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Energy-efficient operation of large telecommunication networks is an important issue today and in the near future. Given that the energy consumption rises with the ever increasing demand for capacity and network speed, there is a growing interest in strategies for a sustainable network management. It is a well-known fact that traffic demands vary significantly over time, most notably in day/night- and in weekly cycles. This provides the main potential for energy-saving strategies. We study the question of how much power is necessary to operate a network with state-of-the-art hardware during peak or low-traffic times. The study respects realistic side constraints, such as protection requirements and routing schemes, and takes the special structure of an extensive nation-wide optical network, including backbone and regional sections, into account. We formulate mixed integer programming models for the corresponding optimization problems using predictions for traffic matrices, as well as state-of-the-art hardware and power models. We address questions as the following: How much energy is spent in the core and in metro regions of the network and how big are the savings in low-demand scenarios if we always assume the system power-minimum in these situations? What is the influence of different hardware on the overall energy consumption? How much do different routing schemes or protection scenarios restrict potential energy savings?
In this paper we study the cost-optimal deployment of optical access networks considering variants of the problem such as fiber to the home (FTTH), fiber to the building (FTTB), fiber to the curb (FTTC), or fiber to the neighborhood (FTTN). We identify the combinatorial structures of the most important sub-problems arising in this area and model these, e.g., as capacitated facility location, concentrator location, or Steiner tree problems. We discuss modeling alternatives as well. We finally construct a “unified” integer programming model that combines all sub-models and provides a global view of all these FTTx problems. We also summarize computational studies of various special cases.
Sports rankings are obtained by applying a system of rules to evaluate the
performance of the participants in a competition.
We consider rankings that result from assigning an ordinal rank to each
competitor according to their performance.
We develop an integer programming model for rankings that allows us
to calculate the number of points needed to guarantee
a team the ith position, as well as the minimum number of points
that could yield the ith place.
The model is very general and can thus be applied to many types of sports.
We discuss examples coming from football (soccer), ice hockey, and
Formula~1. We answer various questions and debunk a few myths along the way.
Are 40 points enough to avoid relegation in the Bundesliga?
Do 95 points guarantee the participation of a team in the NHL playoffs?
Moreover, in the season restructuration currently under consideration in the NHL,
will it be easier or harder to access the playoffs?
Is it possible to win the Formula~1 World Championship without winning at least one race
or without even climbing once on the podium?
Finally, we observe that the optimal solutions of the aforementioned model
are associated to extreme situations which are unlikely to happen. Thus,
to get closer to realistic scenarios, we enhance the model by adding some
constraints inferred from the results of the previous years.