapers have proposed routing algorithms for MAN-ETs based on mobile agents.

An extensive general description of agent-basedrouting principles and design choices can be foundin [11,12]. Agent-based routing algorithms forMANETs have been investigated in [13–16]. Theyhave shown a good dynamic behavior, robustness,and ability to work in a distributed environment.In this paper we contribute on this research trendby proposing a specific routing algorithm which ischaracterized by reduced signaling load and fastconvergence. Our approach may be classified intoa specific class of agent-based algorithms whichare inspired by the ant colonies foraging behavior.

Recent overview papers on Ant Colony Optimi-zation (ACO) are [17,18]. (ACO) has been success-fully applied in many combinatorial optimizationproblems such as the asymmetric traveling salesmanproblem [19,20], the vehicle routing problem [21],the quadratic assignment problem [22], the graphcoloring problem [23].

A comprehensive description of ant routing algo-rithms may be found in [24]. An important propertywhich we try to bring to the networking environ-ment is the ability of ants to make use of individu-als, implementing very simple rules to self organizeand find the optimal path between the nest andthe food location. The approach presented in thiswork consists of using very simple ant-like agents.In fact, we believe that simplicity is a fundamentalfeature in a difficult MANET environment. In thispaper, we analyze the effectiveness of the approachby means of a theoretical analysis and simulations.

In order to achieve a minimum routing signalingoverhead, we decided to implement the routingalgorithm presented in this paper as reactive anddestination-based for the reasons below. In ad hocnetworks with critical connectivity, the long propa-gation delay and high mobility, could prevent tradi-tional table-driven routing protocols, e.g, DSDV,from performing effectively. Because of limitedbandwidth of wireless links, message complexitymust be kept low. DSDV generates much morerouting traffic than on-demand approaches, due tothe fact that DSDV periodically generates routingtraffic. Also the overhead of a topology-based algo-rithm, e.g., DSR, is potentially larger than in desti-nation-based approaches since each DSR packetmust carry the complete list of the intermediatemobile node to reach the destination. Moreover atopology-based algorithm is not a distributed

approach; as the network becomes larger, controlpackets and data packets become larger as well.Clearly, this has a negative impact on the limitedavailable bandwidth.

The structure of the paper is as follows. In Sec-tion 2 we present the general principle of ant routingalgorithms and in Section 3 we define one particularalgorithm belonging to this class. In Section 4 wepresent a simulation approach which enables to ver-ify the effectiveness of the algorithm and the settingof its parameters. In Section 5 we investigate theperformance of such approach in comparison withtraditional ad hoc networks routing algorithmswhen operating in condition of critical connectivity.In Section 6 we drive the conclusions of the work.

2. Background on ant routing

Ant colonies are distributed biological systemsthat, in spite of the simplicity of their components,show highly structured social organization. As aresult, ant colonies can accomplish astonishinglycomplex tasks that could never be performed by asingle insect. The basic principle of an ant routingalgorithm is that ants deposit on the ground a hor-mone, the pheromone, while they roam looking forfood. Ants can also smell pheromone and tend tofollow with higher probability those paths charac-terized by strong pheromone concentrations. Thepheromone trails allow the ants to find their wayto the food source (or back to the nest). The samepheromone trails can be used by other ants to findthe location of the food sources discovered by theirnestmates. It was demonstrated experimentally[25,26] that this pheromone-trail-following behaviorgives raise to the emergence of the shortest path.

An ant routing algorithm can be briefly describedin the following way (cf. also Fig. 1):

• From each network node, a number of discoverypackets (forward ants) are sent towards theselected destination nodes. They propagate con-currently and independently.

• In each node routing tables consists of stochastictables, used to select next hops according toweighted probabilities. These probabilities arecalculated on the basis of the pheromone trailsleft by previous ants.

• While moving, the ants deposit pheromone onthe path links, i.e., in the node routing tables theychange the probability to select a particular nexthop.

Fig. 1. Basic principle of ant routing paradigm.


• Once a forward ant gets to the destination node,it first generates a backward ant and then dies.This way, the new packet created and sent backto the source will propagate through the samepath selected by the forward ant.

• On its way back, the backward ant deposits pher-omone on the reverse path links. Thus it updatesthe routing table of the nodes along the path.Once it has returned to the source node, thebackward ant dies.

A distributed heuristic solution like the ant rout-ing displays several features making it particularlysuitable in ad hoc networks:

• the algorithm is fully distributed ) there is nosingle point of failure;

• the operations to be performed in each node arevery simple;

• the algorithm is based on an asynchronous andautonomous interaction of agents;

• it is self-organizing, thus robust and fault toler-ant ) there is no need of defining path recoveryalgorithms;

• it is intrinsically traffic adaptive without any needfor complex and yet inflexible metrics;

• it is inherently adaptive to all kinds of long-termvariations in topology and traffic demand, whichare difficult to be taken into account by determin-istic approaches.

Ant routing algorithms can be classified in differ-ent ways, according to how the pheromone isupdated, how routing table probabilities are calcu-lated, how often and how many ants are sent perrequest, and so on. In Fig. 2 we present a possibleclassification. Using the schematic notation as intro-duced in the right column therein, the most repre-sentative ant routing algorithms to be found in theliterature can be listed and categorized as follows

(their characteristics are also presented accordingto the described classification in Fig. 1):

– ABC (Ant-Based Control) [27]: {C3; I2/3;M1;P3}

– ADRA (Ant-based Distributed Route for Ad hocnetwork) [28]: {C1; I1; M1;P2/3}

– ANB (Ant algorithm for Non-Bifurcated flows)[29]: {C1; I2; M2;P3}

– AntNet [24]: {C4; I2/3; M2;P1/2}– ARAMA (Ant Routing Algorithm for Mobile

Ad hoc Networks) [30]: {C1; I2/3; M2;P3}– ASGA (Ant System plus Genetic Algorithm)

[31]: {C1; I2/3; M2;P3}– BP-CT (Back Propagation-Cross Target) [32]:

{C1; I2/3; M1;P3}– CAF (Cooperative Asymmetric Forward) [33]:

{C1; I2; M2;P1}– GARA (Genetic Ant Routing Algorithm) [34]:

{C4; I2; M2;P2}– MABR (Mobile Ants Based Routing) [35]: {C3/

4; I1; M1;P3}– PERA (Probabilistic Emergent Routing Algo-

rithm) [36]: {C3/4; I2;M1;P2/3}– RBA (Routing By Ants) [37]: {C1; I2/3; M2;P1}– Regular Ant Algorithm [38]: {C3; I2;M1;P2/3}.

It is worth to be noted that some of the algo-rithms of Table 1 (namely ARAMA, MABR,PERA, ADRA) have been proposed explicitly forMANETs, whereas the others for data communica-tion networks in general. Moreover some of theseapproaches (namely ABC, ANB, ARAMA, ASGA,GARA, RBA) are connection-oriented, whereas theothers connection-less. Other ant-based routingprotocols like Ant-AODV Hybrid Routing protocol[39,40] and GPS Ant-Like Routing Algorithm(GPSAL) [41] have not been included in Table 1because they employ ants only to collect and dis-seminate up-to-date routing information about the

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Table 1Some ant routing algorithms

Algorithm Ants sending Information collected byForward Ants

Parameters considered inchoosing the next hop

Amount of deposited pheromone

ABC [27] – Periodic (destinationsare randomly selected)

– Identities of the crossed nodes– Launching time

– Pheromone – Amount depending on the antage

AntNet [24] – Periodic (destinationsselected according totraffic patterns)

– Identities of the crossed nodes– Time elapsed between ant launch and

arrival at each node

– Pheromone– Queue length at current node

– Constant amount (in some ver-sions of the algorithm)

– Amount depending on the localtraffic model

ADRA [28] – Triggered by connec-tion requests

– Identities of the crossed nodes – Pheromone – Amount function of differentparameters (distance from thesource node, quality of the link,congestion, velocity of the nodes)

ANB [29] – Triggered by connec-tion requests

– Identities of the crossed nodes– Bandwidth requirements of the crossed

nodes

– Pheromone– Residual capacity of arcs– Distance from the current node to the destina-

tion node of the ant

– Amount depending on the lengthof the ant’s route

ARAMA [30] – Triggered by connec-tion requests

– Identities of crossed nodes– Link costs– Other information related to the crossed

links (queuing delay, SNR, bit errorrate, . . .)

– Pheromone– Information on the neighboring node (queu-

ing delay, SNR, bit error rate, remaining bat-tery energy, . . .)

– Amount depending on the qualityof the found path

ASGA [31] – Triggered by connec-tion requests

– Identities of crossed nodes– Link costs (the link costs are expressed

as a function of the link utilization)

– Pheromone– Link costs– Linear combination of the two by means of

genetically encoded weights

– Amount depending on the qualityof the whole path found

BP-CT [32] – Triggered by connec-tion requests

– Identities of crossed nodes– Times at which the nodes have been

traversed

– Pheromone – Amount depending on the timelength of the found path

CAF [33] – Triggered by connec-tion requests

– Identities of crossed nodes– Links’costs

– Pheromonea (a function used to shape theprobabilities in order to favor the best paths)

– Constant

GARA [34] – Periodic (destinationsselected according totraffic patterns)

– Identities of crossed nodes– Times at which the nodes have been

traversed

– Path base is maintained in each node for eachdestination. Each path bases is evolved bygenetic algorithm

– Amount depending on the localtraffic model

MABR [35] – Periodic – Identities of crossed nodes – Pheromone – Amount depending on the logicallink costs

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location of the nodes, and hence, do not make useof the previously described pheromone process forfinding shortest paths.

In [42,43] we have proposed and analyzed a verysimple connection-less ant routing approach forMANET. We called it Distributed Ant Routing(DAR) algorithm. The definition of this approachwas made on the basis of a categorization of themost representative ant routing algorithms, in orderto design an approach which requires a low compu-tational complexity.

Specifically, the four main ant routing algo-rithm characteristics listed in Fig. 2 and Table 1are implemented in DAR in the simplest possibleway, yet preserving the effectiveness of theapproach. In DAR routes are created on-demand,in order to have a low routing signalling load withrespect to proactive approaches. Forward ants col-lect information only about the identities of thecrossed nodes. Forward ants move towards thedestination choosing the next hop only on a pher-omone basis. The amount of pheromone depos-ited by backward ants on each crossed link isconstant.

The simplicity of the protocol could be helpful inachieving seamless routing in networks constitutedby heterogeneous elements. Moreover, if the routingprotocol is simple, the network can be expandedwith additional nodes without requiring complexupdate procedures. For this reason DAR was pro-posed in [42,44,45] as a powerful mean to enhancecommunications in meshed regular and irregularsatellite constellations; in such complex networkscenarios an heuristic approach like DAR is anappealing solution if traditional (deterministic) tech-niques either fail completely or at least face intracta-ble complexity. As shown in the following, even ifDAR is very simple there are several parametersto be set.

With respect to the previously quoted works onDAR, this paper presents a deeper comparison

Table 2General simulation parameters

Transmission range 100 mWireless link shared capacity (Cl) 1 Mb/sNumber of mobile nodes (NMN) 30Traffic type Constant bit rateSimulation time 25000 sPacket rate 4 packets/sPacket size 500 byte


metric analysis and mathematical insight on the per-formance of routing in MANETS.

We study in depth the proposed algorithm andcompare it with the well-known AODV, which isthe most well-known MANET protocol whichshares the main DAR features, e.g., the on-demandand hop-by-hop behaviors. Thus we proceeddescribing their characteristics.

2.1. Ad hoc on-demand distance vector and

distributed ant routing

The AODV algorithm can be essentiallydescribed in the following way:

• When a node has to find a next hop for a packetto a given destination, it broadcasts RouteREQuest packet (RREQs); meanwhile, thepacket that can not be forwarded is buffered untila valid next hop is found.

• Each node which receives this (RREQ) stores areverse route state from itself back to the source.When the reverse routes are timed out, they aredeleted.

• Once the (RREQ) reaches a node (eventually thedestination) with a sufficient fresh route to thedestination, i.e., a route characterized by asequence number which is higher than the onestored in the packet itself, a Route REPly packet(RREP) is generated and sent back to the source,through the reverse route previously created.

• On its way back, the (RREP) updates the routingtable of the nodes along the path.

The DAR algorithm will be described in detailsin the next section. For the moment it is sufficientto highlight its similarities and differences withrespect to AODV. Both DAR and AODV are char-acterized by the following features:

• They enable dynamic, self-starting and multihoprouting in ad hoc networks.

• They are on-demand routing algorithms, thuseach route from any source to any destinationis searched when data have to be sent.

• Each node maintains a routing table with a rout-ing entry for each possible destination.

• When a routing entry for one destination pointsto a valid next hop, the routing entry is said tobe ‘‘available’’ or ‘‘up’’; if the information inthe routing entry is too old or expired the routingentry is ‘‘not available’’ or ‘‘down’’.

• If a packet has to be sent to a destination forwhich the routing entry is ‘‘down’’, a route dis-covery process has to be started to find agood and valid next hop, and the packet isbuffered.

• The state created in each node along the path is ahop-by-hop state, meaning that each node doesnot know the whole path to the destination, butonly the next hop node.

• In order to update the topology of the network,periodic ‘‘HELLO’’ packets are sent from eachnode to its neighbors (that is to the nodes stayingwithin a specified distance).

DAR and AODV differ mainly in the followingfeatures:

• While in AODV the routing tables are determin-istic, in DAR they are stochastic, meaning thatthe next hop is selected according to weightedprobabilities.

• In AODV each routing entry is associated with asequence number which indicates how recentlythe route was used; DAR does not use sequencenumbers: routes not recently used are purgedby means of pheromone evaporation.

• When a link is not available anymore, in AODVa Route ERRor Packet (RERR) is sent to all thenodes using the link to forward packets, so thatrelevant routing tables can be changed; inDAR, error messages are not needed. In fact, ifthe current node cannot forward a datagramdue to the lack of a valid routing table entry, thenthe node starts searching a new route by sendingforward ants.

3. The distributed ant routing algorithm

In DAR, in each node the routing tables are sto-chastic: next hop is selected according to weightedprobabilities, calculated on the basis of the phero-mone trails left by ants. When a node receives a dat-agram with destination d, if the routing entry for d isavailable, then the datagram is forwarded. Other-wise, the datagram is buffered at the node and for-ward ants are sent out at constant rate rae (antemission rate) in order to search a path to d.

Two hop-by-hop routing modes can be imple-mented: hop-by-bop random routing (nodes ran-

domly choose a neighbor to deliver datagrams)and hop-by-hop optimal routing (nodes choose opti-


mal next hop to deliver datagrams).1 Previousresults, e.g., [46], show excellent results for hop-by-bop random routing in the case of static net-works with relatively small topologies. However,as also stated in [36], this might not be a suitablemethod for MANETs with rapid topology changes.For this reason DAR adopts hop-by-hop optimalrouting. The forward ant is routed at each nodeaccording to the probabilities for the next hop inthe routing table at the current node. Thus, the for-warding of the forward ant is probabilistic andallows exploration of paths available in the net-work. Datagrams are routed deterministically basedon the maximum probability at each intermediatenode from the source node to the destination node.This process creates a complete global route byusing local information.

We have designed this ant routing algorithmaccording to the principle of a maximum simplicity,thus we have assumed that ants can only deposit aconstant amount of pheromone while moving andthat they can only be influenced by the presence ofthe pheromone in the path selection. Thus, the for-ward ants store only the identities of the visitednodes in order to avoid cycles. Once a forward antgets to the destination node, it first generates a back-

ward ant and then dies. This way, the new packetcreated and sent back to the source will propagatethrough the same path selected by the forwardant. As a backward ant travels, it deposits phero-mone on the crossed links as described below,updating the routing table of the nodes along thepath. Once it has returned to the source node, thebackward ant dies.

Being j the current node, i the node the backwardant comes from and s a constant value, with0 < s < 1, sin is the amount of pheromone on thelink (j, i) after n backward ants coming back to j.In the process of pheromone update this quantityis multiplied by (1 � s) and then s is added in orderto calculate si(n + 1). The pheromone quantities onthe other links are multiplied by (1 � s). This simu-lates the deposit of a constant amount ofpheromone:

1 Similarly, some connection-oriented approaches, e.g., GARA,are capable to provide two path base dependent source routingmodes: source random routing (source nodes randomly select apath from path base, and send data packets along it) and sourceoptimal routing (source nodes select the optimal path in pathbase, and send data packets along it).

skðnþ 1Þ ¼skðnÞð1� sÞ þ s; k ¼ i;

skðnÞð1� sÞ; k 6¼ i:

�ð1Þ

The probabilities that a forward ant will select aparticular next hop i can be calculated as follows.We will call pi(n) the probability for a forward antin node j to choose the node i as the next hop aftern backward ants coming back to j. If N is the num-ber of neighbors of j, then we have

pi ¼siðnÞPNk¼1skðnÞ

: ð2Þ

This ensures that the sum of all the probabilities rel-evant to all the valid neighbors is 1.

Let yi(n) be a binary variable which is 1 if the nthbackward ant crosses the link (i, j), 0 otherwise. Lets0 denote sk(0) for k ¼ 1 . . . N . It follows that for aparticular next hop i:

sið1Þ ¼ s0ð1� sÞ þ yið1Þs; ð3Þsið2Þ ¼ ½s0ð1� sÞ þ yið1Þs�ð1� sÞ þ yið2Þs

¼ s0ð1� sÞ2 þ yið1Þsð1� sÞ þ yið2Þs ð4Þ

and, in general,

siðnÞ ¼ s0ð1� sÞn þXn

l¼1

yiðlÞsð1� sÞn�l: ð5Þ

The sum of the pheromone on the links departingfrom j after n backward ants coming back to j is

stotðnÞ ¼XN

k¼1

skðnÞ ¼ Ns0ð1� sÞn þXn

l¼1

sð1� sÞn�l:

ð6Þ

Consequently:

piðnÞ ¼s0ð1� sÞn þ

Pnl¼1yiðlÞsð1� sÞn�l

Ns0ð1� sÞn þPn

l¼1sð1� sÞn�l ; ð7Þ

which can be written as

piðnÞ ¼ MðnÞ þXn

l¼1

yiðlÞDplðnÞ; ð8Þ

where

MðnÞ ¼ s0

Nsð0Þ þPn

t¼1sð1� sÞ�t ð9Þ

and

DplðnÞ ¼sð1� sÞ�l

Ns0 þPn

t¼1sð1� sÞ�t : ð10Þ


After n ants coming back, the term Dpl(n) representsthe increment in the probability pi(n) provided bythe l-backward ant, with l 6 n.

3.1. Pheromone evaporation

In real ant colonies pheromone also evaporates;this process allows selecting new directions withoutbeing over-constrained by previous decisions. Thisis particularly important in case of variable densetopologies and it can be included in ant routingimplementations (additional information on phero-mone evaporation can be found for instance in[30,37]).

The pheromone evaporation can be simulated byupdating the values of the pheromone on every linkat regular time intervals Dtev. For the sake of sim-plicity below we will call m the generic time instantm Dtev.

Evaporation is performed simply by multiplyingthe value of the pheromone on the kth link by a fac-tor smaller than 1.

Thus, being j the current node, we can defines0kðmÞ as the new quantity of pheromone on link(j,k), which takes into account the evaporation pro-cess. Now we suppose that between the time instantsm and m + 1 one backward ant crosses the link (i, j).The new operation of pheromone update, whichtakes into account evaporation, is performedaccording to the following two-steps rule:

skðmþ1Þ¼s0kðmÞð1� sÞþ s; k¼ i;

s0kðmÞð1� sÞ; k 6¼ i;

�ð11Þ

s0kðmþ1Þ¼ ½s0kð0Þ� skðmþ1Þ�kevþ skðmþ1Þ: ð12Þ

skðmþ 1Þ is an auxiliary function only needed asintermediate step to calculate s0kðmþ 1Þ. s0kð0Þ isclearly the initial value of pheromone on each linkand kev is a constant <1. For every node s0kð0Þ hasto be a constant "k = 1, . . . ,N, since at the begin-ning the probability to select a particular next hopis the same for all neighbors (pk(0) = 1/N,"k = 1, . . . ,N). We will assume for the sake ofsimplicity s0kð0Þ ¼ 1; 8k ¼ 1; . . . ;N .

It can be easily demonstrated that according tothis evaporation formula, for every possible valueof s0kðmÞ with m ¼ N evn; s0kðmþ lÞ tends to s0kð0Þ if l

goes to infinity, that is selection probabilitiesbecome uniform if pheromone keeps evaporatingwithout being updated.

If we consider at time m any pheromone quantitys0kðmÞ and we consider that from that moment the

pheromone is not updated by backward ants any-more but it evaporates, then the pheromone willbe only changed every Nev timesteps. Thus it willclearly result:

s0kðmþ lÞ ¼ s0k mþ lN ev

� �N ev

� �; ð13Þ

and as a consequence:

liml!þ1

s0kðmþ lÞ ¼ liml!þ1

s0k mþ lN ev

� �N ev

� �¼ lim

p!þ1s0kðmþ pN evÞ; ð14Þ

with p integer. It can be demonstrated by inductionthat, if the pheromone is only changed by evapora-tion every Nev timesteps, we have

s0kðmþ pN evÞ ¼ kevs0kð0Þ

Xp�1

j¼0

ð1� kevÞj

þ s0kðmÞð1� kevÞp: ð15Þ

Thus it clearly results:

liml!þ1

s0kðmþ lÞ ¼ limp!þ1

s0kðmþ pN evÞ ¼ s0kð0Þ: ð16Þ

Thus, before the algorithm starts (m = 0), or in caseof a long evaporation without updates, we obtain auniform distribution of the pheromone and for theprobabilities: si(n) = si(0) = 1 and piðnÞ ¼ pið0Þ ¼1=N ; 8i ¼ 1; . . . ;N .

In the remainder of the section, we use the fol-lowing notation. We suppose that the first evapora-tion is performed after f1 backward ants comingback, the second one after f2 backward ants comingback and, in general, the pth evaporation is per-formed after fp backward ants coming back. Foreach group fm of ants coming back to j, let yk,m(t)be a variable which is 1 if the tth ant sent after the(m � 1)th evaporation crosses the link (k, j), 0otherwise. We define the parameters sk,y(fm) ands(fm) as

sk;yðfmÞ ¼Xfm

t¼1

yk;mðtÞsð1� sÞfm�t ð17Þ

and

sðfmÞ ¼Xfm

t¼1

sð1� sÞfm�t; ð18Þ

respectively. We define p0kðmÞ ¼s0kðmÞs0totðmÞ

as the proba-

bility for a forward ant at node j at the time step


m to choose k as the next node to move to. We de-note as k* the node such that the link (j,k*) belongsto the shortest path between j and the destination ofthe flow.

At the beginning each link departing from j isassigned a constant value of pheromone s0:

skð0Þ ¼ s0: ð19Þ

Suppose f1 backward ants come back to node j:

skð1Þ ¼ s0ð1� sÞf1 þ sk;yðf1Þ: ð20Þ

If an evaporation is performed:

s0kð1Þ ¼ s0ð1� sÞf1ð1� kevÞ þ sk;yðf1Þð1� kevÞ þ s0kev

ð21Þ

Successively f2 backward ants come back to node j:

skð2Þ ¼ s0ð1� sÞf1þf2ð1� kevÞ

þ sk;yðf1Þð1� kevÞð1� sÞf2

þ s0kevð1� sÞf2 þ sk;yðf2Þ: ð22Þ

Again an evaporation is performed:

s0ðmÞ ¼ ð1� kevÞm s0ð1� sÞPm

l¼1fl þ

Xm

l¼1

ð1� sÞPm

v¼lþ1fv

ð1� kevÞlðsk;yðflÞð1� kevÞ þ s0kevÞ

!" #:

s0kð2Þ ¼ s0ð1� sÞf1þf2ð1� kevÞ2

þ sk;yðf1Þð1� kevÞ2ð1� sÞf2

þ ð1� kevÞs0kevð1� sÞf2

þ ð1� kevÞsk;yðf2Þ þ s0kev: ð23Þ

In general,

skðmÞ ¼ s0kðm� 1Þð1� sÞfm þ sk;yðfmÞ; ð24Þ

stotðmÞ ¼ NXN

k¼1

s0kðm� 1Þð1� sÞfm þ sðfmÞ; ð25Þ

s0kðmÞ ¼ kevs0 þ skðm� 1Þð1� kevÞ; ð26Þ

s0totðmÞ ¼ Nðkevs0 þ stotðm� 1Þð1� kevÞÞ: ð27Þ

It can be shown that the above equations are equiv-alent to the following ones:

skðmÞ ¼ s0ð1� sÞPm

l¼1flð1� kevÞm�1

þXm

l¼1

sk;yðflÞð1� sÞPm

v¼lþ1fvð1� kevÞm�l

þXm�1

l¼1

ð1� sÞPm

v¼lþ1fvð1� kevÞm�l�1s0kev;

ð28Þ

stotðmÞ ¼ Ns0ð1� sÞPm

l¼1flð1� kevÞm�1

þXm

l¼1

sðflÞð1� sÞPm

v¼lþ1fvð1� kevÞm�l

þ NXm�1

l¼1

ð1� sÞPm

v¼lþ1fvð1� kevÞm�l�1s0kev;

ð29Þ

s0kðmÞ ¼ s0ð1� sÞPm

l¼1flð1� kevÞm

þXm

l¼1

sk;yðflÞð1� sÞPm

v¼lþ1fvð1� kevÞm�lþ1

þXm

l¼1

ð1� sÞPm

v¼lþ1fvð1� kevÞm�ls0kev;

ð30Þ

which can be equivalently written as

The sum of the quantities of pheromone on thelinks departing from j is:

s0totðmÞ ¼ Ns0ð1� sÞPm

l¼1flð1� kevÞm

þXm

l¼1

sðflÞð1� sÞPm

v¼lþ1fvð1� kevÞm�lþ1

þ NXm

l¼1

ð1� sÞPm

v¼lþ1fvð1� kevÞm�ls0kev:

ð31Þ

Now we are interested in studying the behavior ofthe algorithm with varying the parameters whichcharacterize the pheromone evaporation. In particu-lar we expect that with increasing kev and decreasingthe evaporation interval, the effect of the process isstronger, in the sense that the probability gets closerto its initial value 1/N.


For the simulation shown in the remainder ofthis section, we assume N = 4.0, s = 0.3, s0 = 1.

Fig. 3 shows pk� with kev = 0.1 and with varyingm for different values of a constant number f of antscoming back to j between two successive evapora-tions. For simplicity sake we assume to be in thephase when all backward ants cross the link (k*, j)belonging to the shortest path. From Fig. 3 it canbe seen that, for m > 1, pk� increases when increasingf. This fact is reasonable, since bigger values of f

mean smaller evaporation rates.Fig. 4 shows pk� with varying m for different val-

ues of kev. Again we assume to be in the phase whenall backward ants cross the link (k*, j) belonging tothe shortest path. The average number f of antscoming back to j between two successive evapora-tions is set to N. We assume that for m > 8 no antscome back to j. From Fig. 4 it can be seen that, form > 8, if evaporation is performed, pk� decreaseswhen increasing m until the probability reaches itsinitial value, i.e., 1/N. Clearly, "m, the effect ofthe evaporation increases with increasing kev.

3.2. Threshold probability

As an extension of existing routing algorithms,we adopted a general criterion to decide whether arouting entry has to be considered either valid or

1 2 3 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p k*(m

)

Fig. 3. pk� with varying m for different values of the average number

not. This is a common problem in ad hoc networks,since when a route to a particular destination isfound, the node never knows how long this informa-tion may be kept. Since the node does not knowhow the topology changes, when the next routingrequest for the same destination arrives, it will notknow whether the old information can be still con-sidered valid.

If proactive ant routing protocols are adopted,the routing entry are supposed to be always valid,since the agents are sent periodically to ‘‘probe’’the network. As far as reactive ant routing protocolis concerned, different strategies have been imple-mented. In some protocols, e.g., ANB, when a back-ward ant arrives at its destination node, its memoryis transferred to a global ‘‘daemon’’ which calcu-lates the best path. In other approaches, e.g., inRBA and in ASGA, if a certain percentage of theprevious ants followed the same path, the path isconsidered valid. An allocator agent is then createdto allocate network resources along the best route.We note that the above listed solutions have beenapplied to connection-oriented protocols.

For connection-less approaches, like DAR, a dif-ferent solution is required. For instance in ADRAdatagrams are sent after the first relevant backwardant has come back to the source of the datagram.This solution could be reasonable if the forwarding

5 6 7 8m

f=1f=2f=3f=4

f of ants coming back to j between two successive evaporations.

2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

p k*(m

)

m

kev=0kev=0.01kev=0.5kev=0.1

Fig. 4. pk� with varying m for different values of the average number of kev.


of all the datagrams on the best path is not the maingoal of the algorithm. Nevertheless it might be use-ful to have the possibility to ‘‘tune’’ somehow thelevel of optimality of the routes which can be followby datagrams.

We defined a general criterion for DAR whichcan be checked by each individual node at eachinstant in a very simple way without the need ofan overall view of the network. For this reason thisfeature makes this ant routing algorithm fully dis-tributed. In this way local information (next hopprobabilities) is used in such a way that global infor-mation (a complete route between the source andthe destination) emerges from it without directexchange or synchronization of routing databetween the routers.

We set a probability limit, Lp. Every destinationd has a routing entry containing the different prob-abilities to select the different neighbors as the nexthop. If in the routing entry at least one neighborhas a selection probability pi(n) higher than Lp,then this routing entry is labelled with a flag mean-ing that it is ‘‘available’’. Clearly Lp > pi(0) = 1/N.Thus Lp is a kind of threshold which decides whena routing entry is good enough to be considered asavailable. This is done since after some ants havecome back through one particular neighbor, theprobability to choose that link as the next hop

increases, meaning that it is a good selection. Thisbrings that probability above the threshold and thiswill remain only if evaporation does not decreasethe probability value again. In principle there mightbe more than one neighbor with probabilitypi(n) > Lp, but normally there will be only one,since the ant sending process is stopped when thefirst good next hop is found. However in case twoprobabilities are over the threshold, packets arerouted to the next hop which presents the highervalue. Thus, a certain number of ants coming backfrom one particular neighbor will be required toincrease the probability associated with that neigh-bor and to make that neighbor the next hop for onedestination d.

In Section 4 DAR performance will be assessedwith varying algorithm parameters, in particularthe threshold probability Lp, which is main novelfeature introduced by DAR approach in the frame-work of ant routing algorithms. In particular theconvergence time and the signalling load, as dis-cussed in Section 1, are very important performanceparameter in the framework of ad hoc networkswith critical connectivity. We expect that the behav-ior of the convergence time and the signalling loadwith varying s and Lp is the same of the minimumnumber nb,min of backward ants need to be receivedon a certain link to reach the Lp threshold.


In the initial phase of a route discovery all thelinks departing from the current node have the sameprobability to be chosen by the ants. After this ini-tial transient period, the agents will start to con-verge on the best link. Because of the inherentheuristic nature of ant routing, we are interestedin the minimum number, nb,min, i.e., in the best case,now we calculate this parameter assuming that thebest path is already ‘‘raised’’, i.e., the initial tran-sient phase is finished. For simplicity sake we alsoassume that the pheromone value on the linkbelonging to the best path is 1 (as a consequenceon the other links departing from the current nodewill be smaller than 1).

It can be easily calculated that:

nb;min ¼lnðN � 1Þ þ ln

Lp

1�Lp

� �� lnð1� sÞ

2666

3777: ð32Þ

This minimum value is found by assuming that, dur-ing the entire period of time backward ants are com-ing back, no evaporation takes place and N remainsconstant (the number of neighbors does notchange).

If we call nm the time instant the mth backwardant moves over the link (i, j), and, as we mentionedpreviously, we also assume that si(n1 � 1) = 1, fromEqs. (1) and (2) it easily follows that:

0.1 0.2 0.3 0.40

2

4

6

8

10

12

14

16

18

20

22

n B,m

in(τ

)

Fig. 5. nB,min versus s with

piðn1Þ ¼siðn1ÞPNk¼1skðn1Þ

¼ 1

1þ ðN � 1Þð1� sÞ ; ð33Þ

piðn2Þ ¼siðn2ÞPNk¼1skðn2Þ

¼ 1

1þ ðN � 1Þð1� sÞ2; ð34Þ

and, in general,:

piðnmÞ ¼siðnmÞPNk¼1skðnmÞ

¼ 1

1þ ðN � 1Þð1� sÞm ; ð35Þ

which can be written in the following way:

m ¼lnðN � 1Þ þ ln piðnmÞ

1�piðnmÞ

� �� lnð1� sÞ : ð36Þ

Eq. (32) follows then from the definition of Lp. InFig. 5 nb,min is plotted as a function of s with Lp

as a parameter. The behavior of the function is rea-sonable, it can be easily understood that for highervalues of s (or smaller values of Lp), fewer backwardants nb,min are required to the bring a probability va-lue over the threshold Lp.

In Eq. (36) nb,min is the minimum number ofbackward ants needed to be received on a certain

link to reach the Lp threshold. Now we try to esti-mate the minimum number nb,min of backward antsneeded to be totally received from the node initiatorof the route request before the Lp threshold isreached.

0.5 0.6 0.7 0.8τ

Lp=0.3Lp=0.6Lp=0.75

Lp as a parameter.


We can estimate nb,min from Eq. (7), specificallynb,min can be defined as the minimum n such thatpi(n) P Lp.

0.5 0.6 0.70

2

4

6

8

10

12

14

16

18

20

22

n B,m

in(Y

)

Fig. 6. nB,min versus Y with s a

0.5 0.6 0.70

2

4

6

8

10

12

14

16

18

20

22

n B,m

in(Y

)

Y

Fig. 7. nb,min versus Y with Lp

In order to calculate nb,min we assume thatthe pheromone value on the link belonging to thebest path is 1, the other links departing from j are

0.8 0.9 1Y

τ=0.3τ=0.6τ=0.75

s a parameter (Lp = 0.4).

0.8 0.9 1

Lp=0.3Lp=0.35Lp=0.4

as a parameter (s = 0.3).

2 http://www.isi.edu/nsnam [47].


characterized by a smaller amount of pheromone,no evaporation takes place and N remains constant(the number of neighbors does not change).

We recall that yi(n) is a binary variable which is 1if the nth backward ant crosses the link (i, j), 0 other-wise. We can model the fact that not all the ants fol-low the same path in the following way. We setyk� ðnÞ ¼ Y 8n, where (k*, i) is the link belonging tothe shortest path and Y is a constant, with0 6 Y 6 1. Intuitively, if Y = 1 it means that allthe ants cross the link (k*, i) (as in Fig. 5), ifY = 0.5 it means that half of all the ants cross thelink (k*, i) and so on. In the remainder of the sectionwe assume for simplicity 0.5 6 Y 6 1, since after thetransient phase the ants are supposed to follow withmore probability the best path. This is a quitestrong assumption, which leads to an underestimateof the signalling load and the time employed to findthe path. This fact is particularly true for values ofLp close to 1. Nevertheless, the assumption is neces-sary because, due to the inherent heuristic nature ofant routing, it results quite difficult to exactly esti-mate such values. The assumption allows us toinvestigate algorithm convergence towards the solu-tion with varying algorithm parameters.

Fig. 6 shows nB,min versus Y with s as a parame-ter (Lp = 0.4).

Fig. 7 shows nB,min versus Y with Lp as a param-eter (s = 0.3). In this case nB,min is calculated by sim-ulation using MATLAB. The values are determinedon the basis of its definition.

From Figs. 6 and 7 it can be seen that nb,min

increases with decreasing Y. This is reasonable sinceif the number of ants crossing the link belonging tothe shortest path decreases, the convergence to theoptimal solution slows down. The behavior nB,min

varying Lp and s is the same of nb,min.

4. Setting of the parameters

Even if the DAR algorithm is very simple thereare several parameters to be tuned, e.g., s, rae.Proper tuning of these parameters becomes moredifficult if the ant routing algorithm is not in its sim-plest version and if it involves several additionalparameters and functions. This is considered a com-mon problem for ant routing algorithms.

The approaches commonly used to study antrouting algorithms largely exploit simulation soft-ware, due to the inherent heuristic features of themodel. Thus, in order to understand the character-istics and the performance of the suggested algo-

rithm, a comprehensive simulation campaign hasbeen conducted. Simulations have been done byusing the Network Simulator software NS-2.2

Due to the extreme conditions in which the rout-ing algorithms work in case of critical connectivity,for the DAR we need to tune the algorithm param-eters in a non-critical scenario. Thus we first consid-ered a traditional non-critical ad hoc network ofMobile Nodes (MN) using omni-directional anten-nas with a communication range of 100 m. Thepositions of the MNs are defined by the coordinatevalues x and y, which are randomly chosen in therange of the grid where the nodes can move. Thedimensions of the grid and the number of MNs havebeen chosen in order to have, for the given value ofthe communication range of the antenna, a meanvalue of N equal to 4. This means that on the aver-age each node will have four neighbors during thesimulations. We adopted a Poisson generation traf-fic process between uniformly distributed sourcesand destinations. In the following, the parameter kdenotes the mean flow generation rate over theentire network and l the mean flow release rate(thus 1/l is the average flow duration). We set lto 1/40 s�1. As a consequence the ratio k/l repre-sents the mean number of active flows in the wholenetwork. Nodes generate flows with constant bitrate. Each flow is made of 500-bytes-long datagramssent out every 0.25 s; thus the flow bit rate is 2 kB/s.This was selected assuming that the communicationamong nodes is mainly composed of short messages(the average resulting length of one flow is 80 kB).Now we need to make some considerations to eval-uate what are reasonable values of k to load such anetwork. If we consider that in the network therewill be an average number k/l of active flows, eachone transmitting with a bit rate equal to rF, theoverall capacity requested to the network will bek/lrF. We will consider that one flow is transmittedover a path with average length lp. We can roughlyestimate the maximum theoretical number np of dis-joint paths of average length lp available in a net-work with Nl links, as

np ¼N l

lp

: ð37Þ

For us it is Nl = 4NMN/2, since every node can com-municate on the average with 4 neighbors by meansof a wireless shared link of capacity Cl and each

http://www.isi.edu/nsnam


node has one single omni-directional antenna. Thuswe can think as if in the network there wereNl = 2NMN bidirectional links of capacity Cl/4 each.Since the np paths are assumed to be disjoint, thenetwork can offer on each path a capacity equal toCl/4. Thus the overall maximum theoretical capac-ity the network can offer is npCl/4. Hence:

kl

rF 6Clnp

4: ð38Þ

Thus using Eq. (37) in Eq. (38), we can estimate amaximum value for k to load our network as

k 6 kmax ¼ClN MNl

2lprF

: ð39Þ

Experimental estimations of lp in our scenario resultin a kmax ’ 10 s�1.

We stress that the capacity analysis above hasbeen done only in order to evaluate a maximumvalue for k. In the actual network the assumptionthat the paths are disjoint will not hold. Neverthe-less, considering a value for k which is very smallwith respect to kmax, we can reasonably expect thatthe network can satisfy the overall requestedcapacity.

The simulation time was set to 25000 s, which wehave demonstrated to be sufficient to prove our the-oretical analysis.

The aim here is to verify analytically the Lp-related theoretical analysis presented in Section3.2, in particular the calculus of Eq. (32). SinceEq. (32) was found assuming that N is constant,we assumed a fixed topology. As a consequence,evaporation is not needed. These assumptions,which may not be correct in a traditional ad hocenvironment, reveal to be right in a critical connec-tivity scenario. They are simple enough to set theparameters if the algorithm has to be used in envi-ronments where the main problem is to find a solu-tion, no matter if it is optimal or not (this conceptwill be better outlined in Section 5). For the samereason we do not need to load the network, and thuswe set k to 1/30 s�1, which is small enough withrespect to kmax. The analysis in this section alsoallows us to compare the DAR algorithm with theAODV.

We refer to the convergence time tconv as the timeelapsed between the event that a datagram triggersthe sending of discovery packets in a node and thetime when this datagram is forwarded from thenode. This value is a measure of how fast the rout-ing protocol can find a next hop for a route request,

or equivalently how long it takes to bring a routingentry up, if required.

We define NRL as the ratio of the routing signal-ing load (in bytes) and the total number of bytessent. In DAR the signaling load includes the totalnumber of forward and backward ants; in AODVit includes the total number of RREQ, RREP andRERRs. In order to compare the two algorithms,we do not consider the HELLO messages since theamount of these signaling packets is the same inboth approaches. The size of each routing packetin DAR is 146 bytes (Sa = 146 bytes); in AODVthe size of RREQ, RREP and RERR is 48, 44and 32 bytes, respectively. This was estimated bysimulating the signalling packets with the relevantheaders. The DAR packets are larger since eachant has to store the identities of the nodes it passedthrough. In real implementations these packetscould contain a field of fixed length, proportionalto the maximum number of hops constituting aloop-free path in the network. This is a waste ofresources since some space of the field could oftenremain unused. This problem can be faced by creat-ing a dynamic list in the packet header, as it hap-pens, for instance, in IPv6 [48].

4.1. Setting of s and Lp

As a preliminary consideration, we should esti-mate the range where rae can vary. Clearly the timebetween the sending of two forward ants has to belonger than the ant transmission time. Thus itresults

1=rae > Sa=Cl; rae < Cl=Sa; ð40Þ

where Sa is the size of each ant routing packet andCl is the link capacity. In this case it resultsrae < 850 s�1.

On the other hand it does not make much sensewaiting for the first ant to come back to the sourcebefore sending the second one. Referring to RoundTrip Time (RTT) as the time needed by the last for-ward ant to reach the destination from the sourceplus the time needed by its relevant backward antto come back, we have

1=rae < RTT: ð41Þ

In order to better understand this, we need to makesome further considerations. We can assume thatwhen a discovery process is performed the relevantrouting table is set to ‘‘up’’ when nb ants come back


to the source. If 1/rae is greater than RTT, the pro-cess can be represented as in Fig. 8a.

In this case the routing load on the network isdirectly proportional to nb and it does not dependon rae, since there are no ants roaming in the net-work if the routing table is ‘‘up’’.

If 1/rae > RTT also NRL is almost directly pro-portional to nb,min. We have used the RTT meanvalue obtained by AODV in the same experimentalconditions (0.01 s). Simulation results for

Fig. 8. Scheme of a DAR discovery process (nb =

0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

τ

NR

L

Fig. 9. NRL versus s with

rae = 10 s�1 are shown in Fig. 9, where NRL is plot-ted as a function of s and for different values of Lp.As expected, the behavior of NRL with varying sand Lp is the same as nb,min of Fig. 5. This is reason-able, it can be easily understood that for higher val-ues of s (or smaller values of Lp), fewer backwardants nb,min are required to the increase a probabilityvalue over the threshold Lp. We have ran some sim-ulations under the same experimental conditions byusing the AODV protocol and we have obtained

3) with 1/rae > RTT (a) and 1/rae < RTT (b).

0.5 0.6 0.7 0.8

AODVLp=0.3Lp=0.6Lp=0.75

Lp as a parameter.


0.0533 as NRL (as shown in Fig. 9). As it can beclearly seen from the figures, for some values of sand Lp, DAR outperforms AODV.

In Fig. 10 tconv is plotted as a function of s withN = 4 and with Lp as a parameter. The simulationresults are averaged over the simulation time andpresented as mean convergence time with the 90%convergence intervals. The behavior of the functionis reasonable, again for higher values of s (or smal-ler values of Lp), fewer backward ants nb,min arerequired to the bring next hop selection probabilityover the threshold Lp. On the basis of the resultsshown, we can say that a trade-off solution consistsof having a reasonable low number of backwardants, for example nb,min = 6; in this scenario thiscan be obtained for values of s = 0.3 and Lp = 0.6.

4.2. Setting of the ant emission rate

Until this point we have considered the case1/rae > RTT. On the other hand, if the second antis sent before the first ant comes back to the source,that is if 1/rae < RTT, the situation changes asshown in Fig. 8b. In this case the routing loaddepends on rae, since there might be ants roamingin the network even if the routing entry is ‘‘up’’.In fact, before the routing table goes up, bRTT raecants are sent out, additionally to the nb ants which

0.1 0.2 0.3 0.40

0.5

1

1.5

2

2.5

3

τ

t conv

(τ)[s

]

Fig. 10. Convergence time versus s with Lp as a param

would be strictly necessary. Thus, we can estimateNRL as follows:

NRL ¼ 2Sandpðnb;min þ bRTT raecÞnBs

: ð42Þ

The factor 2 is due to the fact that each ant comingback to the source is associated with two signalingpackets, a forward ant and a backward ant; ndp isthe number of discovery processes done in the wholenetwork and nBs is the total number of data bytessent.

In order to experimentally verify the validity ofEq. (42), we ran some simulations. The resultsobtained are shown in Fig. 11, where NRL is plot-ted as a function of rae for different values of s, withLp = 0.4. The results follow expectations, routingsignaling load increases almost linearly with rae,and the values are comparable to AODV perfor-mance (0.0533). We can argue that rae should besmall in order to have low signalling load but, onthe other hand, having a big rae would allow havinga short convergence time. In fact the minimum pos-sible convergence time tconv min can be expressed as afunction of rae in the following way (see alsoFig. 8b):

tconv minðraeÞ ¼ðnb;min � 1Þ

rae

þRTT: ð43Þ

0.5 0.6 0.7 0.8

Lp=0.3Lp=0.6Lp=0.75

eter, together with the 90% confidence intervals.

100 200 300 400 500 600 700 8000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

rae [s—1]

NR

L

AODVDAR: τ=0.25DAR: τ=0.4DAR: τ=0.9

Fig. 11. NRL versus rae for different values of s.


By substituting Eq. (32) in Eq. (43) we have

tconv minðraeÞ

¼lnðN � 1Þ þ ln

Lp

1�Lp

� �� lnð1� sÞ

2666

3777� 1

0@

1A 1

rae

þRTT:

ð44Þ

We stress that Eq. (44) has been calculated byconsidering Y = 1 (see Section 3.2). In Fig. 12tconv min(rae) is plotted for different values of s withLp = 0.4 and N = 4.

Fig. 13 shows tconv min with varying rae for differ-ent values of Y (with Lp = 0.4 and s = 0.25). In thiscase tconv,min is calculated by simulation usingMATLAB. The values are determined from Eq.(43) substituting nb,min with nB,min.

From Fig. 13 it can be seen that tconv min increaseswith decreasing Y. This is reasonable, because, asalso shown in Figs. 6 and 7 of Section 3.2, if thenumber of ants crossing the link belonging to theshortest path decreases, the convergence to the opti-mal solution slows down.

In order to experimentally verify the validity ofEq. (44), we ran some simulations and we plottedthe measured tconv(rae) for different values of the s.The simulation results are averaged over the simula-tion time and presented as mean convergence time

with the 90% convergence intervals. The behaviorof the experimental function is the same as the the-oretical one. The higher values obtained in Fig. 14are due to the fact that, in computing Eq. (32), fromwhich Eq. (44) is derived, we optimistically assumedthat each forward ant chooses the best path towardsthe destination.

By comparing Figs. 14 and 13 we can estimatethat, on average, 60% of the ants choose the linkbelonging to the shortest path.

Thus it correctly results that tconv minðraeÞ 6tconvðraeÞ; 8rae.

We have ran some simulations under the sameexperimental conditions using the AODV protocoland we have obtained a mean convergence time of0.0175 s. This value is comparable to the onesobtained with DAR, when the values of the param-eters s, Lp and rae are carefully selected.

The simulation results shown in Figs. 11, 12 and14 also confirm that for bigger s we get smaller rout-ing signalling load and convergence time. We canconclude that DAR does not perform worse thanAODV if the parameters are correctly chosen. Inorder to obtain a trade-off in terms of routing loadon the network and convergence time, an optimalvalue for the parameter rae is around 400 s�1. Actu-ally we can also intuitively understand that in orderto have a good route selection, i.e., a low mean end-

100 200 300 400 500 600 700 8000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

t conv

,min(r ae

)[s]

rae[s—1]

Y=0.5Y=0.6Y=0.8Y=1

Fig. 13. Convergence time versus rae with Y as a parameter: analytically estimated minimum mean value.

100 200 300 400 500 600 700 8000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

t conv

,min(r

ae)[

s]

rae

[s–1]

τ=0.25τ=0.4τ=0.9

Fig. 12. Convergence time versus rae with s as a parameter: analytically estimated minimum mean value.


to-end delay, intended as the time elapsed between adatagram is generated by the source node and it issuccessfully received at the destination, we need abig number of backward ants coming back, and this

means having values of s close to 0 and values of Lp

close to 1.The DAR performs operations (weighted ran-

dom selections), which are much simpler than those

100 200 300 400 500 600 700 8000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

rae

[s–1]

t conv

(rae

)[s]

AODVDAR: τ=0.25DAR: τ=0.4DAR: τ=0.9

Fig. 14. Convergence time versus rae with s as a parameter: simulation results together with the 90% confidence intervals.


performed by conventional algorithms, and thiswas also not included in the comparison of the pro-tocol ‘‘cost’’. The authors believe that the simplicityof the protocol and the very low complexity largelycompensate for the small disadvantage of havingone or two more parameters which have to beset.

5. MANET routing in critical connectivity

In this section we investigate the performance ofboth traditional MANET routing algorithms andDAR, when operating in conditions of critical con-nectivity and with very intermittent links. The mainmotivation of using MANET routing in networkswith critical connectivity is to be independent fromthe topology constraints. Clearly a new algorithmspecifically designed for a sparse network with agiven level of connectivity can perform better; butif the level of connectivity changes new algorithmsnormally need to be designed. In addition the degreeof sparseness of a network may change of someorders of magnitude inside the network itself: incluster areas many nodes may be close to each oth-ers, in other areas there may be isolated nodes withshort connection time windows. It would be desir-able to have algorithms which operate indepen-dently from the local characteristics of the

topology, and in particular in the transition regionwhere the connectivity is too low for traditionalMANET routing, but it is still too high for specificrouting algorithms, i.e., when the average numberof neighbors for each node is smaller than someunits.

The aim is to optimize the Packet Delivery Ratio(PDR), defined as the ratio of data packets deliveredto the destination and those generated by the sourcenodes. In ad hoc networks with critical connectivitythe main goal may be not optimal performancecommunications; this might be the case if the net-work is well meshed and the concentration of nodesis high. On the other hand, when the network is verysparse and when it presents long outage periods, itmight also be that the main goal is simply to finda way at all and at some time.

For the simulations of this section we did notimplement pheromone evaporation for the follow-ing reason. Let us consider the shortest pathbetween a node i and a destination d. We definethe path between i and d comprising the link (i, j1)as path1 and the path between i and d comprisingthe link (i, j2) as path2. Now suppose that the short-est path between i and d is path1 and, after someseconds, the topology varies and the shortest pathbetween i and d becomes path2. We consider twocases:


• Case 1: If j1 is still in the transmission range of i,after this change, the ants will continue to selectpath1 since it is characterized by more phero-mone. Nevertheless there will be some forwardants crossing the link (i, j2). The correspondentbackward ants will cross the link (j2, i) beforebackward ants cross the link (j1, i) (since path2is shorter). As a consequence the quantity ofpheromone on link (i, j1) will start decreasing(see Eq. (1)). This process will change the phero-mone on the two links until, depending on thevalues of s and Lp, the forward ants will startselecting more frequently path2. Clearly, greaterthe difference in length between path1 and path2,sooner the forward ants will start selecting withmore probability path2. This effect is acceleratedif evaporation is implemented. Anyway if evapo-ration does not take place, this is not a problemsince, as already pointed out, path1 is still a suit-able path to d and the optimality of the solutionfound is not the first aim in case of networks withcritical connectivity.

• Case 2: Now we consider the case in which j1 isnot in the transmission range of i (i.e. the link(i, j1) does not exist anymore). We note that thiscase is much more likely than Case 1 for ad hocnetworks with critical connectivity. With respectto Case 1, it is less likely that ants will be influ-

0 50 100 150 2000

50

100

150

200

250

300

350

400

Gauss—Marko

X

Y [m

]

Fig. 15. Example of traveling pattern for a mo

enced by past dropped pheromone: After a shorttransient time, they will find the new right way tothe destination by means of their foraging behav-ior. Thus evaporation is not needed in thiscase.

5.1. Mobility model

The performance results of an ad hoc networkprotocol significantly depends on the mobilitymodel adopted for the simulation. A survey ofmobility models that are used in the simulations ofad hoc networks can be found in [49,50]. As statedin [51], the use of a mobility model where the newchoice for speed and direction is not correlated toprevious values, may cause unrealistic movementbehaviors with sudden speed changes and sharpturnings. For this reason, we adopted for our simu-lations the Gauss–Markov mobility model [52,53],which includes both speed and direction dependencefrom the values at the previous step. The following‘‘border rule’’ is adopted: when a mobile nodes issubject to leave the simulation area, it is bouncedback to this area with a direction which is perpen-dicular to the side where the bounce occurred. Anexample of a node movement following theGauss–Markov model is given in Fig. 15. The valuesfor the parameters used are listed in Table 3.

250 300 350 400

v Mobility Model

[m]

bile node (duration 400 s, vave = 0.1 m/s).

Table 3Parameter values of the Gauss–Markov mobility model

Position update interval 0.1 sa 0.95dave Random selected in [0,2p]vave 0.1 m/s


5.2. Results of the analysis

Many different approaches to handle routing inad hoc networks were proposed in recent years[54–56]. In Sections 2 and 4 DAR was presentedand its performance assessed in comparison AODVbecause AODV is the most well-known MANETprotocol which shares the main DAR features,e.g., the on-demand and hop-by-hop behaviors.Table 4 shows the characteristics of DAR togetherwith the most well-known protocols in the area ofMANET routing algorithms. In this way a rangeof design choices is covered, including periodicadvertisements versus on-demand route discoveryand hop-by-hop routing versus source routing.

The DSDV protocol has been included in Table 4as an instance of proactive routing protocol (seealso Section 1). Other proactive MANET routingprotocols are Clusterhead Gateway Switch Routingprotocol (CGSR) [57] and Wireless RoutingProtocol (WRP) [58]. CGSR modifies DSDV byusing a hierarchical cluster-head-to-gate-way rout-ing approach. Each node is associated with a clustermember table where it stores the destination clusterhead for each mobile node in the network. In WRPa shortest-path spanning tree is reported by eachneighbor. For this reason reactions to failures maybe far-reaching (i.e., every node which includes thefailed link in its shortest-path spanning tree isinvolved in the failure reaction).

Other MANET routing protocols proposed inthe literature have not been considered in this paperbecause they show characteristics quite differentfrom DAR. For instance, Location-Aided Routing(LAR) [59] protocol belongs to the class of geo-graphic routing algorithms, which limit the searchfor a route to the so-called request zone, determinedbased on the expected location of the destinationnode at the time of route discovery. This informa-tion is not always available in networks with criticalconnectivity.

An other example of MANET routing algo-rithms is given by hybrid protocols, which groupthe node into zones and use proactive scheme insidethese zones and reactive between zones. In general

they show high computational complexity andrequire additional traffic for creation and maintain-ing of their topology information. Hybrid protocolsare: Core Extraction Distributed Ad Hoc RoutingProtocol (CEDAR) [60], Zone-based HierarchicalLink State Routing Protocol (ZHLS) [61], PreferredLink-based Routing Protocol (PLBR) [62], Opti-mized Link State Routing Protocol (OLSR) [63].A well-known hybrid protocol is ZRP [64]. We didnot consider ZRP for comparison purposes becauseZRP is a routing framework rather than an inde-pendent protocol. ZRP combines two completelydifferent routing methods into one protocol. Withinthe routing zone, the proactive Component IntrAz-one Routing Protocol (IARP) [65] maintains up-to-date routing tables. Routes outside the routing zoneare discovered with the reactive component IntEr-zone Routing Protocol (IERP) [66] using routerequests and replies.

A link in a MANET with critical connectivitycould become unavailable for a relatively long per-iod of time and no other alternative routes couldbe available. Potentially rapidly changing topologymakes it important to find routes quickly, even ifthe route may be suboptimal. Normally the optimalroute can be found only if the source node (and notan intermediate node) is the initiator of the routerequest, but, depending on the changes in topologyand on the nodes movement, this route may notalways remain the shortest. For this reason tradi-tional MANET routing protocols (see for instanceAODV) use error notification messages to discarda route even if only a portion of it becomes unavail-able because of topology changing: most likely theavailable portion will not be a part of the new opti-mal path, thus it is worth to recalculate the wholeroute again. On the other hand in MANETs withcritical connectivity the focus is not really on pathoptimality, but rather on a fast reaction to topologychanges, since one of the major goals is to deliver asmuch data as possible to the destination node. Inthis case it is convenient to store the packets andforward them to the destination once a connectionis resumed. If the current node cannot forward adatagram due to a link which becomes available,AODV drops the datagram and a RERR is sentto all the nodes using the link to forward packets,so that relevant routing tables can be changed. InDAR, the datagram is buffered and the node startssearching for a new route by sending forward ants.We define qlim as the maximum number of packetswhich can be buffered at each node. Fig. 16 shows

Table 4Some MANET routing protocols

Features DSDV DSR TORA AODV DAR

Proactive versusreactive

– Proactive – Reactive – Proactive (and reactive) – Reactive – Reactive

Routingalgorithm

– Distributed Bellman–Ford – Link state – Link-reversal relaxation – Distributed Bellman–Ford – Ant routing

Forwardingalgorithm

– Hop-by-hop – Source routing – Hop-by-hop – Hop-by-hop – Hop-by-hop

Maininformationstored in therouting table

– Deterministic routes aremaintained in a distributedfashion. Routing tableentries are tuples in the form:destination,hops_to_destination,sequence_number

– Each node has adeterministic route cache,where complete routes todesired destinations arestored

– Each node stores the heightmetric associated with eachneighbor and the assignedstatus of the link to suchneighbor

– Deterministic routes aremaintained in a distributedfashion. Routing table entriesare tuples in the form:destination, next_hop,distance

– Stochastic routing table:the next hop is selectedaccording to weightedprobabilities

Route discovery – Periodic advertisement – A RREQ is broadcast.Once the RREQ reaches thedestination, it replies with aRREP that copies the routefrom the RREQ andtraverses it backwards

– The nodes use a ‘‘heigh’’metric, which establishes aDAG rooted at thedestination. Links areassigned a direction based onthe relative height metric ofneighboring nodes

– A RREQ is broadcast. Oncethe RREQ reaches thedestination, it replies with aRREP that copies the routefrom the RREQ and traversesit backwards

– Forward ants are sent.Once they reach thedestination, they generatebackward ants which copythe route from the forwardants and traverses itbackwards

Mechanismsused toguarantee thefreshness ofthe routes

– Each node maintains amonotonically increasingeven sequence number,which is disseminated in thenetwork via update messages

– Intermediates nodes do notneed to maintain up-to-daterouting table

– For each interface a routermaintains a sequence numberthat is incremented uponchanges to the interface modeof operation (reactive/proactive)

– The source sequencenumber is used to maintainfreshness information aboutthe reverse route to the sourceand the destination sequencenumber specifies how fresh aroute to the destination mustbe before it can be accepted bythe source

– Ant routing process,pheromone evaporation

Routemaintenance(behavior incase of linkfailure)

– A RERR is broadcast inorder that any route throughthat next hop is assigned aninfinite metric and an updatesequence number

– A RERR is broadcast tothe source in order to eraseall routes in the route cachesof all intermediate nodes onits path, if the routecontained the failed link

– Done on a proactive basisthrough link-reversal routerepair, whenever topologicalchanges cause a node to looseits last downstream link. Incase of a network partition,the protocol erases all invalidroutes

– A RERR is sent backwardsto the active neighbors, whichforward them to their activeneighbors and so on. Allrouting table entries areerased for which the failedlink is on the active path

– Node starts searching for anew route by sendingforward ants

Route deletion(when route isnot necessary)

– Routes are alwaysmaintained

– Expiration timer – Flooding CLR (clearpacket)

– Expiration timer – The labels of the relevantrouting table entries are setto ‘‘DOWN’’

L.

Ro

sati

eta

l./

Ad

Ho

cN

etwo

rks

6(

20

08

)8

27

–8

59

851

100 1010

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N

PDR

qlim=1qlim=10qlim=100qlim=1000

Fig. 16. Packet Delivery Ratio as a function of N for different values of the buffer size using the DAR algorithm.


that, for the DAR algorithm, PDR increases if themaximum number of packets buffered per node alsoincreases. This implies a higher average end-to-enddelay experienced by the datagrams to reach thedestination, but a higher average fraction of packetdelivery. We aimed at analyzing how PDR variesfor different values of the average value N of neigh-bors that the mobile nodes experience over time. Byusing the same traffic patterns as described in Sec-tion 4 and the simulation parameters summarizedin Table 2, we have run some simulation for 10 dif-ferent values of N. N is varied by adjusting the sim-ulation area and the initial positions of the mobilenode, chosen in order to have N set to 10 valuesequally distributed in logarithmic scale in the range[0.1;10] the number of mobile nodes. The figuresbelow are plotted as functions of the average num-ber N during the whole simulation. During the sim-ulation the mobile nodes move with an averagespeed of 0.1 m/s.

In Fig. 17 we plotted PDR with varying N fordifferent MANET routing protocols, i.e., AODV,TORA, DSR, DAR (qlim = 1000).

The simulated model scenario is based on thecomparison of AODV, DSR and TORA, the threeprominent on-demand routing protocols for ad hocnetworks. A performance comparison of DSR,TORA and AODV is presented, e.g., in [67–69].

The different basic working mechanisms ofAODV, DSR and TORA leads to the differencesin performance. The presence of mobility impliesfrequent link failures and each routing protocolreacts differently during link failures.

Data packets may be dropped for two reasons:the next hop link is broken when the data packetis ready to be transmitted, or there are no availablerouting table entries for the intended destination. Inparticular a number of packets are dropped duringthe route discovery phase.

As we can see from both Figs. 16 and 17, for lowconnectivity, few data packets are delivered due tolack of a route. Many of the sessions abort becauseroutes to the destination are unavailable. The fewsessions that are able to be completed are those witha small path length. As the connectivity increases,however, the number of delivered packets rapidlyincreases.

The performance of MANET routing protocolsdepends on a lot of factors, e.g., the mobility model,the number of mobile nodes, the traffic pattern, any-way, we can notice that DAR has a very good per-formance in comparison with the other algorithms.

The simulations of Fig. 17 show that AODV per-forms better from the point of view of the PDRcompared to DSR and TORA. The same resultwas obtained in other papers, e.g.,in [69] with and

100 1010

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

N

PDR

AODVTORADSRDAR

Fig. 17. Packet Delivery Ratio as a function of N using different MANETs algorithms.


without mobility in networks composed of a largernumber of nodes (precisely greater than 20).

In AODV each link failure triggers new route dis-coveries because the routing table has at most oneroute per destination. AODV also uses route expiry,dropping some packets when a route expires and anew route must be found.

With respect to AODV, TORA causes morepacket drops because the asynchrony in the distrib-uted implementation can cause short-lived inconsis-tencies about the sense of the direction of a link asperceived by the nodes at the end-points of this link.Hence packets drop because of short-lived routingloops. This is a consequence of its link-reversal pro-cess. Moreover the initial route discovery takeslonger in TORA with respect to AODV. In TORAthere is a potential for oscillations to occur, espe-cially when multiple sets of coordinating nodes areconcurrently detecting partitions, erasing routes,and searching new paths based on each other [56].

DSR shows the worst performance from thepoint of view of the PDR. The reason for that bedue to the absence of an explicit mechanism toexpire stale routes (DSR does not depend on anyperiodic or timer based activity) and to its aggres-sive use of source routing and route caching [70].In DSR, in case of link failure, a new path discoveryis delayed until all cached multiple routes for the

destination are not available. With high mobility,the cache might become stale. For this reasonDSR is intended for networks in which the mobilenodes move at moderate speed with respect topacket transmission latency [3]. Assumptions thealgorithm makes for operation are that the networkdiameter is relatively small.

6. Conclusions

In this paper we show the results obtained byant-inspired heuristic and distributed algorithms toroute packets in a MANET. A new ant routingalgorithm, named DAR, has been shown and ana-lyzed by means of theoretical analysis and a simula-tion campaign. The definition of this approach wasmade on the basis of a possible categorization of themost well-known ant routing algorithms to befound in the literature, in order to design anapproach which requires the minimum computa-tional complexity. The performance comparison ofDAR with a well-known reference algorithm in adhoc networks, the AODV, has revealed that withan appropriate tuning of the parameters, DAR givesbetter results from the point of view of the signallingload and the convergence time, in the same experi-mental conditions considered in this paper and thatare representative of a MANET scenario. For this

Table 5 (continued)

pi(n) probability for a forward ant at the current node tochoose the node i

as the next hop after n backward ants coming back tothe current node

qlim buffer sizerae ant emission rate [s�1]rF transmission bit rate [bit/s]Sa size of DAR routing packets [bytes]tconv convergence time [s]tconv min minimum convergence time [s]yi(n) binary variable which is 1 if the nth backward ant

crosses the link (i, j) (with j current node), 0 otherwise


reason DAR is suitable in scenarios with criticalconnectivity, where the QoS requirements consistof a fast reaction to topology changes and a mini-mum signalling overhead regardless path optimal-ity. An important instance is represented by adhoc networks with critical connectivity, where tradi-tional MANETs protocols could be ineffective, dueto their intrinsic design goal to look for an optimalroute. In this challenging scenario the comparisonhas been extended to other known routing protocolused in MANETs. In addition, the simplicity, flexi-bility and robustness of DAR are always appealingfeatures which make the approach a good solutionin different kinds of topology scenarios.

Acknowledgement

This work has been partially funded by the Euro-pean Community under the 6th Framework Pro-gramme IST Networks of Excellence ‘‘SatNEx’’(contract No. 507052) and ‘‘SatNEx II’’ (contractNo. 027393).

Appendix A. Symbols

See Table 5.

Table 5List of notations used for the definition and study of DAR

Dpl(n) increment in the probability pi(n) provided by thel-backward ant, with l 6 n

Dtev evaporation interval [s]k mean flow generation rate [s�1]l mean flow release rate [s�1]mmax maximum node speed [m/s]s quantity of pheromone deposited on each crossed link by

a backward ants0 initial value of pheromone on each linksi(n) amount of pheromone on the link (j, i) after n backward

ants coming back to the current node j

stot(n) sum of the quantities of pheromone on the linksdeparting from the current nodeafter n backward ants coming back to it

Cl wireless shared link capacity [Mbps]kev evaporation constantlp average path lengthLp probability limitN average number of neighborsNl number of unidirectional links in the networknb number of backward antsnBs total load sent in the network [bytes]nb,min minimum number of backwards ants that have to pass a

link before it becomes availablendp number of ant routing discovery processesnp number of paths

Appendix B. DAR pseudocode

Fig. 18 shows a flow-chart description of thealgorithm. All the described actions take place in acompletely distributed and concurrent way overthe network nodes.

Tables 6–9 describe in more details the mainalgorithm steps.

Specifically, when a node receives a datagram,the procedure Receive_Datagram (see Table 6) isimplemented.

If the routing entry of the node relevant to thedestination (dest_node) of the datagram is labeledwith a flag set to ‘‘UP’’, then the datagram is for-warded according to the next hop stored in the rout-ing table, otherwise it is buffered at the node. If thelabel is set to ‘‘IN_REPAR’’, it means that antslooking for the best path towards that destinationhave already been sent. If the flag is ‘‘DOWN’’ thenit is set to ‘‘IN_REPAIR’’ and ants are created andsent (procedure Send_Request, see Table 7). Theprocedure Send_Request describes the behavior ofthe ants. Note that the node where an ant is gener-ated (source_ant_node) can be different from thesource of the flow (source_node). Note also thatthe source of a forward ant, i.e., source_ant_node,and its destination are the destination and thesource of the corresponding backward ant,respectively.

Forward ants choose the next hop according tothe probabilities associated with the links departingfrom the current node (function Select_Link) andstore the crossed nodes in the array List_Crossed_nodes. This array is used by the forward ants toavoid loops, i.e., the next hop is chosen only amongthe neighbors of the current node which are notbeen visited by the ant yet. Moreover the array isused by the correspondent backward ants to findits way back to (source_ant_node).

Fig. 18. Top level flow chart describing DAR algorithm.

Table 6High-level description of Receive_Datagram procedure inpseudo-code

Procedure Receive_Datagram (p,current_node);if (TTL = 0),

Drop(p);return;

end if;dest_node :¼ p dest_node;rt routing_table(current_node,dest_node);case (rt rt_flag):UP

current_node :¼ rt rt_next_hop;;IN_REPAIR

enqueue(datagram,current_node);DOWN

rt_flag :¼ IN_REPAIR;enqueue(datagram,current_node;SEND_REQUEST(current_node,dest_node;

end case;end Procedure Receive_Datagram;


When the backward ant gets to its destination,the procedure Recv_Reply (see Table 8) isimplemented.

According to this procedure, if the condition ofthe threshold probability is satisfied or source_ant_node has only one neighbor, then the relevant rt_flag

is set to ‘‘UP’’ and the datagrams buffered at sour-

ce_ant_node are forwarded according to the routingtable. Each packet (both ants and datagrams) isassociated with a Time To live (TTL), which isincreased of 1 for each hop done by the packet.When a node receives a packet, the value of itsTTL is checked. If the TTL value is 0, then thepacket is dropped.

Beside these procedures, also neighbor manage-ment functions are implemented (see Table 9). Eachnode maintains a list of neighbors. If a node receivesan ‘‘HELLO’’ packet from a node which is in itsneighbor list, then the relevant expiration timer is

Table 7High-level description of Send_Request procedure in pseudo-code

Procedure Send_Request(source_ant_node,dest_node);i :¼ 0;while (current_node 5 dest_node)

if (TTL > 0) and (neighbor(j))next_hop_node :¼ SELECT_LINK

(current_node,dest_node,List_Crossed_nodes);list_crossed_nodes(i) :¼ current_node;i++;current_node :¼ next_hop_node;

else

DROP;end if;

end while;CREATE_BACKWARD_ANT(List_Crossed_nodes);KILL_FORWARD_ANT;while (current_node neq source_ant_node),

UPDATE_LOCAL_ROUTING_TABLE(current_node,dest_node);next_hop_node :¼ list_crossed_nodes(i);i :¼ i � 1;current_node :¼ next_hop_node;

end while;RECV_REPLY(source_ant_node,dest_node);KILL_BACKWARD_ANT;

end Procedure Send_Request;

Table 8High-level description of Recv_Reply procedure in pseudo-code

Procedure Recv_Reply(source_node,dest_node);if (pmax(source_node,dest_node) > Lp) or (only_one neighbor

(source_node)),rt rt_flag:¼RTF_UP;dequeue(current_node);STOP_SENDING_ANTS;

else

rt rt_flag:¼RTF_DOWN;end if;

end Procedure Recv_Reply;

Table 9High-level description of Recv_Hello procedure in pseudo-code

ProcedureRecv_Hello(current_node,neighbor_node);if Nb_Lookup(neighbor_node),

Update_Expiration_Timer(neighbor_node);else;

Add_Neighbor (neighbor_node);end if;Kill_Hello_Packet;

end Procedure Recv_Hello;


updated (procedure Update_Expiration_Timer). If anode does not receive within a pre-defined intervalan ‘‘HELLO’’ packet from one of its current neigh-bors, then this timed-out neighbor is deleted fromthe list. If a node receives an ‘‘HELLO’’ packetfrom a node which is not currently in its neighbor

list, then this neighbor is added in the list (procedureAdd_Neighbor). In both cases, the values of thepheromones and the probabilities associated withthe links departing from the current node areupdated accordingly. Then the ‘‘HELLO’’ packetis dropped.

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Laura Rosati received the Laurea degreein electronic engineering (magna cum

laude), from the University of Perugia,Perugia, Italy, in 2003, where she iscurrently working toward the Ph.D.degree in information and electronicengineering.

Since 2003, she has been with theGerman Aerospace Center (DLR),Oberpfaffenhofen, Germany, in theDigital Networks Group of the Institute

of Communications and Navigation. Her main research activitiesinclude routing on MANETs and resource allocation in hybrid
terrestrial/satellite networks. She is currently involved in the ISTNetwork of excellence SatNEx II.
Matteo Berioli received a Laurea degreein electronic engineering, and the Ph.D.degree in information engineering fromthe University of Perugia (Italy), in 2001and 2005 respectively, both with hon-ours; the title of the Ph.D. thesis was‘‘MPLS and IP tunnels in DynamicSatellite Networks’’. Since 2002, he iswith the German Aerospace Center(DLR). His main research activitiesinclude QoS and protocol analysis in IP-

based dynamic networks, with a focus on satellite systems andtheir integration with terrestrial networks; key research issues are
cross-layer techniques, multicast, dynamic routing, packet-layer
http://www.netlab.hut.fi/opetus/s38030/k02/Papers/08-Nicklas.pdf

http://www.netlab.hut.fi/opetus/s38030/k02/Papers/08-Nicklas.pdf

http://www.ietf.org/proceedings/02nov/I-D/draft-ietf-manet-zone-iarp-02.txt

http://www.ietf.org/proceedings/02nov/I-D/draft-ietf-manet-zone-iarp-02.txt

http://www.ietf.org/proceedings/02nov/I-D/draft-ietf-manet-zone-ierp-02.txt

http://www.ietf.org/proceedings/02nov/I-D/draft-ietf-manet-zone-ierp-02.txt


coding. In the last years he was involved in several European andESA projects, and he has also worked as expert for the EuropeanTelecommunications Standards Institute (ETSI) in the area ofbroadband satellite multimedia; he is currently chairing thesatellite working group of the PSCE Forum (Public SafetyCommunications Europe Forum). He is author/co-author ofmore than 30 papers, which appeared in international journalsand conference proceedings. He has been a reviewer for technicalinternational journals and for many international conferences.

Gianluca Reali is an associate professorof the Department of Information andElectronic Engineering (DIEI) of theUniversity of Perugia since January2005. He received the ‘‘Laurea’’ degree inElectronic Engineering from the Uni-versity of Perugia in 1991, with honours.He received the Ph.D. degree in Tele-communications from the University ofPerugia in 1997. From April 1997 toDecember 2004 we was researcher at

DIEI. From August 1999 to January 2000 he was visitingresearcher at the Computer Science Department of the University
of California at Los Angeles (UCLA) USA. Currently G. REALIcoordinates the research activities and related projects in the areaof Telecommunication Networks done at DIEI. His past andcurrent research activity (published on about 80 papers in peer-refereed international journals and conferences) spans severalareas, including spread spectrum techniques, equalization of
propagation effects in wireless mobile channels, resource alloca-tion over circuit-switched satellite networks, design and perfor-mance evaluation of broadband and wireless networks, IP QoStechniques, routing over terrestrial and satellite networks, pricingstrategies for guaranteed network services, delivery of multimediaservices over packet networks. His research and professionalactivities includes collaborations with many italian and interna-tional universities, companies such as Alcatel-Alenia Space andMagneti Marelli, research centres such as CNR, Centro RicercheProgetto San Marco, Telecom Italia Labs, Fondazione UgoBordoni. He has been involved in management activities forseveral national and international projects: partner coordinatorfor the European projects IST SUITED (2000–2002) and ISTWHYLESS.COM (2001–2003), unit/Task/WP coordinator in theprojects FIRB ‘‘PRIMO’’ (2003–2006) and PRIN ‘‘TWELVE’’(2004–2006), research coordinator for DIEI in research projectsinvolving local and national companies (e.g. Sogei, Telephonica(current TeleUnit s.p.a.), Space Software Italia). He has collab-orated in many other national and international projects andnetworks of excellence, such as ACTS CABSINET, ACTSASSET, IST Simplicity, IST SatNEx and SatNExII (still activeNoE), FIRB Vicom, PRIN Ramon. He has served as TechnicalProgram Committee member and as referee for several interna-tional IEEE/ACM journals and conferences. He also coordinatesthe research and implementation activities of the Telecommuni-cation Networks Research laboratory of DIEI. In 2005 he hasbeen a consultant of the Regione Umbria, acting as the respon-sible of networking support for the realization of a regionalnetwork of high-precision GPS/GNSS stations.

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