Abstract-We consider a class of finite-state Markov channels with feedback. We first introduce a simplified equivalent channel model, and then construct the optimal stationary and nonstationary input processes that maximize the long-term directed mutual information. Furthermore, we give a sufficient condition under which the channel's Shannon capacity can be achieved by a stationary input process. The corresponding converse coding theorem and direct coding theorem are proved.

Among all airport operations, aircraft ground movement plays a key role in improving overall airport capacity as it links other airport operations. Moreover, ever-increasing air traffic, rising costs, and tighter environmental targets create pressure to minimize fuel burn on the ground. However, current routing functions envisioned in Advanced Surface Movement, Guidance and Control Systems almost exclusively consider the most timeefficient solution and apply a conservative separation to ensure conflict-free surface movement, sometimes with additional buffer times to absorb small deviations from the taxi times. Such an overly constrained routing approach may result in either a too tight planning for some aircraft so that fuel efficiency is compromised due to multiple acceleration phases, or performance could be further improved by reducing the separation and buffer times. In light of this, Parts I and II of this paper present a new Active Routing (AR) framework with the aim of providing a more realistic, cost-effective, and environmental friendly surface movement, targeting some of the busiest international hub airports. Part I of this paper focuses on optimal speed profile generation using a physics-based aircraft movement model. Two approaches based, respectively, on the Base of Aircraft Data and the International Civil Aviation Organization engine emissions database have been employed to model fuel consumption. These models are then embedded within a multiobjective optimization framework to capture the essence of different speed profiles in a Pareto optimal sense. The proposed approach represents the first attempt to systematically address speed profiles with competing objectives. Results reveal an apparent tradeoff between fuel burn and taxi times irrespective of fuel consumption modeling approaches. This will have a profound impact on the routing and scheduling and open the door for the new concept of AR discussed in Part II of this paper.

Environmental impact is a very important agenda item in many sectors nowadays, which the air transportation sector is also trying to reduce as much as possible. One area which has remained relatively unexplored in this context is the ground movement problem for aircraft on the airport's surface. Aircraft have to be routed from a gate to a runway and vice versa and it is still unknown whether fuel burn and environmental impact reductions will best result from purely minimising the taxi times or whether it is also important to avoid multiple acceleration phases. This paper presents a newly developed multi-objective approach for analysing the trade-off between taxi time and fuel consumption during taxiing. The approach consists of a combination of a graph-based routing algorithm and a population adaptive immune algorithm to discover different speed profiles of aircraft. Analysis with data from a European hub airport has highlighted the impressive performance of the new approach. Furthermore, it is shown that the trade-off between taxi time and fuel consumption is very sensitive to the fuel-related objective function which is used.

Based on the multi-objective optimal speed profile generation framework for unimpeded taxiing aircraft presented in the precursor paper, this paper deals with how to seamlessly integrate such optimal speed profiles into a holistic decision making framework. The availability of a set of non-dominated unimpeded speed profiles for each taxiway segment with respect to conflicting objectives can significantly change the current airport ground movement research. More specifically, the routing and scheduling function that was previously based on distance, emphasizing time efficiency, could now be based on richer information embedded within speed profiles, such as the taxiing times along segments, the corresponding fuel consumption, and the associated economic implications. The economic implications are exploited over a day of operation to take into account cost differences between busier and quieter times of the airport. Therefore, the most cost-effective and tailored decision can be made, respecting the environmental impact. Preliminary results based on the proposed approach are promising and show a 9%-50% reduction in time and fuel respectively for two international airports, viz. Zurich and Manchester Airports. The study also suggests that, if the average power setting during the acceleration phase could be lifted from the level suggested by the International Civil Aviation Organization (ICAO), ground operations may achieve the best of both worlds, simultaneously improving both time and fuel efficiency. Now might be the time to move away from the conventional distance based routing and scheduling to a more comprehensive framework, capturing the multi-facetted needs of all stakeholders involved in airport ground operations.

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