Preference Based Reconfiguration Algorithm

Chapter 5. Virtual Topology Reconfiguration in Hierarchical Cross-connect WDM Networks

II. Preference Based Reconfiguration Algorithm

Although short tunnels are easily utilized by most of the lightpaths, the wavelength-switching ports can be used up easily since the wavelength-switching ports are required at the ingress and egress nodes of each tunnel. Long tunnels, on the other hand, though save wavelength-switching ports, may not be suitable for the requests since most of the lightpath requests are shorter than the tunnels. Therefore, we restrict that the tunnels follow the tunnel length constraint, i.e., the length of each tunnel should be the same, which is set to the minimum integer that is larger than the average distance of paths between each s-d pair in the network [HoMa01][LoCh01].

PBRA is based on an auxiliary graph to rate for each node pair the preference of having tunnels established between them. We then determine the addition, deletion or keeping of the tunnels based on the derived preference value. Since the length constraint can be derived from the given physical

topology, we can determine the set of node pairs that is qualified to be allocated tunnels easily. That is, only the node pairs whose shortest path distance equal to the length constraint could be allocated tunnels. This is reflected in the construction the auxiliary graph. The whole process comprises four stages: (a) construction of auxiliary graph, (b) cost assignment for edges in the auxiliary graph, (c) load estimation of existent and nonexistent tunnels, and (d) tunnel selection. Details are described as follows.

Fig. 2. Illustration of the construction of auxiliary graph. (a) The physical topology (b) The corresponding auxiliary graph

(a) Construction of auxiliary graph

Let Gp(Vp, Ep) be the physical topology where Vp denotes the set of nodes and Ep is the set of all physical links connecting the nodes. The auxiliary graph Ga(Va, Ea) mainly comprises three layers, which are wavelength waveband and fiber layers and is obtained as follows. Each node i ∈ Vp is replicated into wavelength, waveband and fiber layer. These nodes are denoted as ViW, ViB and ViF ∈ Va. If edge e ∈ Ep connects node i to node j, i, j ∈ Vp, then node ViW is connected to VjW by a directed edge, termed wavelength-switching edge. For each node pair i-j with existent waveband (fiber) tunnel in V1, the node ViB (ViF) is connected to VjB (VjF) by a directed edge, termed existent waveband (fiber) tunnel edge. For each node pair i-j with its shortest physical hop length follow the length constraint and has not yet been allocated waveband (fiber) tunnel, there is also an edge connecting from ViB to VjB (ViF to VjF), termed potential waveband (fiber) edge. For each node i ∈ Vp, there are bidirectional edges between ViW, ViB, and ViF, termed layer transition edges. Fig. 2 gives an example of construction of the auxiliary graph. Fig. 2(a) is the physical topology with its average hop distance equal to two. The corresponding auxiliary graph may be the one shown in Fig. 2(b).

(b) Cost assignment for edges in the auxiliary graph Costs of the edges are assigned as in Table I.

TABLE I

COST FOR EDGES IN Ga

Existent waveband (fiber) tunnel edge

D (Length constraint)

Potential waveband (fiber)

tunnel edge D′ + scale Wavelength-switching edge >>D Layer transition edges 0

Fig. 3. Illustration of calculating CL. (a) Conflictions happen at physical links and at end nodes. (b) A detailed drawing of the confliction at the end nodes.

Since we hope to reconfigure V1 with little changes, the existent tunnel edges have the smallest cost D which is the tunnel length constraint. D′ is used to adjust the degree of preference on the existent tunnels where D′ ≥ D and D′ ∈ Z. The higher D′ we select the less preference the existent tunnels will be used. For each potential waveband (fiber) edge, a scale is associated with it. The scale represents the degree of difficulty to construct a tunnel for the node pair associated with that edge. The more existent tunnels must be deleted to construct a tunnel for a potential tunnel edge, the larger the scale is for that potential tunnel edge. Scale for potential tunnel edge i is defined to be (CLi－CLmin) / (CLmax－CLmin), where CLi is the number of existent tunnels that may hinder the construction of the tunnel for the node pair associated with edge i, CLmax = and CL

j CLj

edges tunnel potentialmax

∈

min = . Figure 5 illustrates the calculation of CL for the potential tunnel edge. Note that the conflictions between the existent and nonexistent tunnels may happen at physical links or the end nodes of the tunnels (They contend for the wavelength switching ports). In Fig. 3(a), the thick and dash lines represent the actual physical paths of existent and nonexistent tunnels, respectively. The nonexistent tunnel (1, 5) conflicts with the existent tunnel (0, 3) at the physical link (1, 3) and with the existent tunnel (2, 5) at the end node 5 (Fig. 3b). Thus, the CL for the potential tunnel edge (1, 5) is 2.

CLj j∈potentialmin tunneledges

(c) Load estimation of existent and nonexistent tunnels

After completion of stage (b), we can then route T2 on the auxiliary graph to estimate the load on each edge of the auxiliary graph. We assume that the load between each node pair will be equally

distributed on all its shortest paths. For example, for the network shown in Fig. 2, assume that the future traffic between node 0 and node 5 is 10 and five shortest paths are found as shown in Fig. 4(a).

Then each of the five paths will be distributed 2 units of the load. After T2 is routed on the auxiliary graph, for each node pair, the summation of the load of the existent/potential waveband/fiber edges for that pair will be recorded in a matrix W. Fig. 4(b) shows the matrix W as a result of Fig. 4(a) where W0,4 = 2, W1,5 = 2 + 2 = 4 and W2,5 = 2 + 2 = 4.

(d) Tunnels selection

W is used to determine the set of tunnels. The process repeatedly examine the node pair with the maximum weight to see whether there are existent tunnels for the node pair, otherwise, it tries to construct a new tunnel for the node pair. If there are already existent tunnels allocated between the selected pair, keep one of them in the virtual topology. Otherwise, construct a tunnel between the selected pair and if necessary, delete the existent tunnels that hinder the construction. Note that whether keeping or constructing a tunnel, the fiber tunnel is considered first. If a fiber tunnel is kept, or constructed successfully, weight of the corresponding node pair is decreased by δF = ΣWi,j/(L⋅FT/D), where Wi,j is the weight of the node pair (i, j), L the number of directional links in the physical topology, FT = F1 + F2 the number of fibers dedicated to tunnel allocation in each directional link and D the length constraint. Similarly, for the waveband tunnel, the weight is decreased by ΣWi,j/(L⋅B⋅FT/D), where B is the number of wavebands in a fiber. If both fiber and waveband tunnels fail to be constructed, the weight is set to 0. The whole algorithm of PBRA is summarized as follows.

Preference Based Reconfiguration Algorithm:

Input:

V1 : Current virtual topology

Fig. 4. Computation of W. (a) Five shortest paths from node 0 to node 5. (b) The corresponding W.

T2 : Future traffic pattern

Step 4: If there are existent fiber tunnels for (i, j), keep one of them, decrease the weight of the node pair by δF, and go to Step 3. Otherwise, go to Step 5.

Step 5: If there are existent waveband tunnels for (i, j), keep one of them, decrease Wi,j by δB, and go to Step 3. Otherwise, go to Step 6.

Step 6: Try to construct a fiber tunnel for (i, j). If successful, decrease Wi,j by δF, and go to Step 3.

Otherwise, go to Step 7.

Step 7: Try to construct a waveband tunnel for (i, j). If successful, decrease Wi,j by δB, and go to Step 3. Otherwise, go to Step 8.

Step 8: Set Wi,j to 0, go to Step 3.

Fig. 5. Physical topology of our simulation environment

Simulation experiments were conducted on the 16-node network shown in Fig. 5. The notation (F1)F(F2)B(F3)L represents the experiment with F1 fibers for fiber switching, F2 fibers for waveband switching and F3 fibers for wavelength switching on each link. We assume that a fiber contains 40 wavelengths and can be divided into four fixed wavebands, with λ1~λ10 being waveband one, λ11~λ20 waveband two…, and λ31~λ40 waveband four. In the simulation, waveband conversion is not allowed while wavelength conversion within the bands is assumed. Two types of traffic patterns are used for the transition between old and new ones. 1) Ring traffic: the load for each node pair (i, (i+1) mod 16), i = 0, …, 15 is in average 10 times larger then others. 2) Uniform traffic: All traffic requests are randomly generated between each node pair.

Although not shown in the result, it is worth noting that when the new and old traffic pattern are similar, reconfiguration is unnecessary since the original virtual topology is already suitable for the new traffic pattern. Fig. 6 and Fig. 7 shows the simulation results of total number of lightpath request vs. blocking probability and percentage of unchanged tunnels under 2F1B2L and 2F2B1L.

The curve “only consider T2” means that the new virtual topology is designed without considering the original using the heuristic presented in [LoCh01] and serve as the best case for the comparison.

“T2 route on V1” means that we directly route the new traffic on the V1 without changing the original topology and serve as the worst case for the comparison. It can be observed that the improvement space between the two curves is rather limited. The parameter D' is tuned to observe the tradeoff.

2F1B2L (ring, uniform)