3.1.

Problem Description

Like multicasting in the WDM mesh networks, a multicast routing and wavelength assignment (MC-RWA) problem also exists for multicasting in WDM ring.^{2, 6} Let $R\left(V\right)$ be the bidirectional WDM ring, where $V$ denotes the set of network nodes. Let $Q(s,D)$ be an optical multicast request, where $D$ denotes the set of destination nodes, and $s$ $(s∊V,s\notin D)$ denotes the source node. The functionality of MC-RWA is to find one or more wavelength channels along either clockwise or counterclockwise of $R\left(V\right)$ to connect $s$ to nodes in $D$ . The wavelength channels can be light paths (point to point wavelength channels) or light trees (point to multipoints wavelength channels). The existing shortest path tree (SPT) and minimum spanning tree (MST) heuristics can also be introduced into WDM ring.⁶ The SPT minimizes the delay from $s$ to every destination node in $D$ , while the MST minimizes the network cost in terms of the total links costs of a routing tree. Figures 2a and 2b illustrate an example of the SPT tree and the MST tree for a multicast group with $s=1$ and $D=\{3,4,6\}$ .

Fig. 2

Example of light trees: (a) SPT, (b) MST, and (c) multicasting in WDM ring employing normal OADM.

Since normal OADMs have no multicast capability to set up light trees for $Q(s,D)$ , we use $\mid D\mid$ different light paths originating from $s$ to simulate a light tree; that is, for each node pair of $(s,d)$ where $d∊D$ , we try to find the shortest path along clockwise or counterclockwise direction under constraints of wavelengths and add/drop ports availability. An example is shown in Fig. 2c for the multicast group $Q(1,\{3,4,6\})$ . We call this scheme the normal scheme (N-Scheme).

As for multicasting in the ring employing MC-OADMs, we first divide $\mid V\mid -1$ nodes in $V$ except $s$ into two half rings according to $s$ . Considering the ring in Fig. 2 where the source node $s=1$ , nodes 2, 3, 4, and 5 fall into the right half ring while nodes 8, 7, and 6 fall into the left half ring. The destination nodes falling into the right half ring are routed in clockwise within the right half ring and those falling into the left half ring are routed in counterclockwise confined in the left half ring. Using this method, SPT trees can be built. We call this scheme multicast scheme (M-Scheme).

As in the mesh topology, there are also two definitions to evaluate service blocking for dynamic multicasting in WDM ring, i.e., session (a multicast group) blocking and member (destination) blocking. For a multicast request $Q(s,D)$ , if there is any member in $D$ being rejected due to no available wavelength channel or no available drop port, all members in $D$ are rejected, which is called session blocking. When only the rejected members are counted, we call it member blocking which is adopted in this work.

3.2.

Performance Simulation and Analysis

We consider both unicast and multicast connections and suppose $P\%$ $(0<P<100)$ of the requests are multicast ones. Note $\mid D\mid$ uniformly changes from 2 up to $\mid V\mid -1$ among the multicast requests. All requests arrive according to a Poisson process with rate $\lambda$ and the holding time of each request is exponentially distributed with a mean $1∕\mu$ , i.e., the load measured in Erlangs is $\lambda ∕\mu$ . Totally ${10}^6$ requests (both unicast and multicast ones) are considered at each load and the member blocking probability is calculated on these ${10}^6$ requests. The resource consumption is calculated in terms of wavelength segments consumed per session. (A wavelength segment is a wavelength channel between two successive nodes along the ring.) The calculated member blocking probability and the wavelength segments consumption at each load on a 10 node ring with three traffic scenarios: 20, 50, and 70% of ${10}^6$ requests being multicast requests, are illustrated in Fig. 3. (There are two fibers at each direction of the ring and 16 wavelengths in each fiber.)

Fig. 3

Network performance of MC-OADM ring: (a) blocking probability, and (b) wavelength consumption.

Figure 3a shows the blocking probability of the N-Scheme at light load is lower than that of the M-Scheme. However, as the load increases, the blocking probability of the N-Scheme increases dramatically and goes higher than that of the M-Scheme. The reasons are that, first, in the RWA for the N-Scheme, if a light path cannot be found in the clockwise (counterclockwise) direction, the RWA will try to find another lightpath in the anticlockwise (clockwise) direction, nevertheless in the RWA for the M-Scheme to construct SPT tree, the light path searching is confined to the clockwise half ring or the counterclockwise half ring rather than the entire ring; second, the RWA for the N-Scheme can find a light path longer than the half ring while the RWA for the M-Scheme always finds a light path no longer than the half ring; third, more than one destination can share the same lightpath to form SPT tree in M-Scheme by using MADEs, i.e., the M-Scheme consumes less resources than the N-Scheme does, as can be seen from Fig. 3b, where the wavelength segments consumed per session for the N-Scheme is larger than that for the M-Scheme, on all three traffic scenarios. Due to these three features, the available wavelength and add/drop ports are sufficient at light load so that the N-Scheme has more chances to find a light path than the M-Scheme does. But at heavy load, since the available resources get severe for the N-Scheme, the blocking probability of the N-Scheme rises sharply and becomes unacceptable 0.1 at 13 erlangs in the scenario of 70% of ${10}^6$ requests being multicast requests and 30% being unicast ones, while that of the M-Scheme remains under 0.08 at 25 erlangs.

Figure 3 also shows that the member blocking probability and the wavelength segments consumed per session will increase as the percentage of multicast requests increasing for both the N-Scheme and the M-Scheme. The reason is that the more multicast requests arrive, the more destination nodes must be connected, then the more resources are occupied, and eventually, the more members are blocked due to the severe resources availability.