Junior Researcher in Software modelling

Innaxis is currently seeking a software-modelling researcher (entry to junior level) to join its research team in Madrid, Spain. We look for a talented and highly motivated individual who wants to pursue a research career in the field of socio-technological systems modelling and simulation. Any individual with a great dose of imagination and problem-solving skills, along with algorithmic mind and passion are encouraged to apply.

As a software modeller, you will be developing algorithms to simulate the intricacies of socio-technological systems, such as the air transportation system and future concepts of European urban mobility. You will be applying several modelling techniques from agent based modelling, to event-driven simulation and stochastic modelling. You will also work with our Data Science team for hybrid approaches, eg. data-driven simulation tools and prescriptive analytics.


Innaxis is a private independent, non-profit, research institute focused on data science and its applications; most notably in aviation, air traffic management, and mobility. As an independent entity, Innaxis decides its own research agenda and has a decade of experience in European research programmes with more than 30 successfully executed research projects.

The Innaxis team consists of an interdisciplinary group of scientists, developers, engineers and programme managers. We work together with an extensive network of external partners and collaborators in Europe, including private companies, universities, public entities and other research institutes.


The ideal candidate complies with the following set of skills:

  • University degree on Computer Science, Mathematics, Physics and/or Engineering.
  • MSc or PhD not required but positively evaluated. Similarly, professional experience is positively evaluated but is not a requirement.
  • Proficient in Python and knowledge of other modern languages.
  • Understanding of different programming paradigms, eg. functional programming.
  • Expertise with the most common algorithm strategies for problem solving, eg. recursive, divide and conquer, dynamic programming, branch and bound, backtracking, greedy and heuristic algorithms.
  • Strong background in statistics.
  • Experience or knowledge of data science, eg. knowledge discovery in databases (artificial intelligence, machine learning), data visualisation.
  • Excellent English communication skills (written and oral), as it is the working language at Innaxis.
  • Great dose of imagination, problem solving skills and passion.

Knowledge of the European air transportation system is highly desirable.


The successful candidate will be offered a position as a software-modelling researcher, including a unique set of benefits:

  • Become part of a young, dynamic, highly qualified, collaborative and heterogeneous international team.
  • Flexible working environment, schedule and location.
  • A horizontal hierarchy, small team of researchers working closely with both creativity and ownership.
  • Long-term and stable position; Innaxis has been steadily growing since its foundation ten years ago.
  • Salary adjusted to skills, experience and education.
  • The possibility to develop a unique career outside of mainstream: academics, private companies and consulting.
  • No outsourcing, all tasks will be performed at Innaxis offices.
  • Opportunity to travel in Europe following the research initiatives.
  • An agile working methodology; Innaxis recently implemented JIRA/Scrum and all the research is done on a collaborative wiki/Confluence.


IMPORTANT: Interested candidates should send their CV, along with an interest letter (around 400 words), and any other relevant information that supports their application to recruitment@innaxis.org. No applications will be considered otherwise.

If your application is accepted, you will be contacted and the interview process will start. We do not rely on a HR department and personally review and interview all candidates.


Vista tactical model – Mercury: because passengers matter

Over the next decades, EU mobility is expected to progressively evolve from the gate-to-gate focus currently prevalent in the aviation and ATM industry towards a seamless and efficient door-to-door-orientated vision.  The paradigm shift from gate-to-gate (hence aircraft centered) to door-to-door (passenger-oriented) is present at virtually all strategic research documents and agendas. The paradigm shift is here to stay. From a passenger perspective, which of the following scenarios create more impact?:

  • Scenario A): a 8 minute delay in an aircraft arrival time with no connecting passengers
  • Scenario B): a 5 minute one that prevents a significant number of passengers doing a connection in that airport and subsequently expand their door-to-door trip in more than 10 hours

How can that impact be predicted in terms of time and cost? One of the very first research exercises was the POEM project (SESAR 1- WPE) etc. This project was the original seed of Mercury. Mercury has been afterwards improved, validated and completed in other reseach initiatives for SESAR and European Commission, reaching its current door-to-door status.

What is mercury?

Mercury is a modelling and simulator tool - a framework capable of measuring the performance of the air transport network. It provides a wide range of performance and mobility metrics, capable of describing in detail different air transport scenarios.

Mercury draws on extensive data, drawn from a wide range of industry sources, including airlines, airports and air navigation service providers. Mercury's data models have been demonstrated through over 5 years of research and development, plus industry consultation.

How passenger matter in mercury?

Mercury is the first air transportation network simulator that puts passengers in the centre. Each day of simulation the itineraries of more than 3 million passengers are reproduced. Each passenger has its individual profile, ticket and decisions to make. According to EU regulation 261/2004 passengers are compensated by delay and cancellations. Extended delays, aborted journeys, overnight stays there are all part of the Mercury simulator.

Of course airlines play a major role as well, Mercury incorporates costs models for canonical airline categories. Each of the airline decision of waiting for certain passengers, cancel a flight or even board the passengers and send a ready message even when a ATFCM slot was assigned is taken according to each airline rational cost model.

The secret ingedient: a spice of randomness

There is no way one could develop a simulator like Mercury taking into account every detail in the air transportation system. Some process are just too complex or simply put we do not understand yet. Whilst others are just exogenous factors far beyond the reach of the air transportation system. 

But what if we could use a different approach. In Mercury each day of operations is repeated, introducing small variations representing everyday uncertainty and exogenous factors.

Ultimately, small changes lead to completely different day of operations, delays and cancellations. Just similarly to what happens with some chaotic systems, the sensitivity to the initial conditions allow to explore overall trends and stable status, in some cases called emergence.

Interested in reading further info about Mercury? Click here to visit the website.

Author: Samuel Cristóbal (Innaxis)

Airport Economic Value study published!

The Modelling Airport Economic Value Study recently published (link here) has been made by the University of Westminster (Andrew Cook, Gerald Gurtner, Graham Tanner and Anne Graham) and Innaxis Research Institute (Samuel Cristobal), supporting EUROCONTROL (Denis Huet and Bruno Desart) within SESAR Project 06.03.01. The study provides a better understanding of the interdependencies of various key performance indicators (KPIs) and assesses the existence and behaviour of an airport economic optimum, in a similar way to the early 2000s, when estimating the economic en-route capacity optimum.


By gathering for the first time real operational, financial and passenger-satisfaction-related data over 32 European airports, it was possible to develop and calibrate a model which produces reliable and realistic results. The fully calibrated results show the presence of a trade-off between the cost of extra capacity and the increase in the number of flights operated. As a consequence, all 32 airports exhibit a maximum in net income as a function of capacity, when the marginal cost of operating extra capacity is sufficiently low. This threshold in the marginal cost is, however, rather different across airports, and only a few airports can sustain a high cost of capacity: these are the largest and most congested airports, which clearly need extra capacity. This threshold is roughly consistent with the airports’ current operational cost of capacity, which means that they should be able to manage this growth, subject to the availability of investment.

The team has also developed a tool that provides access to all the features of the mathematical model with out having to dig into the equations. The underlying mathematical module is written in Python, while the interface is written in Matlab. The communication between the modules is transparent to the user and the software is capable of auto-calibrate the airport model using the existing or new data. The tool is flexible to explore the parameter space and different views of the output variables can be selected for a better understanding of the model outcomes. Results can be saved then in common format for further use (txt, csv, png, fig, etc.)

Screen Shot 2017-02-01 at 13.59.56 sample2122 blog_post32143


We warmly invite you to read the full report here!

Congrats to Samuel/UoW colleagues for such a superb study 😉


The Case for Mobility Modelling in Europe

INX_Mobility Modelling

There are many performance targets for the European aviation system. It is clear that performance-based frameworks are needed and utilised, especially when decision makers need to act on legislative packages or when operational managers need to make procedural changes or decisions regarding technology in aviation. This overarching model of operations proves that any costly decision must ultimately result in an increase in performance.

Different performance frameworks look into different aspects of the European aviation framework, with varying goals that are not necessarily compatible or align in the same direction. To illustrate, the FlightPath 2050 envisions an air transport system that improves safety levels but also guarantees a time-performance for the future passengers in Europe; up to four hours maximum door-to-door travel time for 90% of travellers. This number is not arbitrary, as it corresponds to the type of experience high level experts had envisioned for European passengers. However, punctuality and efficiency metrics are mostly flight centred. Passengers are rarely considered on time performance schemes and therefore very little is known about the actual door-to-door time performance from the passenger perspective. Decisions such as ‘when’ or ‘where’ to act in achieving this goal have proven to be more challenging than initially expected.

The European Commission Single European Sky Unit is working on the Reference Period 3, which delves deeper into the performance scheme for air navigation service and network functions. This performance framework is very detailed, but unfortunately does not yet include provisions for passenger time-performance. Due to the complexity of different, non-interchangeable metrics, the KPAs and goals of the different performance schemes do not necessarily match.

SESAR and CleanSky have detailed, technical performance goals. By looking into specific technology pieces or procedures, it is clear their technologies will surely improve the performance of many concrete operational elements (e.g. runway performance), however it is unclear how much those programmes will contribute to other performance frameworks. For instance, Europe may need additional funding to ensure better technology or have a different distribution of effort across the different technology research areas.

Mobility Modelling with Mercury
It is not realistic to believe a top-down Performance Framework can rule all initiatives. Each initiative has its complexities which justify executing independently, in occasions working with different groups of stakeholders or professionals. Nonetheless, a single vision for European mobility is needed.

Innaxis and the University of Westminster have been working for over 5 years on an integrated mobility model that provides a wide range of performance and mobility metrics, for use by a variety of airlines, network managers and policy makers. This integrated mobility model is called the Mercury Air Transport model (Mercury).

Mercury is capable of modelling passenger connectivities inside the European aviation system, along with a wide range of flight and passenger prioritisation scenarios. In order to cope with this monumental tasks, Mercury uses Soft Computing techniques and it runs in a cloud-based infrastructure. Mercury has been validated by airlines and captures airline decision-making and related costs by fusing a variety of data sources. Furthermore, Mercury works within the integration of different Performance Frameworks to produce the most accurate and useful metrics for each stakeholder.



Presenters needed for Agent-Based Modelling Webinar

The ¨Using Qualitative Data to Develop Rules for Agent-Based Modelling¨ webinar is to be hosted in early June. The webinar coordinators, Rachel Aldred from the University of Westminster and Melania Borit from the University of Tromsø Norway, are seeking presenters and participants.

The webinar will focus on work in progress that is using qualitative data to develop rules for ABM. The format is likely to involve short (10-20 minute) presentations as well as time for discussion, comments, and reflection.

If you are interested in offering a short presentation or joining in the discussions following the presentations, please email Rachel at r.aldred@westminster.ac.uk and Melania at melania.borit@uit.no. Please include the reasons for your interest and if you will be offering a presentation. Also please note that you will need reliable internet connection, a headset, and an updated Java program enabled on your computer to participate.

Alberto´s view on Agent-based modeling

Editor´s Note: At Innaxis we are starting a new series that involves contributions from individuals that work at Innaxis. Below is our first contribution from Alberto.

It’s nice to learn new things every once in a while. I’m not a mathematician but I am definitely intrigued by the way some things work and how they can be studied. Recently I have been investigating lately about agent-based modeling.

Agent-based modeling is a relatively new science that is being used to analyse systems that are composed of many elements. In the Cassiopeia project, these elements are the airplanes, airlines, airports, air navigation service providers, and the passengers.

The nice thing about the agent-based models (ABMs) is that we can assign some decision making attributes to each element and see what happens when we run the program. Another important aspect of ABMs is that we can design the strategy of some elements, since sometimes what’s best for a single element is not the best for the team.

To put this in context, we can look at Russell Crowe’s character ¨John Nash¨ in the movie “A Beautiful Mind.¨ In one scene, his character explains that a group strategy does not necessarily require each member to achieve best possible outcome individually (which was in their case, for no one to approach the blonde woman). Often times when studying aircraft, we need to approach problems in a similar way- figuring out the group strategy that suits everyone in a collective sense. An example of this would be the distribution of delay amongst all the aircraft rather than having a few aircraft support the entire delay. This becomes a bit challenging as it would be much more easier and convenient to have solutions be based on key individual factors (one man approaches the woman; few aircraft bear the burden of delay), however we learn and demonstrate in the Casseiopeia project that agent-based modeling is actually the best way to resolve situations. In the end more is benefited from a involving multiple elements rather than just a few.

INX presents ´Dynamical Model for the Air Transport Network´ at the 23rd European Conference on Modelling and Simulation

This international conference focuses on the state of the art technology in modelling and simulation. Many different themes are covered; ranging from Electrical and Electromechanical engineering to Modelling, Simulation and Control of Technological Processes. The conference took place June 9-12th in Madrid, Spain and was hosted by the Universidad Rey Juan Carlos.

ECMS provides a forum for researchers and practitioners from different fields involved in building innovative simulation systems, simulation and modelling tools and applications on both the research and industrial front. Keynote speakers included Rafael Martí from the Universidad de Valencia, Agustín Maravall from Banco de España, and Kishor Trivedi from Duke University.

The Innaxis publication ¨A Dynamical Model for the Air Transportation Network¨ received great reviews and the team was invited to speak about their findings. Complex Systems researcher Massimiliano Zanin gave the speech about modelling the ATM network in order to withstand and better operate with the forecasted 100% European flight growth.

Dynamical Model for the Air Transport Network

Dynamical Model for the Air Transport Network

Zanin explains how an ATM network can be modelled differently if a scheduled networks approach was used. By including the time factor, secondary nodes representing the duration of the flight is added thus including more information and giving capability of defining metrics such as efficiency, vulnerability, sensitivity to noise, and more.

Evolving the air transport network by increasing the number of nodes and connections,  the network went from a ´Random Structure´ model to a ´Hub and Spoke´ in that if the fitness is high, the network becomes more efficient with the addition of a Hub.

Evolving a network

The presentation concludes with a realistic algorithm for air network growth. A PDF of the presentation can be accessed here.

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