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Ant routing simulation

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A swarm is a decentralized, autonomous multi-agent system consisting of many simple, cooperative agents which behave according to simple rules and use local information in a common environment to achieve global goals. Swarm intelligence attempts to design algorithms or distributed problem solving devices inspired by the collective behaviour of social insect colonies and other animal societies. The idea of applying the natural paradigm of foraging ants to network routing problems has received much attention. The distributed nature of ant colonies and their ability to adapt when conditions change hold much promise for designing optimal routing algorithms in modern telecommunication networks. In this paper we present a simulation of an ant routing protocol which applies swarm intelligence to find optimal routes in IP networks. We investigate the efficiency of two versions of the algorithm in finding optimal routes. We analyze the properties of the multi-path routes discovered by the ant routing algorithms; we investigate how the ant routing algorithms respond to link failures and we investigate path discovery when two previously disconnected routing areas are connected.
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Ant Routing Simulation
B.A. Bagula, H.A.C. de Villiers, J. du Toit, A.E. Krzesinski, M. Loubser, J.G. van der Horst
Department of Computer Science
University of Stellenbosch
7600 Stellenbosch
South Africa
Phone: +27 21 808 4232 Fax: +27 21 808 4416
Email: aek1@cs.sun.ac.za
AbstractA swarm is a decentralized, autonomous multi-
agent system consisting of many simple, cooperative agents which
behave according to simple rules and use local information in a
common environment to achieve global goals. Swarm intelligence
attempts to design algorithms or distributed problem solving
devices inspired by the collective behaviour of social insect
colonies and other animal societies.
The idea of applying the natural paradigm of foraging ants
to network routing problems has received much attention. The
distributed nature of ant colonies and their ability to adapt
when conditions change hold much promise for designing optimal
routing algorithms in modern telecommunication networks.
In this paper we present a simulation of an ant routing protocol
which applies swarm intelligence to find optimal routes in IP
networks. We investigate the efficiency of two versions of the
algorithm in finding optimal routes. We analyze the properties
of the multi-path routes discovered by the ant routing algorithms;
we investigate how the ant routing algorithms respond to link
failures and we investigate path discovery when two previously
disconnected routing areas are connected.
Index Terms— ant routing, load balancing. swarm intelligence,
I. SWARM INTELLIGENCE
Swarm intelligence arises from the interactions among a
large number of basic agents with limited abilities. Natural
ant colonies are an example of swarm intelligence exhibiting
Cooperative behaviour: ants cooperate using as a medium
of communication a path built up through deposition of
a chemical substance called pheromone.
Stigmergetic communication: when ants forage, they ran-
domly wander and lay a pheromone trail which leads
other ants to a source of food. Many individual ants may
discover different routes to the same food.
Autocatalytic behaviour: the number of ants that travel a
path determines the strength of the pheromone trail. The
ants which travel the shortest path reinforce the path with
more pheromone which aids others to follow. After an
initial randomization the ants finally arrive at the shortest
path.
If the path followed by ants is disrupted, the ants will
explore until either the path is found again, or an alternative
route is established to the destination. If multiple paths are
This work is supported by grant numbers 2047362 and 2677 from the
South African National Research Foundation, Siemens Telecommunications
and Telkom SA Limited.
found, an efficient path is selected using the positive feedback
system that favours the shortest path.
II. ANT ROUTING
The ant metaphor can be used to map networks and maintain
efficient routing patterns. The features of natural ant colonies
are highly attractive in a network routing algorithm: the
distributed nature of the path finding system, as well as its
ability to adjust to a dynamic environment can be used to
design a robust, flexible routing algorithm.
A. The ant routing algorithm
Each router in an IP network contains a routing table. The
routing table contains an entry for each destination in the
router’s domain. Each entry specifies the next router (the next-
hop) to be visited on the shortest path to a given destination.
Ant routing algorithms [2], [4], [7], [8] apply swarm
intelligence to solve network routing problems. The basic
mechanisms used in ant colony routing are
Instead of using a single next-hop value, the routing tables
include multiple entries corresponding to several next-hop
choices for a given destination. Each entry is associated
with a probability of choosing this hop as the next hop
along a path to the destination.
The next-hop values are initially equal and are updated
by the ant packets which visit the router.
Each source node sends out ant packets based on the
entries on its own routing table. The ant packets explore
the routes in the network. The ant packets can remember
their outbound routes.
When an ant packet reaches the destination node, the ant
packet returns to the source node along the same route.
The ant packet changes the routing table at each node
on the return path. The rules for updating the routing
tables are: increase the probability of the hop where the
ant packet has immediately come from and decrease the
probabilities of the other hops.
Since the route with higher probability is always
favoured, more ant packets will use that route, and further
increase its use and in turn attract more ant packets. This
positive feed-back loop allows the best path to be quickly
identified.
If the network load or configuration changes, the ant
packets will identify and enforce new optimal paths. Thus
ant routing is dynamic, robust and scalable.
B. Bi-directional exploration
It is possible to distinguish between two castes of ants:
AntOut packets are sent from a router to find a destination
and AntBack packets retrace the route to the originating node.
An AntOut packet is sent from a source node to a destination
node which is selected at random from the known nodes in
the source node routing table. As the AntOut packet passes
through a node, the address of the node and a timestamp
are written into the AntOut packet header. The AntOut packet
updates the routing tables of each node that it visits. Routing
probabilities for previously unknown destination nodes are
added to the routing table. The next hop is selected proba-
bilistically from the routing table and the AntOut packet is
transmitted to the next node. The probability that an AntOut
packet will return to the node that it has just been received
from is decreased to accelerate the convergence of the routing
algorithm. This process is repeated until the AntOut packet
reaches its destination or the TTL expires.
At the destination node an AntBack packet is generated
with the source of the corresponding AntOut packet as its
destination. The list of nodes visited by the AntOut packet is
written into the AntBack packet header. The AntBack packet
follows the route back to the source of the corresponding
AntOut packet, updating the routing tables in the nodes along
its path.
We thus distinguish between uni-directional and bi-
directional updating algorithms. In the uni-directional algo-
rithm the AntOut packets do not update the routing tables; in
the bi-directional algorithm both AntOut and AntBack packets
update the routing tables.
The routers are initialized with a non-existent router in their
routing table. This forces the routers to create AntOut packets
which wander through the network until their TTL expires
(Explorer packets). As the number of entries in the router
table increases, ants with valid destinations are generated more
often, filling the role of the initial Explorer packets. The
number of Explorer packets will decrease and their role will
be filled by ants with valid destinations. Note that all ant
packets contribute to the mapping of the network, even those
ant packets which expire en route to a destination are useful.
Finally, a scale factor αis used to adjust the magnitude of
a routing table update
a=0.1+0.2/2τ+2
where τis the link propagation delay. The scale factor is a
monotone decreasing function of τso that nearby nodes have
a greater effect on the entries in the routing table than nodes
that are further away. This will result in shorter routes being
favoured over longer routes.
The scale factor aa lower limit of 0.1 so that distant nodes
can influence the routing table. The inverse square root decays
slowly enough to allow useful differentiation between link
latencies up to τ=25
. The value of ais sufficiently small to
avoid instability in the network which might occur by over-
reacting to a single ant packet. The scale factor would have to
be adapted for networks where many links have propagation
delays τ>25.
III. EXPERIMENTAL RESULTS
Both variations of the algorithm were implemented in
Objective C using the Swarm libraries [9]. Swarm provides
data structures and scheduling facilities suited to simulating
the multi-agent environment.
We initially modelled networks whose links have unlimited
capacity so that there is no competition for resources between
the ant packets and the data packets.
A. Network convergence
We first investigate whether the ant routing algorithm can
effectively find paths in the network. We also evaluate if the
algorithm allows competing equal-cost paths to be exploited
equally, so that efficient multi-path routing emerges.
Consider the network model presented in Figure 1. All the
links are of equal cost (latency) and infinite capacity. The
simulation was run twice for 2000 time steps each using the
bi- and uni-directional algorithms.
2
3
1
78
9
45
6
Fig. 1. The TriNet topology
Consider the four routes between node 2 and node 8.
Figure 2 reveals that the bi-directional algorithm finds the
routes faster than the uni-directional algorithm. Note that
the bi-directional algorithm gives preference to both of the
shortest paths (2,4,6,8) and (2,3,7,8) while the uni-directional
algorithm finds only one of the alternatives. The bi-directional
algorithm thus succeeds in distributing the traffic flow over
multiple viable paths.
Figure 3 shows the long term behaviour of the two al-
gorithms. Note that the uni-directional algorithm fails to
distribute data across the multiple shortest paths. In contrast,
the bi-directional algorithm favours the shortest paths, but also
uses the longer paths.
Figure 4 shows the evolution of the path length distribution
(the probability of a packet taking nhops) in travelling from
node 8 to node 3. The variance of the distribution decreases
with time. Note that at time t=20the probability of a packet
taking one of the shortest routes (2 hops) is about 0.255,
whereas at time t= 300 the probability is 0.61.
In summary, both the uni- and the bi-directional routing al-
gorithms converge to valid and viable paths. The bi-directional
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Probability
Time
Path Probabilities from 2 to 8
[2, 3, 7, 8]
[2, 4, 6, 8]
[2, 3, 7, 9, 8]
[2, 4, 5, 6, 8]
(a) bi-directional algorithm
0
0.1
0.2
0.3
0.4
0.5
0.6
0 50 100 150 200 250 300
Probability
Time
Path Probabilities from 2 to 8
[2, 3, 7, 8]
[2, 4, 6, 8]
[2, 3, 7, 9, 8]
[2, 4, 5, 6, 8]
(b) uni-directional algorithm
Fig. 2. Path probabilities: short term
algorithm converged more rapidly and found multi-path routes.
The uni-directional algorithm found one of the shortest paths,
but failed to distribute traffic among alternative routes.
B. Link failure and recovery
In this section we investigate how the bi- and uni-directional
ant routing algorithms respond to changes in the network
topology. We will investigate what happens when a single link
in a network fails after the routing algorithms have converged.
The link is later re-established and we investigate whether the
algorithms take advantage of the recovered link.
The TriNet model presented in Figure 1 was simulated. At
time step 500 the link between node 3 and node 7 was failed
by reducing the capacity of the link to 0. The link is restored
at time step 1500 by resetting the capacity of the link to near-
infinite.
When an AntOut packet encounters a failed link it chooses
an alternative link. If no such link is found, which is unlikely
in this experiment, the AntOut packet is dropped.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
Probability
Time
Path Probabilities from 2 to 8
[2, 3, 7, 8]
[2, 4, 6, 8]
[2, 3, 7, 9, 8]
[2, 4, 5, 6, 8]
(a) bi-directional algorithm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000
Probability
Time
Path Probabilities from 2 to 8
[2, 3, 7, 8]
[2, 4, 6, 8]
[2, 3, 7, 9, 8]
[2, 4, 5, 6, 8]
(b) uni-directional algorithm
Fig. 3. Path probabilities: longer term
Figure 5 shows the probability of various routes between
nodes 3 and node 8 for both algorithms. Note that there is
one shortest path (3,7,8). This path is invalid after time step
500 when the link (3,7) fails.
The bi-directional algorithm responds almost immediately:
after about 40 time steps the probability of route (3,7,8)
decreases sharply in favour of the new shortest path (3,2,4,6,8).
At time step 650 the old path has been largely abandoned
in favour of the new path. Note that another alternative
(3,2,4,5,6,8) was found which shares all but one of the nodes
with the most favoured route.
In contrast, the uni-directional algorithm struggles to re-
spond effectively to the change in the network. At time step
750 the probability of selecting route (3,7,8) is still about 0.2
whereas the bi-directional algorithm has effectively suppressed
of this route with a probability of 0.02.
The link recovers at time t= 1500. The bi-directional
algorithm responds immediately and returns in about 200 time
steps to a state similar to that before the link was broken. In
0
0.05
0.1
0.15
0.2
0.25
0.3
0 5 10 15 20 25 30 35 40
Probability
Hops
Monte Carlo Simulation for path 8 to 3
Probability
(a) t=20
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12
Probability
Hops
Monte Carlo Simulation for path 8 to 3
Probability
(b) t= 300
Fig. 4. Evolution of path length distribution
contrast, the uni-directional algorithm fails to respond to the
link recovery, not detecting the new shortest path, even though
it is two hops shorter than the most popular path.
These preliminary results show the advantages of utiliz-
ing the AntOut packets in changing the routing tables. The
bi-directional algorithm improves the network’s response to
changes in the network topology: updates to the routing tables
are frequent, making competition between routes more fierce.
This indicates the potential usefulness of the bi-directional
algorithm for managing wireless networks, where links are
constantly established and broken.
In summary, the bi-directional algorithm outperformed the
uni-directional algorithm when changes to the network occur.
This indicates that, when the correct rules for dropping ant
packets on congested links have been found, the bi-directional
algorithm should also adjust to network congestion in a
flexible way. In contrast, the uni-directional algorithm does
not react to adjust routing characteristics unless it is forced,
even if a new optimal route exists.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 500 1000 1500 2000 2500 3000
Probability
Time
Path Probabilities from 3 to 8
[3, 7, 8]
[3, 7, 9, 8]
[3, 2, 4, 6, 8]
[3, 2, 4, 5, 6, 8]
(a) bi-directional algorithm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 500 1000 1500 2000 2500 3000
Probability
Time
Path Probabilities from 3 to 8
[3, 7, 8]
[3, 7, 9, 8]
[3, 2, 4, 6, 8]
[3, 2, 4, 5, 6, 8]
(b) uni-directional algorithm
Fig. 5. Path probabilities
C. Connecting two routing areas
In this section we compare the behaviour of the uni- and
bi-directional algorithms when two previously unconnected
routing areas are connected by a single link.
Figure 6 illustrates two subnetworks which communicate via
a single link. This link, which is initially disabled, is connected
at time t= 200 after the separate networks have mapped
themselves. The sudden, large scale expansion requires that
the all the nodes in the each of the networks discover and
route to the nodes in the other network.
AntOut packets are released every 5 time steps to routers
randomly selected from the routing table. The routing tables
are initialized to contain the address of a non-existent route.
All initial AntOut packets (which have this router as their
destination) explore the network and notify other routers about
the existence of their source.
All the links in the network have unit propagation delay
(τ=1
) and the delay caused by the routers is negligible. No
data traffic is transmitted. The ant traffic volume is several
12
3
512
413
7
68
9
11
10
Connects at t = 200
Fig. 6. Topology of the network
orders of magnitude less than the capacity of the links so that
no packet losses occurr.
Several simulations were run using the uni- and bi-
directional algorithms. Similar results were repeatedly ob-
tained. The results of two randomly chosen runs are discussed
below to illustrate the behaviour of the algorithms.
The speed with which the networks detect new nodes was
tested by investigating the routing probability between the two
most distant nodes 1 and 9. When these two nodes discover
each other, all the other nodes will also be aware of the new
nodes in the network.
Figure 7 displays the evolution of the routing probabilities
from node 1 to node 9 (only the four most popular routes are
displayed). At time t= 200 all the nodes in each subnet know
the routes to the other nodes in the same subnet, but none is yet
aware of the existence of the other network. Nodes 4 and 13
are connected at time t= 200.
The uni-directional algorithm finds a path from node 1 to
node 9 at time t= 273. Another path is found at time t=
299. These paths slowly increase in popularity, with the path
(1,2,4,13,12,11,10,9) being the most popular, and the shortest
path (1,2,4,13,7,8,9) steadily gaining favour. It takes about 200
time steps to settle into a relatively steady state, whereafter the
routing probabilities slowly adapt as AntBack packets arrive.
The bi-directional updating algorithm finds its first path
from node 1 to node 9 at time t= 212, only 12 time steps
after the two subnetworks were connected. The shortest path
(1,2,4,13,7,8,9) emerges as the most popular.
In both cases the most favourable routes settle at an average
probability of about 25–30%. However, the bi-directional algo-
rithm achieves this goal more quickly than the uni-directional
algorithm.
The role played by volatility
Figure 7 shows that the uni-directional algorithm has a less
volatile probability plot than the bi-directional algorithm. The
volatility is caused by the AntOut packets which influence the
probability tables in the router, instead of only the AntBack
packets.
It can be argued that the volatility is compensated by the
amount of information provided by the AntOut packets. When
an AntOut packet crosses the (4,13) link, it carries with it all
the information concerning the source network and it shares
this information with each of the nodes it passes through in the
destination network. With many of the nodes informed about
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 200 400 600 800 1000 1200
Probability
Time
Path Probabilities from 1 to 9
[1, 3, 2, 4, 13, 7, 8, 9]
[1, 2, 4, 13, 12, 11, 10, 9]
[1, 2, 4, 13, 7, 8, 9]
[1, 2, 4, 13, 7, 11, 10, 9]
(a) bi-directional algorithm
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 200 400 600 800 1000 1200
Probability
Time
Path Probabilities from 1 to 9
[1, 2, 4, 13, 7, 8, 9]
[1, 2, 4, 13, 12, 11, 10, 9]
[1, 3, 2, 4, 13, 12, 11, 10, 9]
[1, 3, 5, 4, 13, 12, 11, 10, 9]
(b) uni-directional algorithm
Fig. 7. Routing probabilities between nodes 1 and 9
each other, more ants packets are soon sent out to improve
the connection, leading to reinforcement for all the nodes
involved.
The uni-directional system is less volatile, but the reaction
to changes takes much longer. The network overhead is used
less efficiently, because AntOut packets make no contribution
to the routing on the network.
AntOut packets thus give rise to volatility but allow the
network to adapt faster. The volatility can be controlled by
limiting the magnitude of the updates effected by AntOut pack-
ets, at the cost of increasing the time needed for adaptation.
For networks in stable environments, where little dynamic
adjustment is needed, no updating by AntOut packets would
deliver better results. However, in environments where the
topology can change frequently and significantly, updating by
AntOut packets would allow the network to respond quickly
to new conditions.
IV. CONCLUSIONS
This paper compares two ant routing algorithms implement-
ing respectively uni- and bi-directional updates to the routing
tables.
For the network models under consideration the uni-
directional algorithm delivers stable routing probabilities
which slowly converge to the most efficient paths. However,
the uni-directional algorithm is slow to adapt to changes
in the network topology and appears oblivious to changes
which provide a better load distribution. The uni-directional
algorithm appears best suited to mapping networks with a
constant topology and a relatively constant traffic flow.
In contrast, the bi-directional algorithm quickly finds several
quite efficient paths. This is useful in networks where the
traffic loads approach the available capacity. The bi-directional
algorithm allows the network to be sensitive to changes in traf-
fic flow and allows it to react quickly to changes in the network
topology. A side effect of this sensitivity is the volatility of
the path probabilities and the resulting lower efficiency of the
network. This volatility is due to the AntOut packets. The bi-
directional algorithm therefore seems more suited to networks
with unpredictable data flow and an unsettled topology.
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pp 317-365
[3] G. Di Caro & M. Dorigo. AntNet: A Mobile Agents Approach to Adaptive
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Bruxelles, (1997) Belgium.
[4] G. Di Caro & M. Dorigo. Two Ant Colony Algorithms for Best-
Effort Routing in Datagram Networks Proceedings of PDCS’98 - 10th
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[5] G. Di Caro & M. Dorigo. Ant Colony Optimization: A New Meta-
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[9] The Swarm Development Group. www.swarm.com
Anthony Krzesinski obtained the MSc from the University of Cape Town and
the PhD from Cambridge University, England. He is a Professor of Computer
Science at the University of Stellenbosch. His research interests centre on the
performance evaluation of communication networks.
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Distributed Stigmergetic Control for Communications Networks
  • Di Caro
  • Antnet
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