Multi-hour network planning based on domination between sets of traffic matrices

In multi-hour network design, periodic traffic variations along time are considered in the dimensioning process. Then, the non coincidence of traffic peaks along the day or the week can be exploited. This paper investigates the application of the traffic domination relation between sets of traffic matrices to multi-hour network planning. Two problem variants are considered: a network with a static, and with a dynamic traffic routing. We derive a set of techniques for, given a multi-hour traffic demand potentially composed of hundreds of matrices, obtaining a traffic series with a smaller number of matrices. The traffic domination relation guarantees that the network designed for the simplified series is suitable for the original one. Also, we apply the domination relation to derive lower bounds to the network cost, and upper bounds to the suboptimality incurred by simplifying the traffic demand. The algorithms proposed are tested in a case of study with the Abilene network. In our tests, a long traffic series could be reduced to a small number of traffic matrices, and be effective for network planning.