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Minimum Hop Count and Load Balancing Metrics based on Ant Behavior over a Haps Mesh Floriano De Rango, Mauro Tropea

Apollonia Provato

DEIS Department University of Calabria Rende, Italy Email: [email protected] [email protected]

DEIS Department University of Calabria Rende, Italy Email: [email protected]

Amilcare Francesco Santamaria and Salvatore Marano DEIS Department University of Calabria Rende, Italy Email: [email protected] [email protected]

Abstract—In this paper we propose a routing algorithm based on Swarm Intelligence studies. In particular, this algorithm is based on AntNet routing with the extensions of novel metrics for the multi-objective optimization, that are minimum hop count and traffic load balancing. In order to build an optimal solution, the proposed algorithm will make use of ANT agents that consist of probe packets sent on the HAPs network. We have chosen as reference network a HAPs mesh in order to get advantages of the dynamic characteristics of these platforms. In this work we perform a comparison of a classical shortest length path and our algorithm that will try to find the minimum hop path respecting a maximum end-to-end delay bound and an equally distribution of the traffic on the HAPs network.

I. I NTRODUCTION In the last few years Swarm Intelligence (SI) techniques [1] [11] are becoming important to solve routing problems. SI is a distributed intelligent technique for solving optimization problems that originally took inspiration from the biological examples by swarming, flocking and herding phenomena. The main advantages of SI are usually self-organization, self-autonomous, naturally scalable permitting to dynamically add or remove new units. In this paper, we investigate the performance of a new ant algorithm that is based on SI and solves complex problems through cooperation. This algorithm is inspired by the behavior of real ants that have the capability to cooperate utilizing a form of indirect communication through the environment called stigmergy deposing on the path a substance called pheromone. In this algorithm each ant is represented by a specific packet that travel in the network. They discovered the minimal path length through the pheromone quantity released on the route. The management of this substance in a software algorithm permits a better exploration of the network and then to find the optimal solution. In literature some works that provide algorithm in order to manage the pheromone [3], [4] exist. In this work a new pheromone management policy is provided. In this work we have chosen as a reference scenario a HAPs mesh network in order to get advantages of their dynamic characteristics (see Fig. 1). In order to show that routing algorithms based on SI are better than the classical algorithm, e.g. Dijkstra [5], BellmanFord [6], we have performed a comparison between our ant

Fig. 1.

Reference Scenario

routing algorithms with a Shortest Path Algorithm (SPA) [7]. Specifically, we have shown that our ant routing algorithm has the capability of better managing the system resources and augment the number of calls admitted by the system. Moreover, we have considered two version of the ant routing algorithm, an ant algorithm with only the Minimum Hop Count metric (A MHC), that after having saturated the shortest link uses the second better link for routing calls between source and destination, and an ant algorithm with Load Balancing metrics (A LB) that is capable of distributing calls on overall network respecting the maximum end-to-end delay requested by the users without saturating any links. This paper is organized as follows: section 2 presents the related works about Swarm Intelligence in telecommunication networks; section 3 explains in a detailed manner the proposed algorithm with the considered metrics in order to satisfy the QoS constraints; the detailed performance evaluation conducted through an ad-hoc simulator written in C++ language is explained in section 4; at last, in section 5 are summarized the conclusions. II. R ELATED W ORKS In the last years Ants-based routing algorithms are becoming very important in the fields of robotics, operations research, and telecommunications because they are more ro-

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bust, reliable and scalable than other conventional routing algorithms. These algorithms are inspired by the collective foraging behavior of specific ant specie. This is a technique designed for solving distributed problems. Among the different works inspired by SI, two well known approaches are known as ACO (Ant Colony Optimization) [8], [9], [10] and PSO (Particle Swarm Optimization) [11]. ACO deals with artificial systems that are inspired from the foraging behavior of real ants, which are used to solve discrete optimization problems. As more ants pass by, more pheromone is deposited on the path. Since ants depose pheromone, the richer the trail of pheromone in a path, the more likely it would be followed by other ants. These software agents mimic the foraging behavior of their biological counterparts in finding the shortest-path to the food source. Recently, ACO has been applied to solve a set of NP-hard problems with high dimension and some combined optimization problems. PSO was originally designed by Kennedy and Eberhart [12]. The technique involves simulating social behavior among individuals (particles) flying through a multidimensional search space, each particle representing a single intersection of all search dimensions. The particles evaluate their positions relative to a goal (fitness) at every iteration, and particles in a local neighborhood share memories of their best positions, then use those memories to adjust their own velocities, and thus subsequent positions. PSO has the advantages of parallel computation, robustness and so on, and it can find out the global optimization solution with a higher probability and efficiency than traditional methods. The biggest advantage of PSO is easy to realize, fast converging and intelligent. It can be applied in both scientific research and engineering fields. A very successful example of swarm-based routing algorithms is the AntNet adaptive agent-based routing algorithm [3]. In the AntNet algorithm, routing is determined through complex interactions of network exploration agents, called ants. These agents are divided into two classes, the forward ants and the backward ants. The idea behind this sub-division of agents is to allow the backward ants to utilize the useful information gathered by the forward ants on their trip from source to destination. Based on this principle, no node routing updates are performed by the forward ants, whose only purpose in life is to report network delay conditions to the backward ants. This information appears in the form of trip times between each network node. The backward ants inherit this raw data and use it to update the routing tables of the nodes. III. A NT A LGORITHM FOR ROUTING P ROBLEM In this paper a multi-objective routing algorithm is proposed capable of optimizing path length, maximum end-to-end delay and traffic load distribution [13]. Differently by [13] in which the authors have studied in detail the algorithm convergence time in this paper the attention will be focused on the protocol analysis showing an approach based on merged metrics. The considered scenario is a HAPs mesh network (as shown in

Fig.1) in order to get advantages of their dynamism due to the rapid setting up of a network in situations of disaster recovery or rescue operations or in the case of HAP replacement for refuel or pilot changing [14], [15]. In this scenario together with the ant routing algorithm it has been used an IntServ architecture in order to guarantee the maximum end-to-end delay required by the users. Also, the RSVP protocol has been used in order to build an initial solution in the setup phase. The protocol previews the classical PATH and RESV messages. The PATH message is flooded into the network and the destination node can decide to process all messages or a limited number k of these. For each RESV arrived at the source node a Forward Ant (FANT) message is generated in order to explore the network to find the better solution traveling from the source to the destination. Moreover, the FANT messages are also generated on periodical basis in order to discover always more update solutions. A Backward Ant (BANT) messages is generated for each FANT that arrives to the destination node following the reverse path forwarding in order to update the link selection probability. The formula for updating the link probability is shown in the following: pi,j = 

[τi,j ]α · [ηi,j ]β α β j∈Ni [τi,j ] · [ηi,j ]

(1)

Where τi,j and ηi,j represent respectively the pheromone quantity released by BANT and the value of the local heuristic evaluated at the ants traveling. This probability is applied on each link crossed by an ant. α and β represent respectively the pheromone scale factor and visibility factor associated with the local heuristic. These two variables can modulate the weight given to the local heuristic or to the global solution currently found by the ants. The data packets are forwarded in a deterministic way selecting the next HAP as shown by (2) where Ni is the set of neighbors nodes to the i − th HAP and nextHAPiD represents the next HAP with respect to i − th HAP in order to reach the HAP Destination (HAP D). D ] · [ηi,j ]} nextHAPiD = argmaxj∈Ni {[τi,j

(2)

In this work two algorithms based on ant colonies behavior have been proposed. Specifically, one tries to find the minimum hop path and a second one adds the load traffic distribution metric. A. Minimum Hop Count metric (A MHC) The first considered metric is the Minimum Hop Count metric that tries to select the path between a source and a destination with the minimum number of nodes. Indeed, this metric tries to reduce also the end-to-end delay in this path because this algorithm is based on RSVP protocol. Before showing the formulas some parameters, applied in the math formulation of the problem and used in the paper, are listed: D • τi,j is the pheromone quantity released by n − th ant for going towards the j − th HAP from the i − th HAP in order to reach the HAP D;

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ρD i,j indicates the pathgrade calculated on the HAP D where is connected the receiver terminal; the better the solution discovered by the current ant, the higher will be the value of the pathgrade; • f (.) is a function that depends on the path grade and represents the ”vanishing function”; • g(.) is a function that depends on the path grade and represents the ”enforcing function”; • PS−D (n) is the path from the HAP Source (HAP S) to HAP D. This algorithm behavior is represented by these two formulas: •

D D D (n) = f (ρD τi,j i,j )τi,j (n − 1) + g(ρi,j )

(3)

With j ∈ Ni and with link (i, j) ∈ PS−D (n). D D τi,j (n) = f (ρD i,j )τi,j (n − 1)

(4)

With j ∈ Ni and link (i, j) ∈ / PS−D (n). Moreover, in (3) and (4) two functions, f and g, were introduced. These functions depend on the pathgrade in an opposite way. In particular, function f represents the ”vanishing factor” in order to reduce the effects of the memory of the previously found solutions: f (ρ) = 1 − ρ

(5)

On the contrary, function g represents an ”enforcing function” that increases for higher pathgrade values: g(ρ) = ρk

(6)

where 0 ≤ ρ ≤ 1 ⇒ 0 ≤ f (ρ) ≤ 1, 0 ≤ g(ρ) ≤ 1, and k ∈ N represents the decayingf actor. The higher k, the lower is the contribute of enforcement function, because the pathgrade is 0 ≤ ρ ≤ 1. In this work, in accordance with [16], the pathgrade is a function of two indexes IbestPS−D (n) and (n). The first term represents the goodness of the path IPtot S−D found by previous ants at the destination when the n − th ant goes through the network. Thus, this term accounts for the past in the solution discovery process. In particular, in our algorithm an ants window W was considered, where the path quality indexes, discovered by past W ants sent from HAP S to the HAP D, are stored. On the other (n) represents the pathgrade discovered by the hand, IPtot S−D current n − th ant. On the basis of this value and on the difference between the current pathgrade and the solutions discovered by the previous W ants, whether and how much to increase or decrease the ρ value is established. In the following (n) are the equation to calculate ρ, IbestPS−D (n) and IPtot S−D reported: ρ = F (IPS−D (n), IbestPS−D (n))

(7)

where IbestPS−D (n) = max{IPtot (i), i = n−1−W, ..., n−1} (8) S−D

LS−D (n)

IPtot (n) = S−D



Ii

(9)

i=1

With i ∈ Ni and i ∈ PS−D if 0 ≤ Ii ≤ 1 ⇒ 0 ≤ IPS−D tot (n) ≤ 1 . In order to regulate the impact on the pheromone update, the pathgrade values found by the previous W ants are modulated by two factors A and B. The B value was fixed to 0 in order to reduce the complexity; in future works the behavior of this parameter will be analyzed. Through this consideration, the pathgrade can be calculated as follows: ρi,j D (n) =

1 +B W A · [IbestP (n) − IPtot (n)] S−D S−D

(10)

Considering a cost associated with each node of the network as constant, Ii = C with 0 ≤ C ≤ 1, there is a cost associated with the path of the n − th ant as follows: (n) = IPtot S−D

L 

Ii = C L

(11)

i=1

Where L represents the path length in terms of hop number. From the previous formulas it is possible to observe that when the characteristics of the path found by the n − th ant is worse compared to the current optimal solution, the pathgrade ρ assumes lower values. Whereas, if an ant goes to a shorter path, ρ will give a higher contribution and this implies that the evaporation function (5) reduces the effect of the pheromone released on the path between the HAP S and HAP D. In the start up phase, a prefixed IbestPS−D (n) is adopted and, after W ants forwarding, a novel IbestPS−D (n) can be calculated to determine the value. The IbestPS−D (n) index can be assigned as follows:  W (n) IbestP S−D

=

C with 0 ≤ C ≤ 1 if W = 1 −1 , C) if W > 1 min(IPWS−D

(12)

where the C value is selected equal to 1 in order to consider a not optimal solution in the start up phase of the algorithm, which can be updated after the first iteration of W ants. This W (n) approach permits an immediate updating of the IbestP S−D index and an exploration of a novel solution in the route discovery process. If enforcement and evaporation function values are substituted in (3) and (4), the following equations can be obtained: D D D k (n) = (1 − ρD τi,j i,j ) · τi,j (n − 1) + (ρi,j )

(13)

with j ∈ Ni and with link (i, j) ∈ PS−D (n). D D (n) = (1 − ρD τi,j i,j ) · τi,j (n − 1)

(14)

/ PS−D (n). If these with j ∈ Ni and with link (i, j) ∈ last equations (13) and (14) are inserted in the link selection probability (1), considering α and β equals 1, we have:

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pD i,j = 

Where we define I1 the index of the minimum hop count metric and I2 the index of load balancing. Moreover, each of these indexes are multiplied for a constant Ci with i ∈ [1, 2]. The constant value Ci can assume values in the range [0, 1] and it has to satisfy this condition:

D D τi,j (n) · ηi,j = D D j∈Ni τi,j (n) · ηi,j D k D (1 − ρD ) · τi,j (n − 1) · ηi,j + (ρD i,j ) · ηi,j i,j D D D j∈Ni (1 − ρi,j ) · τi,j (n − 1) · ηi,j

(15)

2 

B. Load Balancing metric (A LB) In the case of traffic load distribution another index has been defined to equally distribute the data traffic on the links associated to the HAP belonging to path from a HAP S to a HAP D. This index takes into account the bandwidth availability on the link (i, j) that goes from HAP i−th to HAP j − th. This bandwidth availability can be defined utilizing the concept of link utilization. Let U(i,j) the link utilization of the link (i, j) that goes from HAP i − th to HAP j − th, the bandwidth availability of the link (i, j) defined as bA(i,j) can be expressed as following: bA(i,j) = 1 − U(i,j)

(16)

In particular, for each link (i, j) a value Ii has been considered as follows: Ii = bA(i,j)

(17)

This index can assume values in the range [0, 1] since the U(i,j) is a values between 0 and 1. Now it is possible to (n)]D associated with the define the normalized index [IPtot S−D path crossed by the FANT and calculate at the receiver. It is expressed as follows: (n)]D = mini∈PS−D (Ii ) [IPtot S−D

W IbestP (n) S−D

=

max([IPtot (n)]D ) S−D

(19)

Where max operator means that the destination receives more than one index related to different path between source and destination and then it choices the path with the maximum bandwidth availability in order to maximize the network utilization. This index will allow a better traffic distribution because low congested regions (paths) will offer higher bandwidth availability. C. Merged Metric Once defined all two metrics we can define a total index that takes into account the minimum hop count metric and the load balancing metric. It is possible to define this total index as follows: Itot = C1 · I1 + C2 · I2

(20)

(21)

This constant gives the possibility of taking into account one or all two metrics contemporarily, or it gives the possibility of associating a different weight to the metric on the basis of the value that can be assigned to constant Ci . In this paper, we present a detailed simulative campaigns in order to show how this total index influence on the performance of the considered system. D. Dynamic utilization based on local heuristic In this work, for the load balancing algorithm, we have also used a local heuristic based on link utilization. The local heuristic allows to avoid local optimum during convergence time of the algorithm. In order to avoid the increase of probability on a specific link belonging to a path the local heuristic is used to contrast this effect. Thus, when a link is overloaded and its pheromone is higher than the pheromone quantity on other links the probability to select that link can be too high and the exploration of other paths and solutions are not possible. However, using the local heuristic we are able to reduce the contribution of pheromone giving a lower value to ηi,j . In order to use local heuristic as an opposite effect to increasing pheromone value we define the term ηi,j as follows:

(18)

Now, after the calculation of this index, it is possible to determine the pathgrade taking into account (17) and (18). In this case the W ants window is always used to determine the best path found in the past by the last W ants. In this case, W (n) can be computed as follows: the IbestP S−D

Ci = 1

i=1

ηi,j = 1 − Ui,j

(22)

Where Ui,j , that represents the utilization associated with the link (i, j), is defined as follows: Ui,j = RBoundi,j /Ci,j

(23)

Where Ci,j represents the link (i, j) capacity and RBoundi,j represents the effective bandwidth used for that specific (i, j) link. In the following the computation of RBoundi,j is described. We have used an approach similar to that called Dynamic Packet State (DPS) [17], [18], [19]. In this approach the time is divided into intervals of dimension Tw : tk − tk+1 . Each HAP monitors the amount of bits transmitted by any call in the interval Tw . Bi,j (tk , tk+1 ) is denominated as the sum of the bits received for each call in an inter-HAP link (i, j). So, at the end of any interval Tw , each HAP computes the actual rate RDP Si,j and then, based on RDP Si,j , it computes a new variable RCali,j defined as follows: RDSPi,j (tk+1 ) = Bi,j (tk+1 )/(tk+1 − tk )

(24)

RCali,j (tk+1 ) = RDSPi,j (tk+1 )/(1 − f ) + Rnewi,j (tk+1 ) (25)

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TABLE I S IMULATION PARAMETERS Simulation Parameters

Value

Round Trip Time Target burst loss probability (γ) Return Channel’s slots Forward Channel’s slots Atomic satellite channel (slot) Return and Forward Channel’s trama RCST typology Max number of sources for RCST peak rate (p) average rate (r) token bucket size Delay Bound (DB) calls rate (λ) average call duration (d) simulation duration (dS) C D

0.4 ms 0.01 469 469 32 Kbps 47 ms D (2048 Kbps) 16 256 kbps 128 kbps 256 kb 1000 ms 4 calls/min 5 min 100 min 13624 47 ms

Fig. 3.

Fig. 4.

Fig. 2.

Simulation Topology

Where f represents the frequency of rate recalibration and it is calculated as f = (Ti + Tj )/Tw , with Ti is the maximum inter-departure time between two consecutive packets of a flow (call), Tj is the maximum delay jitter of a flow (call) and they are both much smaller than Tw ; for details see [17], [19]. Rnewi,j represents a variable locally initialized by each HAP at the beginning of any new interval Tw and accounting for the contributes in terms of rate R of any new call accepted Rnewi,j = Rnewi,j + R. So it is possible to recalculate RBoundi,j in this way: RBoundi,j = min(RBoundi,j , RCali,j (tk+1 ))

(26)

For details of RDSP and RCal computation refer to [17], [18], [19]. IV. P ERFORMANCE E VALUATION In this section the performances of the proposed algorithms are shown varying the coefficients associated with the total index (C1 and C2 ). The simulation results have shown the goodness of the proposals. In particular, the results show how effectively the A MHC is capable of finding the best path between HAP S and HAP D and permits of using the other paths in the case of saturation, and the A LB is capable of better managing the system resources allowing also an augment of the overall admitted calls. A network of 10 HAPs has been considered as it is possible to view in Fig. 2. In table 1 the simulation parameters common to all the simulation campaigns are summarized. The parameters considered

Average end-to-end delay

Maximum end-to-end delay

for performance evaluation are system utilization, end-to-end delay and admitted calls. All the campaign simulations have been performed considering a confidence interval of 5%. A. Algorithm parameters In this work we have used specific parameters values that we have chosen through many simulation campaigns. They are: ants window (W) is 10; A and B coefficients are respectively 60 and 0.3; α and β coefficient are 1 and 0 for A MHC and respectively 1 and 2 for A LB; initial value of τ is 0.4; decaying factor k is 3. In addition, concerning the computation of local heuristic and link utilization we have considered a Tw equals to 2 seconds. B. Simulation results This section presents a comparison between a SPA and our proposals, A MHC and A LB. We have considered C1 and C2 values respectively of 0 and 1, 0.3 and 0.7, 0.5 and 0.5, 0.7 and 0.3 and 1 and 0. All simulations have been conducted considering a maximum delay bound of 1000 ms. Fig. 3 and Fig. 4 show the average and the maximum end-toend delay varying the coefficients of the total index Itot . It is possible to view that with the combination C1 =1 and C2 =0 the only metric considered is the minimum hop count and no load balancing is performed. This produces the minimum end-toend delay due to the delay considered only on the shortest path between HAP S and HAP D. Decreasing the C1 factor and, consequently, the increase of the C2 factor produces an increase of the end-to-end delay that results maximum in the case of C1 =0 and C2 =1. This is due to the fact that with these coefficients combination the data travel also through path

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end-to-end delay and/or bandwidth taking into account also the traffic load distribution. The proposed algorithm has been realized using a novel technique called Ant Routing that is based on the ant colony behavior. Many simulation campaigns have been performed in order to evaluate the goodness of our proposed algorithm. We have performed a comparison between our algorithm and a SPA. We have considered an index capable of taking into account two metrics, minimum hop count and load balancing, in order to show how these two metrics impact on the system resources. Fig. 5.

Fig. 6.

Link utilization

R EFERENCES

Admitted and refused calls

longer than the shortest one. It is possible also to note that the algorithm respects the maximum delay bound requested by the users due to RSVP protocol used for the admission of the call. A comparison between the link utilization varying the coefficients of the index Itot is shown in Fig. 5. It is possible to note how increasing the coefficient related to A LB the link utilization is better distributed between the three links outgoing from the considered HAP. In particular, it is possible to note that increasing the C2 coefficient, related to the load balancing metric, decreases the gap between the link utilization. This phenomena permits of managing the system resources in a better way avoiding to create congestion region in the network. At last, we present the graphic of the admitted and refused calls number (see Fig. 6). The lower number of admitted calls and the higher number of refused calls is determined by SPA algorithm because it selects only the path with the lower number of hops and uses always this path independently of the path congestion. This graphic shows that the A MHC algorithm allows a lower number of admitted calls and, consequently, the major number of refused calls in comparison with the A LB algorithm that permits more accepted calls because it routes calls in each outgoing link distributing the resources of the system in a better way. V. C ONCLUSIONS In this paper we have proposed a novel algorithm based on Swarm Intelligence. We have chosen as reference architecture a HAPs mesh network in order to take advantage of some useful characteristics such as high bandwidth, lower propagation delay and its dynamism. This algorithm permits to discover minimal length paths that satisfy requirements of

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