Modelling and Simulations for Tourism and Hospitality: An Introduction

1  Systems and Tourism Systems

Introduction

In this initial chapter, we set out the conceptual bases for the domain of modelling and simulations. Understanding how systems are structured and the relationships between their elements, and the possibility to exploit this understanding is the essence of scientific method. Study outcomes have allowed us to better realise how many phenomena have progressed and improved our abilities (even if sometimes limited) to predict future patterns. These enquiries have also allowed us to find similarities in different situations, thereby extending our ability to describe events and solve problems. Probably more than any other human activity, tourism is a complex phenomenon composed of different entities (companies, groups, individuals, etc.) and resources interacting in non-trivial ways to satisfy the needs and wishes of its users, the tourists.

Managing and governing this phenomenon and the systems that are part of it requires approaches that differ from traditional perspectives, and attempts need to be made at experimenting for possible solutions or arrangements that cannot be obtained by ‘experimenting’ in real life. Thus, the need for a set of ‘artificial’ ways to achieve these objectives has led to the building of numeric and computerised models that form the basis for simulating different settings. These, in turn, pose the necessity for a systemic holistic view, which is more suitable than traditional reductionist approaches. This perspective is rooted in the research tradition of what is today known as complexity science (Bertuglia & Vaio, 2005; Edmonds, 2000).

The main object of our studies is a system: ‘an interconnected set of elements that is coherently organized in a way that achieves something’ (Meadows, 2008: 11). This definition accurately describes the three important components – the elements, the interconnections between them and the function or purpose of a system.

In the tourism and hospitality domains, the set of interconnected actors, from travel agencies to accommodation entities, from services such as restaurants and private tours to transportation, and public actors as well as associations and the local population form a system with the objective to promote or favour tourism in a specific destination to increase the social and economic wealth of the entities involved. If we think of tourism as a system, then the behaviour of the overall system depends on how all its parts (accommodation, services, transportation, etc.) interact and exchange information, financial flow, knowledge and strategies.

Towards a Systemic View: A Short History

As will become clear in the following pages, a system is more than just the sum of its parts. Usually it is a dynamic entity that may exhibit adaptive and evolutionary behaviour. Therefore, it is important to consider a system in its entirety, to shift the attention from the parts to the whole.

In the course of its history, our civilisation has set up and refined a relatively standard way of studying a phenomenon, tackling an issue or solving a problem. However, in many cases, the standard way is modified by individual convictions and viewpoints that, even if seldom defined completely or coherently, may have wide effects. Moreover, personal philosophical and epistemological beliefs have always played a crucial role in the history of science, and in many cases have greatly influenced the development of ideas and knowledge (Baggio, 2013).

The general approach is composed of a series of phases: (i) define an objective and the object of study; (ii) decide whether the knowledge and methods are sufficient to address it; (iii) explore what and how others have produced in comparable cases; (iv) plan and collect empirical evidence; (v) derive the appropriate conclusions; and, finally, (vi) outline an action to meet the aims of the work conducted. In doing so, researchers use a vast array of specific techniques, epistemological positions and philosophical beliefs (Losee, 2001).

In this scenario, one element has historically been well supported and accepted. When facing a big problem, a large system or a convoluted phenomenon, the best line of attack is to split it into smaller parts that can be more easily managed. Once all the partial results have been obtained, they can be recomposed to find a general solution. This notion is known as reductionism. It can be summarised in the words of René Descartes (1637) who formalised the idea. In Discourse on Method (1637: part II), he states that it is necessary ‘to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution’.

Moreover, in the Regulae ad directionem ingenii (rules for the direction of the mind), Descartes (1701) clearly states in rule V that ‘Method consists entirely in the order and disposition of the objects towards which our mental vision must be directed if we would find out any truth. We shall comply with it exactly if we reduce involved and obscure propositions step by step to those that are simpler, and then starting with the intuitive apprehension of all those that are absolutely simple, attempt to ascend to the knowledge of all others by precisely similar steps’; and in rule XIII that ‘If we are to understand a problem perfectly, we must free it from any superfluous conceptions, reduce it to its simplest terms, and by process of enumeration, split it up into its smallest possible parts’.

Reductionism, however, has a much longer history. It is rooted in ideas and concepts that evolved from the pre-Socratic attempts to find the universal principles that would explain nature and the quest for the ultimate constituents of matter. The whole Western tradition then elaborated on these concepts that were admirably distilled in the 16th and 17th centuries. Copernicus, Galileo, Descartes, Bacon and Kepler came to a rigorous formulation of the method needed to give a truthful meaning to science. This work was very effectively refined by Isaac Newton (1687) in his Philosophiae Naturalis Principia Mathematica. The book was so successful and so widely distributed that scholars of all disciplines started to apply the same ideas to their own field of study, especially in those domains that did not have a strong empirical tradition such as the study of human societies and actions.

The reasons for this wide influence were, essentially, the coherence and apparent completeness of the Newtonian proposal coupled with its agreement with intuition and common sense. In the following years, many scientists tried to extend this perspective to other environments. Scholars such as Thomas Hobbes, David Hume, Adolphe Quetelet and Auguste Comte worked with the objective to explain aggregate human behaviour using analogies from the world of physics, and employing its laws. Vilfredo Pareto and Adam Smith, for example, presented and agreed on a ‘utilitarian’ view of the social world, which suggests that the use-value of any good can be fully reflected in its exchange-value (price). With these bases, they tried to adapt the mechanical paradigm to the field of economics. The idea of defining universal laws, setting mathematical analytic expressions and formulating gravity models or terms such as equilibrium is directly derived from the Principia.

The universality of Newton’s proposals, however, was questioned when the scientific community began to realise that going beyond simple individual objects created a number of additional variables due to mutual interactions, so that solutions to even simple-looking problems could not be easily obtained unless the ‘finer details’ in the mathematical formulation were disregarded and descriptions limited to a simplified and linearised description.

For example, the gravitational theory was accurate in dealing with simple sets of objects, but failed when applied to more numerous assemblies. The motion of planets in the solar system was initially well described, but some deviations, such as the curious perturbations observed in Mercury’s orbit, could not find a proper place in the model. Deeper investigations showed that an increase in the number of bodies in a gravitational system, made the motion of the different elements almost unpredictable. Poincaré (1884) eventually realised that even a small three-body system can produce complicated outcomes and that the equations describing it become extremely difficult to determine and practically unsolvable. The stability conditions for equilibrium in the motion of a system were later studied and characterised by Lyapunov (1892). He provided the first evidence of the fact that, in some cases, even minor changes in initial conditions, described by deterministic relationships, can result in widely differing system evolutionary trajectories. This is what we term dynamical instability or sensitivity to initial conditions, and today we identify as chaos.

The issue of dealing with a system composed of many elements gained attention in the first half of the 19th century. The practical issue of increasing the efficiency of the newly developed steam engine led several scientists to leave the path drawn by Newton and approach the matter from a different point of view. The problem was to study the behaviour of a gas in which a very large number of particles interact (1 L of air contains about 3·10²² molecules). Explicitly writing numerous equations and solving the problem was impossible. Thus, statistical techniques were thought to be the only possible way to tackle the problem. Nicolas Sadi Carnot, James Joule, Rudolf Clausius and William Thomson (Lord Kelvin) created the new discipline, thermodynamics, based on these ideas.

Their results were successful and, elaborating on them at the end of the 19th century, James Clerk Maxwell, Ludwig Boltzmann and Josiah Willard Gibbs structured the matter into what is known today as statistical mechanics (or statistical physics). The central idea is that the knowledge of an incomplete set of measurements of some system’s properties can be used to find the probability distributions for other properties of the system. For example, knowing the number of molecules in a gas in a certain volume and its temperature at thermal equilibrium (i.e. when no spatial or temporal variations in temperature exist), it is possible to calculate the pressure, the specific heat and other quantities.

Statistical physics is a very rigorous formal framework for studying the properties of many-body systems (i.e. composed of many interacting particles), where macroscopic properties are statistically derived from extensive (dependent on the size or the amount of material) and intensive (independent of the amount of material) quantities, and their microscopic properties can be described in terms of probability distributions. Furthermore, it is possible to have a better understanding of the conditions in which critical modifications of a system or sudden changes to its state (phase transitions) occur. This understanding of phase transitions and critical phenomena led to the development of two important new concepts: universality and scaling (Amaral & Ottino, 2004).

When studying critical phenomena, or critical conditions in a system’s evolution, a set of relations, called scaling laws, may be determined to help relate the various critical-point features by portraying the behaviour of some system parameters and of the response functions. The predictions of a scaling hypothesis are supported by a wide range of experimental work, and by numerous calculations on model systems (Kadanoff, 1990).

The concept of universality has the basic objective of capturing the essence of different systems and classifying them into distinct classes. The universality of critical behaviour drives explorations to consider the features of microscopic relationships as important in determining critical-point exponents and scaling functions. Statistical approaches can thus be very effective in systems when the number of degrees of freedom (and elements described by several variables) is so large that an exact solution is neither practical nor possible. Even in cases where it is possible to use analytical approximations, most current research utilises the processing power of modern computers to simulate numerical solutions. Here, too, experimental work and numerical simulations have thoroughly supported the idea (Stanley, 1999).

The main result and the power of this approach are in recognition that many systems exhibit universal properties that are independent of the specific form of their constituents. This suggests the hypothesis that certain universal laws may apply to many different types of systems, be they social, economic, natural or artificial. For example, biotic environments can be well described in terms of their food webs. Analyses of a wide number of such systems, examined in terms of their networks composed of different species and their predation relationships, show remarkable similarities in the shapes (topologies) of these networks (Garlaschelli et al., 2003). This happens independently because of apparently significant differences in factors such as size, hierarchical organisation, specific environments and history. The universality and scaling hypotheses thus seem valid in this field and might open the way to reconsidering the possibility of establishing some general treatment for the problems in environmental engineering.

In other words, these assumptions give us the basis to justify an extensive use of analogy, so that an inference can be drawn based on a similarity in certain characteristics of different systems, typically their structural configuration (topology). That is to say, if a system or a process A is known to have certain traits, and if a system or process B is known to have at least some of those traits, an inference is drawn that B also has the others. Often, mathematical models can be built and numerical simulations run to transfer information from one particular system to another particular system (Daniel, 1955; Gentner, 2002).

Complex Adaptive Systems

A systemic view is focused on considering a configuration of elements joined together by a web of relationships, sensitive to external forces that may modify its structure or behaviour. In this approach, we leave the traditional idea of cause and effect, directly connected with that of predictability, and use statistical methods for creating possible scenarios and assign them a probability to happen. This is the idea of complex adaptive systems (CAS).

The natural language concept of complexity has several meanings, usually associated with the size and number of components in a system. There is still no universally accepted definition nor a rigorous theoretical formalisation of complexity; however, intuitively, we may characterise a complex system as ‘a system for which it is difficult, if not impossible to reduce the number of parameters or characterizing variables without losing its essential global functional properties’ (Pavard & Dugdale, 2000: 40).

Basically, we consider that a system is complex if its parts interact in a non-linear manner. Rarely are there simple cause-and-effect relationships between elements, and a small spur may cause a large effect or no effect at all. The non-linearity of interactions generates a series of specific properties that characterise the complexity of a system’s behaviour.

Broadly speaking, systems can be categorised into simple, complicated and complex systems. The most important difference between these categories is that simple and complicated systems are predictable and results are repeatable: that is, if a specific strategy, assemblage, policy, etc., initially worked, it will always work for the same system thereafter. Complex systems, on the other hand, are neither fully predictable nor fully repeatable. Further, simple and complicated systems can be understood by assessing how each part that composes the system works and by analysing the details. However, when dealing with complex systems, we can only achieve a partial understanding of the system, and only by looking at the behaviour of the system in its entirety. That is, we would not be able to understand the interactions and outcomes of a tourism destination by reducing it to specific entities and analysing them, but only by observing or analysing how the overall system behaves. Even then, we would only achieve a partial understanding of the overall system.

Complicated systems are systems in which there are clear and defined cause–effect relationships, but a system may have many components and, as such, there may be multiple ways to achieve a solution to a problem. However, there is only one correct solution. In other words, complicated systems are the sum of multiple simple systems, and thus we can understand and achieve a solution by decomposing the system into multiple simple systems, solving problems that have only one solution and then putting the simple system back together. This shows the importance of coordinating how different parts should be assembled, implying a further step than just putting simple systems back together. In a complex system, multiple possibilities exist that have many interacting parts, are dynamic and adapt themselves to interacting with local conditions, often producing new (emergent) structures and behaviours. As Stacey (1996: 10) states, in a complex adaptive system – the term used to denote this type of system – the parts ‘interact with each other according to sets of rules that require them to examine and respond to each other’s behaviour in order to improve their behaviour and thus the behaviour of the system they comprise’. A schematic view of the main differences between simple, complicated and complex systems is shown in Table 1.1.

Table 1.1 Characteristics of simple, complicated and complex systems

Complex systems are difficult to define and there is no consensus on a possible formal characterisation. However, scholars and practitioners in the field have provided a long list of complex systems characteristics, apart from size considerations. The most relevant are (Bar-Yam, 1997; Waldrop, 1992):

Distributed nature: Properties and functions cannot be precisely located and there may be redundancies and overlaps.

Non-determinism: No precise anticipation of behaviour is possible, even knowing the functional relationships between elements. The dependence of the system’s behaviour from the initial conditions is extremely sensitive, and the only predictions that can be made are probabilistic.

Presence of feedback cycles (positive or negative): Relationships among elements become more important than their own specific characteristics and reinforcing or balancing actions can influence the overall behaviour of the system.

Emergence and self-organisation: Several properties are not directly accessible (identifiable or predictable) from knowledge of the components. Global or local structures may emerge when certain parameters (a system’s characteristics) pass a critical threshold. The system is capable of absorbing the shock and remaining in a given state, regaining its original state or adapting to new conditions unpredictably fast (system is resilient). From an empirical point of view, it is virtually impossible to determine why a system prefers one specific configuration over possible alternatives, or the type of perturbations that may disrupt or be absorbed.

Self-similarity: The system considered will look like itself on a different scale, if magnified or made smaller in a suitable way. The self-similarity is evidence of the possible internal complex dynamics of a system.

Limited decomposability: The properties of a dynamic structure cannot be studied