Heuristics for Tunnel Allocation

We first briefly introduce Capacity-Balanced Static Tunnel Allocation (CB-STA) proposed in [1]. Then we present our heuristic Constant Length Weighted Tunnel Allocation (CLWTA) that aims to improve CB-STA.

Capacity-Balanced Static Tunnel Allocation (CB-STA)

CB-STA aims to allocate tunnels off-line before start serving the lightpath requests.

The process comprises three stages: (a) tunnel ingress-egress (I-E) pair selection, (b) tunnel allocation and (c) makeup process. In (a), a series of I-E pairs are selected sequentially for the tunnel allocation stage in (b). To select I-E pairs, CB-STA estimates the amount of traffic traveling through each node by routing a historical traffic matrix in the network. Then the nodes with maximal traffic going out and maximal traffic coming in are selected repeatedly for tunnel allocation. In (b),

CB-STA tries to allocate a tunnel for each I-E pair selected in (a). After (a) and (b), the makeup process (c) is performed to further utilize the remaining resources to fill the fiber- and waveband-switching layer with as many tunnels as possible.

The tunnel allocated at stage (b) is required to follow a tunnel length constraint which is set to the minimum integer that is larger than the average physical hop distance between each node pair in the network. This is because when the tunnel length is too small, although the short tunnels are flexible and easily utilized by most of the lightpaths, the wavelength-switching ports are used up easily since the wavelength-switching ports are required at the ingress and egress nodes of each tunnel.

When the tunnel length is too large, although wavelength-switching ports can be greatly saved, the tunnels may not be suitable for the requests since most of the lightpath requests are shorter than the tunnels. We observe that the I-E pairs selected in stage (a) of CB-STA does not consider the tunnel length constraint, therefore most of the tunnels are allocated at the stage (c), leaving the performance of CB-STA some space to be improved.

Constant Length Weighted Tunnel Allocation (CLWTA)

CLWTA is proposed to overcome the problem in CB-STA. CLWTA allocate tunnels off-line and is based on an auxiliary used to rate the preference of tunnel allocation for each node pair. The process comprises four stages: (a) construction of auxiliary graph, (b) weight calculation for edges in the auxiliary graph, (c) weighted auxiliary graph based tunnel allocation, and (d) makeup process.

(a) construction of auxiliary graph Let G(V, Ep) be the original topology where V denotes the set of nodes and Ep represents the set of all physical links connecting the nodes. The auxiliary graph G’(V, E’) is constructed by adding auxiliary links El between the node pairs that have their shortest physical hop length

follow the length constraint (i.e., E’ = Ep + El). The auxiliary links represent the potential tunnels that could be allocated on the network.

(a)

D B

A F

C E

(b

ig. 6 gives an example of construction of auxiliary graph where Fig. 6(a) is the original topology with the average hop dist

Network Link S ach auxiliar

)

B D

A F

C E

Fig. 6 An example of auxiliary graph

F

ance equal to two and Fig. 6(b) is the corresponding auxiliary graph, in which dashed links represent the auxiliary links.

(b) weight calculation for edges in the auxiliary graph The Weighted tate (W-NLS) [1] is applied to determine the weight of e y link in the auxiliary graph. The weight of an auxiliary link is the predicted loads for the two nodes at the ends of that link. The larger the weight of an auxiliary link, the higher priority the node pair for that link gains to be allocated tunnels.

s d

Fig. 7 An example of deriving the W-NLS for each link in the network

Fig. 7 gives an example of how the weights are derived. There are three shortest paths from node s to d. The load from s to d is assumed to be equally distributed on the three paths. The weight of each link traversed by the shortest paths is thus increased by one third of the load from s to d. The weight of all the auxiliary links can be derived by applying the above procedure for all the node pairs in the network.

(c) weighted auxiliary graph based tunnel allocation This stage applies a greedy approach to allocate a set of tunnels according to the weight derived in the previous stage. The auxiliary link in G’ with the maximum weight is first selected, and an attempt is made to allocate a fiber tunnel for this auxiliary link. If the fiber tunnel can be allocated successfully, the weight of the corresponding auxiliary link is

decreased by

δ , where Wi,j is the weight of the auxiliary link connecting

node i and j, L the number of directional links in the original network topology, FT the number of fibers dedicated for tunnel allocation in each directional link and D the length constraint. Otherwise, we try to allocate a waveband tunnel for this auxiliary link. If a waveband tunnel can be successfully allocated, the weight of this auxiliary

link is decreased by

If both fiber and waveband tunnels fail to be allocated, the weight of this auxiliary

link is set to 0. The above procedure is repeated until all of the weights of the auxiliary links in G’ are equal to or less than 0.

(d) makeup process This process is used to further utilize the remaining resource after stage (c). The tunnels allocated in this stage do not have to follow the length constraint.

The whole algorithm of CLWTA is summarized as follows.

Constant Length Weighted Tunnel Allocation (CLWTA)

Step1. Form the auxiliary graph by adding all possible tunnels to the physical network.

Step2. Compute weight for each possible tunnel by routing the traffic matrix on the auxiliary graph

Step3. Stop if the weight for each auxiliary link is smaller or equal to 0.

Step4. Try to allocate fiber tunnel for the auxiliary link with maximum weight. If successful, decrease the weight of this auxiliary link by δF

and go to Step 3. Otherwise, go to Step 5.

Step5. Try to allocate waveband tunnel for this auxiliary link. Decrease the weight of this auxiliary link by δB. Go to Step 3.

In CLWTA and CB-STA, a tunnel can be allocated if free link capacity on the route between the ingress and egress of the tunnel is available. An allocated tunnel needs to be further brought up to be utilized by lightpaths. When a tunnel is brought up, wavelength-switching ports are needed so that wavelengths can be group or de-group at two ends of the tunnel. The number of wavelength-switching ports consumed at each end of the tunnel so that the tunnel can be brought up is equal to the capacity (in wavelength) of that tunnel.

We also propose another heuristic, Port Constraint- Constant Length Weighted Tunnel Allocation (PC-CLWTA) with slight modification on CLWTA. In PC-CLWTA,

after a tunnel is allocated, wavelength-switching ports at the ingress and egress nodes of the tunnel are dedicated to the tunnel. That is, a tunnel can not be allocated if any on the two ends of the tunnel has insufficient wavelength-switching ports.

PC-CLWTA improves the performance when the wavelength-switching ports is significantly fewer than the resources in the fiber-switching and waveband-switching layers. The performances of schemes described above are evaluated in the following section.