PLANIFICACIÓN Y CONTROL DE LA PRODUCCIÓN

ACRWA utilises a distributed approach in which the ant colonies share information among each other with the objective of improving the overall performance of the network. The ACRWA protocol is based on the Ant Colony System (ACS) protocol which was originally developed as a solution for resolving problems such as the Travelling Salesman Problem (TSP), but has been modified to solve the problem

of RWA on WCC optical networks (Triay and Cervello-Pastor, 2010). ACRWA make use of OBS and its convenient properties for their ACO solution in terms of representing the ant as the OBS BCP as it navigates its way to the destination (Triay and Cervello-Pastor, 2010). The ACRWA algorithm provides an interesting solution to the RWA process for a connection request. ACRWA selects the next node and wavelength based on the best product of the pheromone concentration of the output link, the wavelength and the desirability of using such an output link. The algorithm does not make use of random or First Fit wavelength assignment, but has rather linked the wavelength and path (if only for the initial hop and not from source to destination). Thereafter, at every hop, the ACRWA would repeat the process of selecting the next output link. The results obtained by this previous work are promising, making a suitable candidate for benchmark testing as the algorithm has been developed for OBS with the WCC and has demonstrated a link between wavelength and route to destination.

3.2.5.1 Initialisation

The ACRWA algorithm is comprised of two protocols, the initialisation protocol which is followed by the RWA process governing the specific behaviour of the ants. The initialisation protocol is responsible for initialising the parameter values and routing tables. This protocol is performed at each of the nodes within the network initialising the routing, pheromone tables and pheromone values. Pheromone val- ues are assigned for every switching configuration of input link, output link and wavelength at a node. Table 3.1 is an example of an initialised pheromone table for a node with two links, in a network with four wavelengths. A routing protocol is used to generate a list of k-shortest routes to all the remaining nodes within the network with each route using a different output link. Each node, n, constructs a candidate list S_nm of available neighbour nodes for every destination node m from the previously generated list of k-shortest routes. The list of k-shortest routes is

Table 3.1: ACRWA Pheromone Table (Triay and Cervello-Pastor, 2010) Output Link

Input Link Wave Link1 Link 2

Link 1 1 τ1,1,1 τ1,2,1 2 τ1,1,2 τ1,2,2 3 τ1,1,3 τ1,2,3 4 τ1,1,4 τ1,2,4 Link 2 1 τ2,1,1 τ2,2,1 2 τ2,1,2 τ2,2,2 3 τ2,1,3 τ2,2,3 4 τ2,1,4 τ2,2,4

used to calculate the desirability values for each link j ∈ Sm n:

ηnmj =

1 Lnmj

(3.5) where Lnmjis equal to the length of the shortest path between node n and destination

node m using output link j. A list of wavelength candidates Dm_n is also initialised, equal to cD, the total number of wavelengths available in the network.

3.2.5.2 Routing and Wavelength Assignment

The RWA protocol governs the specific behaviour of the ants once the initialisation process has been completed. This protocol is executed by the nodes within the network for each new transmission request. The objective of the algorithm is to select the most beneficial output link, u ∈ Sm

n, and wavelength, λ ∈ Dnm, combination to

assign the ant. This assignment is a greedy selection of the u and λ pair that has the greatest benefit calculated using the product of desirability of a certain output link and pheromone deposition described by the following equation:

(u, λ) = argmaxj∈Sm

n(t),k∈Dmn(t){τijk(t)η

β

where u is the selected output link and λ the selected wavelength. τijk is the

pheromone level stored at the node for input link i and output link j on wave- length k and where Dm

n is the set of existing wavelengths at node n that have been

initialized for destination m. β is a constant used to emphasize the use of shorter paths.

3.2.5.3 State Transition Rule

The initial RWA performed on the ant at the source node, n, assigns a permanent wavelength to the ant, requiring only the selection of output links for further routing. The state transition rule is responsible for selecting the next hop (output link) in the ant routing process toward its destination. The transition rule selects the next node u (or output link) to switch by means of exploiting or exploring. Let r be a random number r ∼ U (0, 1). The user-specified parameter r0 ∈ [0, 1] is used to

balance between exploitation and exploration. In the case that r ≤ r0, the algorithm

will exploit otherwise r > r0 and the algorithm will explore. If it is determined the

ant must exploit, the algorithm will iterate through the output links j and select the output link with the greatest product of pheromone level τijk and output link

desirability ηnj using the following equation:

u = argmaxj∈Sm

n(t){τijk(t)η

β

nj(t)} (3.7)

Otherwise, the ant will choose to explore by selecting an output link with each link being assigned a probability, Piuk, based on τijk and ηnj as follows:

Piuk(t) = τiuk(t)ηnuβ (t) P j∈Sm n τijk(t)η β nj(t) (3.8) The output link is selected based on an empirical distribution based on the assigned probabilities above.

3.2.5.4 Global Update

The global updating rule is performed by the feedback ants. The feedback ants backtracks the path of the ant and updates the pheromone trails using the global

update. All feedback ants are allowed to reinforce or weaken the pheromone concen- trations. If the ant successfully reached its destination, the pheromone is updated as follows:

τijk(t + 1) = (1 − ρ)τijk(t) + ρ∆τijk (3.9)

Otherwise, if the ant did not successfully reach its destination:

τijk(t + 1) = (1 − ρ)τijk(t) − ρ∆τijk (3.10)

where ρ is a user-specified parameter for the pheromone evaporation coefficient. The amount of new pheromone deposited by the feedback ant depends on the length of the path followed by the feedback ant so far:

∆τijk = e−ω∆l (3.11)

where ω is the global decay constant (user specified parameter), ∆l is the difference in length of the reverse path followed by the feedback ant so far and the length of the shortest path to the origin of that ant from the current node that processes it.

3.2.5.5 Local Update

The purpose of the local updating rule is to diversify the search space to include good local solutions. The routing protocol attempts to reserve the optical resources of output link j and wavelength k for the ant. If the reservation is successful, the ant is sent to the adjacent node on output link j and a positive pheromone update is performed on τijk according to the local update equation:

τijk(t + 1) = τijk(t) + αe−φ∆l (3.12)

where α is a user-specified value that controls the amount of emphasis placed on good local solutions and the parameter φ is the local decay constant.