Here we show how the grooming analysis can be reduced to a problem that can be studied with a theoretical model based on WDMM introduced in Section 3.2. To perform the reduction we need some specific assumptions on the data layer traffic and the adaptation of the model to handle this traffic.
5.2.1 Considered traffic model and grooming scheme
Although it is not well suited to characteristics of IP traffic we consider at the data layer constant bitrate flow requests with bandwidth guarantees. We assume homogeneity in the required bandwidth, i.e., the bitrate is identical for all the requests. For the arrival process and for the holding time of flows we use the same assumptions as taken in Section 3.2 for the optical connection requests.
Allowing time division multiplexing inside the optical channels, we can define nels, called subwave channels that correspond to the timeslots. A data transmission chan-nel consists of a series of subwave chanchan-nels. The connection of subwave chanchan-nels can be restricted by several rules derived from the wavelength conversion and timeslot reorder-ing capability of the OXCs.
As a flow request arrives the generalised routing task is performed in both the data layer and the optical layer. In the latter we apply fixed routing and random wavelength assignment described in Section 3.2. Considering the concept of subwave channels the routing in the virtual layer is very simple: only one hop routes are allowed, i.e., a direct transmission channel transmits the flow data. This channel is dedicated to one flow re-quest and it is set up and torn down at the arrival of the rere-quest and at the finishing of the data transmit of the flow respectively.
Note, that such a routing solution can be realised only when the dynamic grooming scheme supports the full cooperation of the two layers, i.e., it has a peer architecture. We refer the reader to [6, 28, 29] for more about the grooming architectures of different level of cooperation.
We assume that network nodes are homogenous from point of view of the wavelength conversion and the timeslot reordering capability. Moreover, they apply the same guide-lines in connecting subwave channels. According to the assumptions in Section 3.2 each fiber supports the same number of wavelengths and each optical channel on each fiber is divided the same way into subwave channels. Thus, a set of trunks can be constructed out of these channels identified by their wavelength, or timeslot number, or both according to the node capabilities. Only subwave channels of the trunks with identical identifier can be connected in a transmission channel.
We apply a very simple connection admission control mechanism. Since users require
bandwidth guarantees, if no suitable path is found, i.e., no direct channel can be set up, the request is blocked. As main performance measure we find the blocking probability defined as the number of blocked requests divided by the number of all requests.
5.2.2 Description of the model
Let us present the extension of the WDMM to a Homogenous Guaranteed-traffic Groom-ing Model, HGGM. The algorithm of the blockGroom-ing probability computation does not change, but some parameters are interpreted in a different way, according to the concept of subwave channels.
Let us considerbhthe bitrate of the connections to be the bandwidth of a transmission channel. The number of subwave channels in an optical channel equalsU = bCO/bhc, where CO is the bandwidth of one whole wavelength. On each links the number of subwave channel trunksTSO is equal to:
• C, when only timeslot reordering is allowed,
• U, when only wavelength conversion is allowed,
• 1, when both these functions are enabled,
• C·U, when none of them are allowed.
Each step of the analysis can be performed using subwave channel trunks instead of wavelength trunks. In the computations we have to use the valueTSO instead ofC and the valuesCj/TSO instead of the valuesMj.
5.2.3 Numerical results
To evaluate the accuracy of the extended model we compared its results to simulation by reporting request blocking probability in function of network load. The simulation model had to be extended to consider the grooming scheme and the concept of subwave chan-nels. The trunk interpretation was changed according to the extension of the theoretical model.
We analysed the impact of traffic granularity on blocking in regular and irregular topology scenarios similarly as in Section 3.2.3. Here we show the results network CWEN presented on Figure 3.5. The link capacity values has to be understood this time in 100 Mbps, e.g., 64 means 6.4 Gbps. Each fiber contains 4 wavelengths of 0.8 Gbps capacity. We consider neither wavelength conversion nor reordering of timeslots and we use the same traffic relation matrix as in Section 3.2.3.
1e-04 1e-03 1e-02
48 50 52 54 56 58 60 62 64 66 68
Connection Blocking Probability
Network load (Gbps) Simulation
HGGM 1e-04
1e-03 1e-02
48 50 52 54 56 58 60 62 64 66 68
Connection Blocking Probability
Network load (Gbps) Simulation
HGGM
Figure 5.1: Blocking probability in the CWEN network, guaranteed bandwidthbhis 100 Mbps (left) and 200 Mbps (right)
First, the guaranteed bandwidth of the flows was 100 Mbps and the left plot of Figure 5.1 reports the results obtained with HGGM and simulation. A different granularity of the traffic was analysed usingbh equal to 200 Mbps. The results can be seen on the right plot of Figure 5.1. On these plots the total network load is given in Gbps.
Thanks to the consistent extension of the theoretical and the simulation models we can observe high accuracy, similarly to the case of the optical layer analysis in Section 3.2.3.