Purpose The use of the 4D trajectory operational concept in the future air traffic management (ATM) system will require the aircraft to meet very accurately an arrival time over a designated checkpoint. To do this, time intervals known as time windows (TW) are defined. The purpose of this paper is to develop a methodology to characterise these TWs and to manage the uncertainty associated with the evolution of 4D trajectories. Design/methodology/approach 4D trajectories are modelled using a point mass model and EUROCONTROL’s BADA methodology. The authors stochastically evaluate the variability of the parameters that influence 4D trajectories using Monte Carlo simulation. This enables the authors to delimit TWs for several checkpoints. Finally, the authors set out a causal model, based on a Bayesian network approach, to evaluate the impact of variations in fundamental parameters at the chosen checkpoints. Findings The initial results show that the proposed TW model limits the deviation in time to less than 27 s at the checkpoints of an en-route segment (300 NM). Practical implications The objective of new trajectory-based operations is to efficiently and strategically manage the expected increase in air traffic volumes and to apply tactical interventions as a last resort only. We need new tools to support 4D trajectory management functions such as strategic and collaborative planning. The authors propose a novel approach for to ensure aircraft punctuality. Originality/value The main contribution of the paper is the development of a model to deal with uncertainty and to increase predictability in 4D trajectories, which are key elements of the future airspace operational environment.

A 39-year-old Caucasian man was referred to University Hospital Salamanca from a primary care unit due to the presence of an erythematous violaceous nodule at the superior portion of his nose. Physical examination indicated that the firm, fixed erythematous violaceous nodule measured approximately 2 cm in diameter and was located inferior to a scar on the nasal bridge. Cutaneous involvement in sarcoidosis occurs in 25% of cases. A wide range of clinical presentations of cutaneous sarcoidosis is recognized. Skin lesions are classified as either non-specific, of which erythema nodosum is the most representative and specific, or as granulomatous, which includes maculopapular nodules, plaques, infiltrated scars, lupus pernio, ulcerations, warty lesions and erythroderma. Scar sarcoidosis is a type of cutaneous sarcoidosis.