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Please provide a valid post code. Please provide your house number. Please provide your address. Moreover, in literature, exist many contradictory applications of the terms disturbance, stress and perturbation. So, it was necessary to clarify their particular meaning in the context of ATM. Taking into account the aims mentioned above, a framework, which incorporates a concept of the interdependencies between robustness, resilience and other relevant terms, has been developed in [1] [2].

In this new framework the terms of disturbance, stress and perturbation are linked together to create a new terminology of resilience and robustness in the context of a socio-technical system. There, the term disturbance is defined as a cause, whereas stress and perturbation have been determined as an effect caused by a disturbance. The idea to this logical differentiation of the terms disturbance, stress and perturbation is originated in ecosystems.

The term system used in the definitions denotes a socio-technical system or an ATM System as its particular case. State of a system is defined by a set of its performance indicators. Current state of a system is defined by the current values of its performance indicators. Reference state or normal state of a system is the specified set of its performance indicators values. A reference state at the moment of its specification relative to the current state of the system can be either.

To illustrate the introduced states, let us consider an airport as an ATM System and the average delay at the airport as the performance indicator that defines state of the system. Then as a reference state can be, for instance, the state where the average delay does not exceed x minutes, i. The current state represents then the current value of the average delay at the considered moment of time. Since resilience and robustness of a system depend on disturbances, it is necessary to define disturbance in the context of a socio-technical system:.

Disturbance - a cause a phenomenon, factor, or process, either internal or external, which may cause a stress in a system; is relative to the specified reference state and considered system; is categorized and quantified by type, frequency, intensity and duration. It is important to note see [3] , that.

Therefore, the scale in which a system is considered and the level of hierarchy in it determine the relevance of a disturbance and the level of detail in its characterization. Stress - an effect - a reaction of a system the state of a system caused by a disturbance which differs from the reference state and is characterized by deviation from this reference condition; can be.

Perturbation - an effect - an action of a system the response of a system to the possible or current significant undesirable changes of the state of the system caused by a disturbance. So a system, which is influenced by a disturbance, can have no stress or can react by stress and in the case of survival stress act by transient or permanent perturbation see Figure 1.

This framework enables us to define robustness and resilience of a system. Robustness is described as the ability of a system to absorb a disturbance while resilience is given as the ability of a system to return back within a specified time horizon since a disturbance had occurred.

Robustness - the ability of a system to experience no stress since a disturbance had occurred, i. Resilience - the ability of a system to respond on a disturbance within a time horizon by transient perturbation, i.

Both introduced terms - robustness and resilience of a system - are time dependent, i. The action of a system remaining in the framework see Figure 1 - permanent perturbation - leads to a new reference state of the system and the remained reaction of a system - lethal stress - causes its modification.

The developed concept has clear differentiation between the terms robustness and resilience. A grade of an influence of a disturbance on a system is illustrated in Figure 1 schematically by a color and by a depth of the colored blocks: Because of the universal character of the terminology with respect to the characteristics of socio-technical systems, it can be applied generally or at specific subsystems of an ATM System as well.

Therefore it enables investigating resilience and robustness at different levels of detail as well as at different scales of expansion of an ATM System. A further important point in the developed framework enables measurement of resilience and robustness, since if they are not quantifiable they are not improvable.

This section is based on [1] [4]. However, this situation is possible at the airports working under its nominal capacity only. More realistic is that the throughput becomes smaller, for instance. It is only a simple example that illustrates the developed framework see Figure 1. This example stresses the importance of the time horizon for evaluation of resilience or robustness of an ATM system. One decision-making chain corresponding to the framework is shown in Figure 2. The colors of arrows in Figure 2 are similar to the colors of the analogous blocks in Figure 1.

This section is based on [1]. As it is already indicated in the definitions 7 and 8, robustness and resilience of a system depend on its specified reference state. The specification of an actual reference state enables all five reactions and actions of the system on a disturbance, which are summarized in Figure 1. Hence, the system can be robust or resilient against the considered disturbance. However, if a realistic potential reference state is specified, the system cannot be robust against a disturbance, since the system is under stress at the moment of the specification see Figure 3.

The specification of a nonrealistic potential reference state influences the system so that it cannot be robust or resilient against a disturbance, because it is under stress and cannot return back to this reference state see Figure 4.

The specification of a potential reference state, realistic or not, should be considered as a disturbance factor for the system. This disturbance causes stress and the system cannot be robust against such disturbance. However, it can be resilient against a realistic potential reference state. A nonrealistic potential reference state leads either to lethal stress or to survival stress with permanent perturbation and, as a consequence, either to modification of the system or to a new reference state.

The time of deviation with respect to its reference state is the duration, whilst the state of a system accumulates its maximal difference, taken on from the moment when the system abandons this state. Time of recovery is the duration a system needs to return from the maximal deviation state to the reference state.

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