Section 14.5. Wavelength Allocation in Networks

14.5. Wavelength Allocation in Networks

Similar to nonoptical networks, optical networks consist of a number of routing nodes connected by communication links. In optical networks, nodes may have optical multiplexing, switching, and routing components , and links are optical fibers. In the early generations of optical fibers, transmission of signals was degraded on short distances mainly because of lack of amplification. In later versions of optical-fiber systems, the loss of signals was significantly reduced through carefully designed amplifiers. In the latest generations of optical communication systems, the overall cost has been lowered , the effect of dispersion has been eliminated, the data bit rate has been enhanced up to beyond tens of gigabits per second, optical amplifiers has replaced regenerators, and WDM technology has been used for multiplexing purposes.

All-optical networks can be designed to carry data using any wavelength regardless of the protocol and framing structure. All-optical networks were encouraged by the development of ultralong-haul fibers mounted on a single physical fiber. By transmitting each signal at a different frequency, network providers could send many signals on one fiber, just as though each signal were traveling on its own fiber. All-optical networks handle the intermediate data at the optical level. This efficient functioning of the network provides a number of advantages in handling data: reduced overall cost and increased system bandwidth.

A lightpath carries not only the direct traffic between the nodes it interconnects but also traffic from nodes upstream of the source to downstream of the destination. Thus, a lightpath can reduce the number of allocated wavelengths and improve the network throughput. In practice, a large number of lightpaths may be set up on the network in order to embed a virtual topology.

14.5.1. Classification of Optical Networks

Optical networks can be classified according to the type of nodes being used in the network. Figure 14.9 (a) shows an optical network of broadcast nodes. A broadcast node combines all incoming signals and delivers a fraction of the power from each signal on to each output port. A tunable optical filter can then select the desired wavelength for reception .

Figure 14.9. An optical network with (a) broadcast nodes and (b) wavelength routing nodes

Figure 14.9 (b) illustrates a network that uses wavelength routing nodes. These types of nodes are capable of reusing wavelengths and handling many simultaneous lightpaths with the same wavelength in the network. Two lightpathsR ₁ -R ₂ -R ₃ -R ₄ and R ₇ -R ₆ -R ₅ do not use any shared link and can therefore be assigned the same wavelength » ₁ . Because lightpaths R ₁ -R ₂ -R ₃ -R ₄ and R ₇ -R ₂ -R ₃ -R ₅ share part of their common path (R ₂ -R ₃ ), they must therefore use a different wavelength.

14.5.2. Wavelength Allocation

Consider an all-optical network in which each link in the network can carry a maximum of » _n wavelengths. Because of the maximum wavelength capacity, a network may not be able to handle all lightpath requests, so some requests may be blocked. To keep lightpaths separated on the same link, they should be allocated different wavelengths. For example, consider the all-optical network shown in Figure 14.10, with five lightpaths: L ₁ through L ₅ . On link R ₂ -R ₃ , the same wavelength cannot be allocated.

Figure 14.10. Allocation of wavelengths in an optical network

A lightpath with wavelength » _i at any node's input can be converted to any available wavelength » _j ˆˆ{ » ₁ , ..., » _n } on the node's output link. If no wavelength is available, a lightpath uses the same wavelength on all links of its path. Based on our earlier discussion, wavelength allocations for this case can be arranged as follows : L ₁ is assigned » ₁ ,L ₂ is assigned » ₂ ,L ₃ is assigned » ₁ ,L ₄ is assigned » ₃ , and L ₅ is assigned » ₄ .

The concept of wavelength allocation can be analyzed in two ways. One way is to assume that the probability of a wavelength being used on a link is independent of the use of the same wavelength on all other links of the lightpath. Although this method is not practical, the analysis provides a quick approximation on how effective the assignment of wavelengths is. The second method removes the assumption of independence.

Wavelength Allocation Without Dependency

The wavelength-allocation algorithm assigns an arbitrary but identical wavelength on every link of a lightpath when one such wavelength is free on every piece of its path. In this section, we assume that the probability of a wavelength being used on a link is independent of the use of the same wavelength on all other links of the lightpath. Consider a single link in which » _n wavelengths are available. For each lightpath request, the first available wavelength is assigned. The wavelength-request arrival is assumed to be Poisson with the rate that leads to a utilization . Then, the blocking probability on this link follows the Erlang-B formula expressed by Equation (11.46):

Equation 14.3

This formula calculates the probability that an arriving request finds no available wavelength while there is no waiting line for request. For gaining the highest efficiency on assigning wavelengths to requests, wavelengths must be reused effectively. If lightpaths overlap, the wavelength-conversion gain would be low.

Not only the overlap between lightpaths impacts the wavelength-conversion gain; so too does the number of nodes. Assume that for each lightpath, the route through the network is specified. Let the probability that a wavelength is used on a link be p . If the network has » _n wavelengths on every link and a lightpath request chooses a route with r links, the probability that a given wavelength is not free on at least one of existing r links of the route can be derived by

Equation 14.4

Note that for P _b , we use the rules developed in Section 7.6.4. The probability that a given wavelength is free on any given link is (1 - p). Consequently, the probability that a wavelength is not free on all the r links of the path is 1 - (1 - p ) ^{» _n} . Using the parallel rule explained in Section 7.6.4, P _b expresses the probability that a given wavelength is not available on at least one of existing r links of the route. Similarly, the probability that a lightpath request is blocked is

Equation 14.5

The wavelength allocation with dependency is much more complicated. Next, we try to present a simplified analysis for this case.

Wavelength Allocation with Dependency

In practice, the allocation of a free wavelength to a lightpath on its every link is dependent on the use of other wavelengths on the same link. Let be the probability that a wavelength is used on link i , given that the wavelength is not used on link i - 1. Also, let P( _{i i -1} ) be the probability that a wavelength is used on link i , given that the wavelength is used on link i - 1. Then:

Equation 14.6

If we substitute for p in Equation (14.4), P _b can be reexpressed for the dependency condition as

Equation 14.7

We can now estimate the packet delay over a lightpath on link i , j from node i to node j . Assume that packet-transmission times are exponentially distributed with mean time 1 / µ , and Poisson packet arrival distribution with mean arrival rate . Let s _i,j be the loading value on link i , j , or the number of source/destination pairs whose traffic is routed across link i , j . Then, we can obtain the average delay on link i , j by using Equation (11.21):

Equation 14.8

If a network has a total of n nodes, the average queueing delay incurred for a packet through all nodes over all source/destination pairs is expressed by

Equation 14.9