Often network planning or research studies have to be conducted without the luxury of a known or reliably forecast demand matrix.
Obtaining accurate forecasts of the real demand is a whole discipline of its own. In other contexts, however, one is conducting comparative network planning or research studies and needs only a representative demand model on which to base comparative design studies. While there is an infinite number of demand patterns that could be tested, the practical researcher or planner has to use only a few test-case demand patterns to try to reach generally true comparative conclusions about alternatives. A variety of different test-case demand patterns can be made up from the following models:
Pure logical mesh with equal number of demands on all node pairs 1.
Random distributed demand: uniform random number of demands on each pair 2.
The first two models are self explanatory. The hub and dual hub patterns often characterize metro or regional area networks involving one or two main hub sites. In general, the demand between a hub and a non-hub node may also be inversely proportional to the distance between them. All other node pairs (i.e., between two non-hub nodes) exchange either a constant or uniform random number of demand units. A numerical model that can be used is:
Equation 1.5
Equation 1.6
where d0 and l0 are demand and distance scale constants, respectively, and li,hub is the distance from node i to the respective hub, di,hub is the (integer) number of demands generated. The second part of the model generates a constant mutual demand between all other non-hub nodes.
A principle that is believed to underlie real traffic intensities at long-distance scales is the concept of mutual attraction, independent of distance. For example, New York City and Los Angeles are two of the most important centers in the U.S. New York City also exchanges traffic with Ottawa, but it is lower because of Ottawa's lower population and economic status compared to Los Angeles. Population data can be one measure of this notion of importance in the real world, but to generate test-case demand patterns with the same overall characteristics, "importance factors" can be assigned to nodes at random. Another approach is to view nodal degree as a surrogate for the presumed demographic importance. The argument is that large centers will tend to have higher nodal degree. In either case, once the
"importance factors" Ii are assigned to each node i, the mutual attraction demand model is:
Equation 1.7
The pure mutual attraction model is independent of distance between centers. The "gravity" demand model adds an inverse distance dependency, partially offsetting the mutual importance effect. For example, extending our prior example to include Paris, we might agree that Paris, New York and Los Angeles are all of the same "importance" class, but "distance" (including geographical, cultural, time-zone offset, etc.) tends to attenuate the Los Angeles–Paris demand relative to the Los Angeles–New York demand. The fully general "gravity"
model produces a number of demands for each (i,j) node pair that responds to both importance and distance as follows:
Equation 1.8
where a is an exponent modeling the inverse-distance effect and d0 is a scaling constant set so that the individual demand quantities are in the range intended. Of course the name "gravity" suggests a = 2. But in practice where this method has been compared to actual demand patterns, a much closer to one (e.g., 1.1 to 1.3) have been typically found to be more accurate.
There is evidence that as IP data volumes outpace voice, demand in real backbone networks is tending even more toward distance independence (i.e.,a 0). This may also be due in part to flat-rate (distance independent) voice calling plans. A 2001 study of North American long-haul demand evolution showed that pair-wise total demand between nodes was almost uncorrelated to geographical distance. This can be seen in Figure 1-16(a). In a sense, with the Internet, all points are now an insignificant "distance" apart from a social or commercial standpoint. This gives increasing justification for network planning studies to use a distance independent demand model.
Figure 1-16. Evolution of demand patterns to be almost independent of distance within a
national network implying that most nodal flow is also transiting traffic (adapted from [FrSo01]).
An implication of distance-independent demand is that most traffic at backbone network nodes tends to be transiting traffic. To illustrate, Figure 1-16(b) shows the distribution of physical span distances between adjacent (i.e., directly connected) nodes in the same network to which the data of Figure 1-16(a) pertain. Together Figure 1-16(a) and (b) imply that in the average backbone node, 70% of the flow at a node transits the site. On average only 30% originates (or terminates) at a node. (This is another compelling argument for the role of cross-connects in a transport layer to pass such flow through at low cost and high speed, without any electrical payload manipulation at transiting nodes.)
Note that distance-independence does not imply that all demands are also equal in their magnitude. Figure 1-17(a) illustrates this with data from an inter-exchange carrier network. The histogram shows the statistical frequency of various numbers of STS-1 equivalents of demand between node pairs. (Data is only plotted for those node pairs exchanging a non-zero demand quantity.) About 90% of all possible demand pairs exchange at least one STS-1. What the data show is that there tends to be three components to the overall demand model:
A fraction of node pairs exchanging no transport-level demands.
A large number of demand pairs exchanging demands that are distributed consistent with the pure attraction (product of importance factors) model.
A small number of demand pairs exchanging relatively huge demand values lying far out on the tail of the overall distribution.
Figure 1-17. (a) Histogram of demand magnitudes in an inter-exchange carrier network, (b)
Histogram of the product of uniformly distributed "importance" numbers for comparison.
Let us comment on each of these three components. First, for clarification, when a node pair exchanges no demands in the transport network, it does not mean that there is no traffic between these centres. It just means that the traffic they exchange is being routed via regional access networks through different transport hubs. At the other extreme is the set of super-demands that seem to be completely independent of the rest of the distribution. In this particular data there were 22 values above 50 STS-1s, with individual values of 89, 113 and so on, irregularly up to as high as 210 STS-1s. The number of such super-demands is under 10% of all node pairs and is distributed in no recognizable way in terms of the histogram, but in the full data they clearly correspond to the largest city pairs in the country. Although
<10% in number, they contribute almost 50% of the total demand over all node pairs.
The middle grouping of the overall demand distribution (corresponding to the second bullet above) produce the most prominent
characteristic of Figure 1-17. This includes about 80% of all the possible demand pairs and amounts to about half the total demand. What we mean by the most prominent characteristic in Figure 1-17 is the overall binomial-like shape in Figure 1-17. This distribution is
remarkably consistent with the mutual attraction model in which a uniform random "importance number" is assigned to each node and the product of importance values determines the demand for each node pair. To illustrate how characteristic the attraction model is of the actual data, Figure 1-17(b) shows the distribution of the products of uniform random importance values assigned to 50 nodes on the range [10...110].
For more discussion and useful data about demand patterns, and the breakdown of demand into voice and Internet transactions, etc., [MaCo03] is an excellent reference. It also provides several examples of European inter-city transport network graphs in particular.
[ Team LiB ]
[ Team LiB ]
1.6 Short and Long-Term Transport Network Planning Contexts
One of the dividing lines between different planning contexts is short-term versus long-term. Long term studies are sometimes also called fundamental planning or technology planning studies. A primary distinction between these two contexts is whether the network capacity is already placed, or where capacity assignment is the goal, typically with a minimum cost objective. In the short-term context where specific capacity is already deployed, the concern is typically with maximizing the amount of demand the as-built network can support. In a future with truly dynamic random demand arrival this will mean minimizing the probability of blocking new service path requests. Algorithms for the best routing of paths and/or logical reconfiguration of existing routes and capacity are the primary focus in this context. The focus in the short-time scale is on operational aspects of the network and on trying to maximize its performance in terms of blocking of new service requests, service provisioning delays or other dynamic performance measures. [Dixi03] (p. 305) presents a somewhat complementary discussion to what follows in that he recognizes a connection-level time scale and a separate capacity-planning time scale of "months or longer" that includes consideration of both working capacity and protection techniques and