- Email: [email protected]
stability paradox: A European perspective
Journal of Air Transport Management 16 (2010) 81–85
Contents lists available at ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Capacity dynamics and the formulation of the airport capacity/stability paradox: A European perspective Bruno Desart a, *, David Gillingwater a, Milan Janic b a b
Transport Studies Group, Civil & Building Engineering, Loughborough University, LE11 3TU, United Kingdom OTB Research Institute, Delft University of Technology, the Netherlands
a b s t r a c t Keywords: Unpredictability Capacity degradation Capacity dynamics Capacity stability Airport planning Capacity management
Access to capacity is often considered to be uncertain, causing airlines to build buffer times into their flight schedules in anticipation of potential delays. Similarly, air navigation service providers use capacity buffers to overcome potential safety standard violations. However, the use of excessive buffers is detrimental to cost efficiency in the air transport system. This paper improves our understanding of capacity predictability. The concepts of capacity dynamics and stability are taken as integral parts of an airport’s plan to mitigate the risk of capacity degradation. Based on the concepts of capacity dynamics and stability, the capacity/stability paradox is introduced and discussed. 2009 Elsevier Ltd. All rights reserved.
1. Introduction If air traffic doubles by 2020, many European airports will struggle to accommodate demand, with an estimated 60 airports congested and the top 20 airports saturated 8–10 h a day (Eurocontrol, 2004). In April 2004, the European Commission (EC) initiated the Single European Sky (SES) performance-based framework, with the intention of changing the future structure of air traffic control across Europe. The ultimate objective is to replace step-by-step the air traffic management (ATM) working arrangements, which are largely based on national boundaries, by a more efficient ATM system based on flight patterns. In support of SES, the EC also initiated the SES Air Traffic Management Research and Modernisation Programme (SESAR), an ambitious attempt to response to the ATM challenge. It has the objectives of enabling a three-fold increase in capacity; improving safety by a factor of ten; facilitating a 10% reduction in the environmental impacts of aviation; and providing ATM services at a cost which is at least 50% less than now (SESAR, 2006), which according to Eurocontrol (2005a) is currently V800 per flight gate-to-gate. The target for capacity enhancement is that the European ATM System (EATMS) can accommodate a 73% increase in traffic by 2020, based on a 2005 baseline, whilst meeting the targets for safety and quality of service. Many factors cause increases in air traffic congestion and delays. According to Caves and Gosling (1999), the most important
* Corresponding author. E-mail address: [email protected] (B. Desart). 0969-6997/$ – see front matter 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2009.10.006
contributing factors are growing demand, lack of sufficient system capacity, hub-and-spoke networks, and environmental constraints. What is more, airports in particular and the air transport system in general are subject to fluctuations in demand and capacity. According to Janic (2000), the capacity of any airport component can be expressed by four different measures that represent capacity attributes: the physical infrastructure, fluctuations of demand over time, profiles of user entities, and the quality of service provision. Because of the airport coordination process (European Commission, 2004), including slot scheduling, and air traffic flow management (ATFM), actual delays normally do not originate from lack of declared capacity. Airports have to declare capacity six months in advance and, for those ‘scheduled’ airports, the surplus traffic in saturated periods is transferred through slot negotiation to less busy periods. However, for a given flight schedule, based on declared capacity, any capacity fluctuation that is uncontrolled, unmanaged, or unpredicted, results in delay. Delay therefore originates from sudden and unpredicted capacity changes or, more precisely, from either inaccurate planning or lack of capacity stability. Poor weather conditions and industrial actions in Europe are shown to be the most important factors that disrupt airline and airport schedules, generating congestion, delays, diversions and cancellations of flights (Janic, 2003). Meteorological conditions are, without doubt, the more dynamic and certainly the most unpredictable factor (Krollova, 2004). According to Eurocontrol (2005a), around 40% of airport ATFM delays and 10% of en-route delays are due to weather, often made worse by ineffective and reactionbased planning when such conditions occur. Based on a Eurocontrol (2005a) performance review, the lack of gate-to-gate transit time predictability also incurs major annual
82
B. Desart et al. / Journal of Air Transport Management 16 (2010) 81–85
resource costs for operators. To mitigate unpredictability and satisfy customers, airlines often build in buffer times to their flight schedules. By doing so, flights may suffer a short delay and yet be on time. However, the use of buffers is detrimental to ATM costeffectiveness (Cook, 2007). For instance, it is estimated that a minute of buffer time for an Airbus A320 is worth V49 per flight. By cutting 5 min off 50% of schedules, some V1 billion per annum could be saved and better used by operators. It is also a common practice by air navigation service providers (ANSP’s) to overcome potential safety standards violations through capacity buffers that enable controllers to reduce additional workload and stress caused by sudden and unpredicted capacity shortage. Better knowledge of capacity fluctuations and mitigation of degradation could save the industry substantial costs. Predictability could be improved through better collaborative decision-making, system-wide information management (SWIM), better management of reaction to bad weather conditions and better control of take-off times. It is clear that the research community needs to pursue innovative approaches to modelling unpredictability in air transport operations to a greater extent and seek more cost effective approaches for operators.
of capacity change, by estimating how quickly a change can occur at any specific point for use in goal-seeking optimisation. If F={ f1,., fn} represents the vector variable, a set of all the factors fi that impact on capacity g in varying degrees, then airport capacity is defined by a complex relationship g ¼ qðf1 ; .; fn Þ between all the factors fi that affect it. Capacity can also be defined as a dynamic system characterised by a given state. The capacity ! state is the vector variable S ¼ ðv1 ; .; vi ; .; vn Þ determined by the collection of values ni assigned to each factor fi in such a way that, ! g ¼ qðv1 ; .; vi ; .; vn Þ ¼ qð S Þ. Capacity can therefore be defined as a function of the n-dimensional capacity state, and the complex relationship that links each factor can be represented in a very general way by,
!
q : Rþ . Rþ /Rþ 0 : g ¼ qð S Þ
(1)
The capacity dynamics with respect to the various factors fi is defined as the gradient of capacity g with respect to these factors fi. ! ! This capacity dynamics is noted dðqðf1 ; .; fi ; .; fn ÞÞ, dðgÞ or dg , and is formulated as,
!
dg ¼ gradðqÞ ¼ Vf1 ;.;fn qðf1 ; .; fn Þ; cfi ˛F
2. Definition and interpretation of directional capacity dynamics Most analysis has focused on static performance indicators and a deterministic approach to capacity assessment. However, little has been done to address the specific problem of capacity dynamics and planning for extraordinary capacity fluctuations. This often leads to the conclusion that the only way to mitigate airport delays is through capacity enhancement. However, this is by no means the only approach to deal with the problem. The capacity of a system, airport capacity in particular, is subject to time and space changes. Some factors affecting runway capacity remain relatively static, in particular the number, configuration and inter-dependency of runways and the type of radio-navigational facilities. However, runway system capacity has often been shown to be unstable due to the dynamics and instability of many factors (Stamatopoulos et al., 2003) such as volume and time-dependent pattern of traffic demand, mix of inbound and outbound traffic flows, aircraft fleet mix pattern and meteorological conditions. Although it is recognised that the lack of robustness of capacity assessment is heavily dependent on fluctuations of various factors, the marginal impact of those factors has rarely been analysed. Many factors affecting capacity are interdependent and influence each other. The rate of change of capacity is, therefore, not necessarily proportional to the rate of change of some specific factors, considered on an individual and isolated basis: one factor might be significantly improved and another slightly reduced yet the result is enhanced capacity. For instance, a reduction in runway occupancy time has little impact on capacity in some conditions of in-trail spacing minima. Similarly an increase in approach speed has little impact: although higher approach speed contributes to lower intrail spacing minima, usually entailing higher runway occupancy time blocking out the potential benefit of lower in-trail time. Capacity change can be analysed through a ‘bottom-up’ approach based on an a priori understanding of the system to be modelled. Seeking capacity optimisation by looking for sensitivity or ‘what-if’ scenario analyses cannot with certainty obtain the solution to represent a global optimum. Hence, the capacity dynamics concept aims at addressing and proposing a possible solution using such a ‘bottom-up’ approach, contributing to an a priori understanding of the system to be modelled. The purpose of the capacity dynamics concept is to quantify the instantaneous rate
(2)
Whilst using the Leibniz notation, capacity dynamics can also be expressed as a column vector whose components are the partial derivatives of the capacity influencing factors fi, as,
0 !
vg B vf1
1
dg ¼ @ « C A
(3)
vg vfn
If capacity is expressed with respect to its possible states (Eq. (1)), then capacity dynamics is the gradient of capacity with respect to those states, and provides the direction to the most promising capacity state, i.e. the capacity optimum:
!
!
! !
dg ¼ gradðqÞ ¼ VS qð S Þ
(4)
The capacity dynamics vector shows the direction in which capacity changes most quickly. At any point, it describes the measure of the capacity slope: steepness, fall or incline. Some measure of the magnitude of this capacity change can be represented by a scalar. Let the 2-norm represent this measure. The 2-norm of a vector ! v ¼ ðv1 ; .; vi ; .; vn Þ corresponds to the rffiffiffiffiffiffiffiffiffiffi P 2ffi vi . In particular, the Euclidean length and is defined as k! vk ¼ 2 i
magnitude dg of the capacity change represented by the capacity ! dynamics vector dg is defined as,
! dg ¼ dg
(5)
The capacity dynamics gradient also indicates how capacity changes in directions other than the direction of the largest change. It provides the airport planner with a quantification of the inclination of the field of capacity change potential at any point along a given trajectory of change, i.e. the magnitude of capacity dynamics indicates to airport planners and decision-makers how fast capacity changes in a given planning direction. Indeed, given the surface representing the field of capacity change potential, and given a unit vector on that surface, the inclination or grade of the surface in a particular direction is the dot product of the capacity dynamics with that vector. By analogy, consider a walker who attempts to reach the top of a hill, but who does not set off to climb a mountain. The gradient, at the point where the walker stands, points at the direction of the steepest slope. For instance,
B. Desart et al. / Journal of Air Transport Management 16 (2010) 81–85
assume the magnitude of the gradient is 30 in the uphill direction, i.e. relatively hard to climb. Rather than using the 30 slope road which goes directly uphill, the walker takes a path under an angle of 60 with the uphill direction when projected onto the horizontal plane. Then, the slope of the road followed by the walker is reduced to 15 , which is 30 times the cosine of 60 . In summary, the magnitude of capacity dynamics dotted with a unit vector gives the slope of the capacity change potential in the direction of that vector. In such a way, the directional derivative of capacity leads to what we term directional capacity dynamics. A further possible use of the directional capacity dynamics concept is the smooth implementation of capacity enhancement, through its ability to show other directions rather than the direction of largest change. Based on Eq. (4), directional capacity dynamics enables the identification of intermediate capacity states to be considered for smooth implementation of capacity enhancement action plans. 3. Definition and interpretation of capacity stability Predictability of capacity degradation can be a key measure of the intrinsic quality of planning. Capacity fluctuation has a major impact on the accuracy of slot allocation and slot scheduling. To ensure planning accuracy of any economic system, there is a need to measure the robustness of its capacity. A useful question then becomes, ‘‘How robust is airport capacity, given all the various factors that may affect it due to their fluctuations?’’ The more capacity fluctuates, the less accurate airport planning will be, unless the risks associated with fluctuation can be rigorously quantified and controlled with appropriate mitigation plans (Desart et al., 2002). In general, stability measures how robust a system is with respect to external forces and how resistant it is to potential change in the variables of interest. The stability concept, also called constancy or persistence in other fields, provides a measure of the system’s response to some perturbation. Stability is often related to both resistance, that is a measure of how little a given variable of interest changes in response to stress or external pressures, and inertia that represents a change at some rate that is relatively constant in response to external fluctuation. Stability can therefore be understood as the resistance to capacity degradation, driven by a hostile perturbation of its affecting factors. A skyscraper with ball-and-socket joint foundations is robust because it can resist earthquakes. Similarly, capacity is intuitively robust if it can resist the fluctuation of its affecting factors. If so, capacity can be considered as being stable. With capacity dynamics, it is possible to measure how robust capacity is, against potential disruptions. The capacity stability mg with respect to a set F ¼ ff1 ; .; fi ; .; fn g of capacity disrupters, noted mg ðf1 ; .; fi ; .; fn Þ, is a performance indicator that can be formulated as the inverse of the magnitude of capacity dynamics with respect to a set of influencing factors,
83
order to keep this formulation as clear as possible, assumptions of traffic demand constancy and fleet homogeneity need to be made. First, the characteristics of local air traffic demand for airport access and service constitutes, after weather conditions, the most dynamic factor influencing airport capacity. The capacity dynamics with respect to traffic pattern is intrinsically dependent on the time horizon during which this factor can remain in a relatively stable state. The shorter the time horizon, the more dynamic the traffic pattern seems to be, especially when those shorter periods are related to peaks; hence, making capacity planning more difficult. Traffic demand is especially dynamic at airports accommodating charter flights or low-cost carriers. Airports accommodating high level of scheduled traffic are less subject to traffic pattern fluctuation, especially if subject to International Air Transport Association slot scheduling meetings. In order to stabilise operations, minimise delay and optimise air traffic and capacity management, those airports are co-ordinated or schedule-facilitated (European Commission, 2004). Based on these considerations, the traffic demand constancy assumption is based on the fact that traffic demand and, therefore, accommodated traffic are statistically representative over a relatively long period of time. Consequently, the average inbound and outbound fleet mixes are relatively constant. Second, fleet homogeneity is assumed, that is all aircraft types form a single class, characterised by an average performance, weighted by a fleet mix representation. Based on these two assumptions, capacity g can be formulated as the reciprocal of the arithmetic mean of the time intervals s between successive movements,
.
þ gðsÞ : Rþ 0 /R0 : s/gðsÞ ¼ 1 s
½movements per unit of time
ð7Þ
The primary formulation reported in Eq. (7) is sufficiently generic for it to be applied to both arrival and departure capacity. In this relationship, capacity approaches infinite values when spacing between successive events (movements) tend toward infinitesimal numbers, whilst capacity tends to zero for large values of spacing. The function has, therefore, two asymptotes: a vertical one that is expressed by lim gðsÞ ¼ N, and a second one that is horizontal and s/0
defined by lim gðsÞ ¼ 0, as represented in Fig. 1. The capacity s/N
function is a rectangular hyperbola. Capacity is expressed in terms of number of movements (arrivals, departures or mix of both) per unit of time (usually per hour). Capacity dynamics is based on differentiation of the capacity function. Based on Eqs. (3) and (7), the capacity dynamics dg with respect to spacing s results in
g 1 dg :Rþ 0 /R0 : s/dg ¼ s2 ¼ s ½capacity unit per unit of time
ð8Þ
1 1 ¼ ! jdg ðf1 ; .; fi ; .; fn Þj kdg ðf1 ; .; fi ; .; fn Þk (6)
The image of the first-order differentiation of capacity is the set of negative and non null real numbers, noted R 0 . As represented in Fig. 1, the capacity dynamics dg with respect to spacing s also includes two asymptotes: a vertical one expressed by
Hence, capacity stability measures the inertia of capacity to change, i.e. its robustness regarding changes. The more stable the capacity, the less its responsiveness to disruption.
gs lim d ð Þ ¼ N, and a second that is horizontal and defined as s/0 ds gs lim d ð Þ ¼ 0. As with capacity, capacity dynamics is theoretically s/N ds
mg ðf1 ; .; fi ; .; fn Þ ¼
4. Primary formulation of capacity dynamics and stability To be useful to airport planners and modellers, the concepts of capacity dynamics and stability needs to be further formulated. In
a rectangular hyperbola, but negative. This second horizontal asymptote is however theoretical only; in practice, the minimum level of capacity dynamics depends upon the relative accuracy of the capacity influencing factors. Roughly speaking, it cannot be expected that the output of a system will be more precise than the
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B. Desart et al. / Journal of Air Transport Management 16 (2010) 81–85
Fig. 1. The capacity dynamics and stability functions.
accuracy of its inputs, and its dynamics to be smaller than the natural fluctuation of the factors influencing that system. A recent study on the average distance-based separation and landing capacity shows that 144 s in-trail spacing is, on average, a representative separation for 6 NM (Eurocontrol, 2005b); this corresponds to an average speed of 150 Kts, which is a common operational value for instrument-based final approaches in Europe. Referring to Eq. (7) and (8), 144 s in-trail spacing results in 25 arrivals/h and any marginal change (increase or decrease) of intrail spacing by 1 s leads to a capacity fluctuation of 0.17 arrivals/ h/s. This is illustrated in the zoom view of Fig. 1 by the two points (143:25.17) and (145:24.83). Based on Eqs. (6) and (7), the capacity stability mg with respect to spacing s is synthesised as, þ 2 mg :Rþ 0 /R0 : s/mg ¼ s ¼
s g
½unit of time per capacity unit
ð9Þ
Capacity stability being the positive inverse of capacity dynamics can be expressed in terms of unit of time per capacity unit: arrival capacity stability at 144 s in-trail spacing is 5.76 s per arrivals/h whilst it decreases to 1.44 s per arrivals/h, for 72 s in-trail spacing, as represented in Fig. 1.
5. The capacity/stability paradox The purpose of operating an economic system, whatever it may be (e.g. an airport, telecommunications, productive industry, etc), is to maximise outputs over inputs. To do this, it needs to be operated at optimal capacity. On one hand, systems may be under-operated and slack capacity is created, enabling good quality of service and few delays. However, this is inefficient in terms of profitability. On the other hand, economic systems may be saturated causing delays with associated service quality problems and costs. As a result, any economic system needs to be operated with an acceptable level of delay to maximise profits (Janic, 2000, 2003). This requires finding the optimum trade-off between throughput and quality of service. To determine this, capacity stability is a key component: pulling the capacity ‘rope’ almost to breaking point. The art of capacity planning resides to some extent in the identification of this breaking point. As illustrated in the zoom view of Fig. 1, any marginal change of in-trail spacing by 1 s in the vicinity of 144 s leads to an arrival capacity fluctuation of 0.17 arrivals per h. As confirmed by Eurocontrol (2005b), a decrease of distance-based separation from 6 to 3 NM leads to a decrease of in-trail spacing to 72 s, resulting in an increase of capacity to 50 arrivals per h. However, the same 1 s marginal change around 72 s in-trail spacing results in a capacity
B. Desart et al. / Journal of Air Transport Management 16 (2010) 81–85
fluctuation of 0.69 arrivals/h, that is to say that the impact is four times more significant than around 144 s in-trail spacing. Paradoxically, reducing in-trail spacing from 6 NM to 3 NM enables capacity to be doubled, but also entails capacity to be four times more sensitive to the same marginal fluctuation of in-trail spacing, and consequently four times less stable (see Eq. (8) and Fig. 1). Indeed, arrival capacity stability at 144 s in-trail spacing is 5.76 s per arrivals/hr whilst it decreases to 1.44 s per arrivals/hr for 72 s in-trail spacing. Vice-versa, doubling spacing divides capacity by a factor of two, but leads to a magnitude of potential change of capacity divided by four, and to a capacity four times more robust. This is what we term the capacity/stability paradox. Put simply, this states that the higher an airport is performing from a capacity perspective, the more sensitive is its capacity to potential fluctuation of some of its disrupters, and therefore the less stable it becomes. In other words, from a capacity perspective, an airport becomes less stable the higher its level of performance. Two important implications arise as a result of this paradox. First, the problem of airport capacity allocation lies in the ability to select the appropriate capacity value from the given arrival/ departure ratio ranges to best satisfy traffic demand, bearing in mind the possible dynamic variation of this demand. The objective therefore consists of maximising the use of available capacity to be allocated to traffic demand subject to allocation criteria, in order to achieve specified objectives like, for instance, minimisation of queues, delays and associated costs (Janic, 2004). In a similar way, Gilbo (1993) describes the capacity allocation problem as the evaluation of decision variables, airport capacities, in accordance with predefined optimisation criteria. Gilbo identified two types of criteria to determine the operational effectiveness of traffic accommodation over a given time period: first, the number of flights in the queue; and, second, the delay time of the accommodated traffic (i.e. waiting time in the arrival, stack, and departure queues). These two criteria are strongly correlated: the larger the queues, the longer the delays. An optimal solution that minimises the flights in the queue is also expected to provide favourable conditions to minimise delays. However, the choice of the appropriate optimisation criterion mainly depends on the type of input data available and the relative complexity of calculating the solutions. Setting criteria for the size of the queues may be preferred at the strategic airport planning level, when aggregated data are available (e.g. demand per 15 min or one-hour time intervals). In contrast, delay time may be preferred for tactical planning purposes, when flight-by-flight data are available. Based on an acceptable level of stability defined by appropriate risk analysis, the capacity/stability paradox definitely constitutes one valid criterion to be considered in the scope of capacity allocation. Second, with the same airport planning methodology, planning is more robust if it is related to a low-performing system than to a high-performing system, because the latter is subject to less stability. This constitutes a paradox because the more a system is used close to saturation, the better it should perform and, consequently, the more accurate planning is needed. The capacity/ stability paradox, therefore, raises serious questions about the constant capacity maximisation and questions the ultimate goal of
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capacity enhancement with respect to stability. Capacity stability should be part of risk quantification of airport planning. 6. Conclusions This paper has examined capacity dynamics and stability as one approach to planning for capacity fluctuation and degradation. Experience shows that unpredictability of capacity degradation challenges both airport planners’ and modellers’ intuition. The capacity dynamics concept provides an indication of how quickly capacity can change in response to fluctuations brought about by one or more influencing factors, whilst capacity stability provides airport planners with a measure of capacity robustness. Both concepts enable the rigorous quantification of the degradation impact. In contrast to conventional approaches based on trial-anderror, these two concepts contribute to a better a priori understanding of the airport system because of enhanced quantification of the impact and sensitivity assessment of factors affecting it. These two concepts have unravelled a capacity/stability paradox: the better an airport is performing from a capacity perspective, the more sensitive is its capacity to potential fluctuation in some influencing factors; consequently the less stable it becomes, the more likely it is to experience increasing delays. In brief, by highlighting potential risks of capacity degradation that could not have been identified otherwise, the capacity dynamics and stability concepts offer a new dimension to airport planning. References Caves, R.E., Gosling, G.D., 1999. Strategic Airport Planning. Pergamon, Elsevier Science, Amsterdam. Cook, A., 2007. The Management and Costs of Delay. In: Cook, A. (Ed.), European Air Traffic Management. Ashgate, Aldershot. Desart, B., Caves, R.E., Gillingwater, D., Hirst, M., 2002. Robustness of slot allocation for multiple runway-use configurations: a formulation of the capacity instability problem. Proceedings of the ATRS Conference. Seattle. Eurocontrol, 2004. Challenges to Growth 2004 Report. European Organisation for the Safety of Air Navigation, Brussels. Eurocontrol, 2005a. Performance Review Report 2005. European Organisation for the Safety of Air Navigation, Brussels. Eurocontrol, 2005b. European Wake Vortex Mitigation Benefits Study; High-level Benefits Analysis and Systemic Analysis, WP3 Deliverable. European Organisation for the Safety of Air Navigation, Brussels. European Commission, 2004. European council regulation 793/04 on common rules for the allocation of slots at community airports, Brussels: Official Journal of the European Union, Luxembourg. Gilbo, E.P., 1993. Airport capacity: representation, estimation, optimization. IEEE Transactions on Control Systems Technology 1, 144–154. Janic, M., 2000. Air Transport System: Analysis and Modelling. Gordon & Breach, Amsterdam. Janic, M., 2003. A model for assessment of the economic consequences of large scale disruptions of an airline network. Proceedings of the 82nd TRB Annual Conference. Washington DC. Janic, M., 2004. Air traffic flow management: a model for tactical allocation of airport capacity. Proceedings of the ATRS Conference. Istanbul. Krollova, S., 2004. Dynamic climatological processing of flight weather hazards data at airports. Proceedings of the 1st International Conference on Research in Air Transportation (ICRAT 2004). Zilina. SESAR, 2006. Air Transport Framework – The Performance Target, SESAR Definition Phase Deliverable 2, DLM-0607-001-02-00. SESAR Consortium, Brussels. Stamatopoulos, M.A., Zografos, K.G., Odoni, A.R., 2003. A decision support system for airport strategic planning. Transportation Research C 12, 91–117.
Contents lists available at ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Capacity dynamics and the formulation of the airport capacity/stability paradox: A European perspective Bruno Desart a, *, David Gillingwater a, Milan Janic b a b
Transport Studies Group, Civil & Building Engineering, Loughborough University, LE11 3TU, United Kingdom OTB Research Institute, Delft University of Technology, the Netherlands
a b s t r a c t Keywords: Unpredictability Capacity degradation Capacity dynamics Capacity stability Airport planning Capacity management
Access to capacity is often considered to be uncertain, causing airlines to build buffer times into their flight schedules in anticipation of potential delays. Similarly, air navigation service providers use capacity buffers to overcome potential safety standard violations. However, the use of excessive buffers is detrimental to cost efficiency in the air transport system. This paper improves our understanding of capacity predictability. The concepts of capacity dynamics and stability are taken as integral parts of an airport’s plan to mitigate the risk of capacity degradation. Based on the concepts of capacity dynamics and stability, the capacity/stability paradox is introduced and discussed. 2009 Elsevier Ltd. All rights reserved.
1. Introduction If air traffic doubles by 2020, many European airports will struggle to accommodate demand, with an estimated 60 airports congested and the top 20 airports saturated 8–10 h a day (Eurocontrol, 2004). In April 2004, the European Commission (EC) initiated the Single European Sky (SES) performance-based framework, with the intention of changing the future structure of air traffic control across Europe. The ultimate objective is to replace step-by-step the air traffic management (ATM) working arrangements, which are largely based on national boundaries, by a more efficient ATM system based on flight patterns. In support of SES, the EC also initiated the SES Air Traffic Management Research and Modernisation Programme (SESAR), an ambitious attempt to response to the ATM challenge. It has the objectives of enabling a three-fold increase in capacity; improving safety by a factor of ten; facilitating a 10% reduction in the environmental impacts of aviation; and providing ATM services at a cost which is at least 50% less than now (SESAR, 2006), which according to Eurocontrol (2005a) is currently V800 per flight gate-to-gate. The target for capacity enhancement is that the European ATM System (EATMS) can accommodate a 73% increase in traffic by 2020, based on a 2005 baseline, whilst meeting the targets for safety and quality of service. Many factors cause increases in air traffic congestion and delays. According to Caves and Gosling (1999), the most important
* Corresponding author. E-mail address: [email protected] (B. Desart). 0969-6997/$ – see front matter 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jairtraman.2009.10.006
contributing factors are growing demand, lack of sufficient system capacity, hub-and-spoke networks, and environmental constraints. What is more, airports in particular and the air transport system in general are subject to fluctuations in demand and capacity. According to Janic (2000), the capacity of any airport component can be expressed by four different measures that represent capacity attributes: the physical infrastructure, fluctuations of demand over time, profiles of user entities, and the quality of service provision. Because of the airport coordination process (European Commission, 2004), including slot scheduling, and air traffic flow management (ATFM), actual delays normally do not originate from lack of declared capacity. Airports have to declare capacity six months in advance and, for those ‘scheduled’ airports, the surplus traffic in saturated periods is transferred through slot negotiation to less busy periods. However, for a given flight schedule, based on declared capacity, any capacity fluctuation that is uncontrolled, unmanaged, or unpredicted, results in delay. Delay therefore originates from sudden and unpredicted capacity changes or, more precisely, from either inaccurate planning or lack of capacity stability. Poor weather conditions and industrial actions in Europe are shown to be the most important factors that disrupt airline and airport schedules, generating congestion, delays, diversions and cancellations of flights (Janic, 2003). Meteorological conditions are, without doubt, the more dynamic and certainly the most unpredictable factor (Krollova, 2004). According to Eurocontrol (2005a), around 40% of airport ATFM delays and 10% of en-route delays are due to weather, often made worse by ineffective and reactionbased planning when such conditions occur. Based on a Eurocontrol (2005a) performance review, the lack of gate-to-gate transit time predictability also incurs major annual
82
B. Desart et al. / Journal of Air Transport Management 16 (2010) 81–85
resource costs for operators. To mitigate unpredictability and satisfy customers, airlines often build in buffer times to their flight schedules. By doing so, flights may suffer a short delay and yet be on time. However, the use of buffers is detrimental to ATM costeffectiveness (Cook, 2007). For instance, it is estimated that a minute of buffer time for an Airbus A320 is worth V49 per flight. By cutting 5 min off 50% of schedules, some V1 billion per annum could be saved and better used by operators. It is also a common practice by air navigation service providers (ANSP’s) to overcome potential safety standards violations through capacity buffers that enable controllers to reduce additional workload and stress caused by sudden and unpredicted capacity shortage. Better knowledge of capacity fluctuations and mitigation of degradation could save the industry substantial costs. Predictability could be improved through better collaborative decision-making, system-wide information management (SWIM), better management of reaction to bad weather conditions and better control of take-off times. It is clear that the research community needs to pursue innovative approaches to modelling unpredictability in air transport operations to a greater extent and seek more cost effective approaches for operators.
of capacity change, by estimating how quickly a change can occur at any specific point for use in goal-seeking optimisation. If F={ f1,., fn} represents the vector variable, a set of all the factors fi that impact on capacity g in varying degrees, then airport capacity is defined by a complex relationship g ¼ qðf1 ; .; fn Þ between all the factors fi that affect it. Capacity can also be defined as a dynamic system characterised by a given state. The capacity ! state is the vector variable S ¼ ðv1 ; .; vi ; .; vn Þ determined by the collection of values ni assigned to each factor fi in such a way that, ! g ¼ qðv1 ; .; vi ; .; vn Þ ¼ qð S Þ. Capacity can therefore be defined as a function of the n-dimensional capacity state, and the complex relationship that links each factor can be represented in a very general way by,
!
q : Rþ . Rþ /Rþ 0 : g ¼ qð S Þ
(1)
The capacity dynamics with respect to the various factors fi is defined as the gradient of capacity g with respect to these factors fi. ! ! This capacity dynamics is noted dðqðf1 ; .; fi ; .; fn ÞÞ, dðgÞ or dg , and is formulated as,
!
dg ¼ gradðqÞ ¼ Vf1 ;.;fn qðf1 ; .; fn Þ; cfi ˛F
2. Definition and interpretation of directional capacity dynamics Most analysis has focused on static performance indicators and a deterministic approach to capacity assessment. However, little has been done to address the specific problem of capacity dynamics and planning for extraordinary capacity fluctuations. This often leads to the conclusion that the only way to mitigate airport delays is through capacity enhancement. However, this is by no means the only approach to deal with the problem. The capacity of a system, airport capacity in particular, is subject to time and space changes. Some factors affecting runway capacity remain relatively static, in particular the number, configuration and inter-dependency of runways and the type of radio-navigational facilities. However, runway system capacity has often been shown to be unstable due to the dynamics and instability of many factors (Stamatopoulos et al., 2003) such as volume and time-dependent pattern of traffic demand, mix of inbound and outbound traffic flows, aircraft fleet mix pattern and meteorological conditions. Although it is recognised that the lack of robustness of capacity assessment is heavily dependent on fluctuations of various factors, the marginal impact of those factors has rarely been analysed. Many factors affecting capacity are interdependent and influence each other. The rate of change of capacity is, therefore, not necessarily proportional to the rate of change of some specific factors, considered on an individual and isolated basis: one factor might be significantly improved and another slightly reduced yet the result is enhanced capacity. For instance, a reduction in runway occupancy time has little impact on capacity in some conditions of in-trail spacing minima. Similarly an increase in approach speed has little impact: although higher approach speed contributes to lower intrail spacing minima, usually entailing higher runway occupancy time blocking out the potential benefit of lower in-trail time. Capacity change can be analysed through a ‘bottom-up’ approach based on an a priori understanding of the system to be modelled. Seeking capacity optimisation by looking for sensitivity or ‘what-if’ scenario analyses cannot with certainty obtain the solution to represent a global optimum. Hence, the capacity dynamics concept aims at addressing and proposing a possible solution using such a ‘bottom-up’ approach, contributing to an a priori understanding of the system to be modelled. The purpose of the capacity dynamics concept is to quantify the instantaneous rate
(2)
Whilst using the Leibniz notation, capacity dynamics can also be expressed as a column vector whose components are the partial derivatives of the capacity influencing factors fi, as,
0 !
vg B vf1
1
dg ¼ @ « C A
(3)
vg vfn
If capacity is expressed with respect to its possible states (Eq. (1)), then capacity dynamics is the gradient of capacity with respect to those states, and provides the direction to the most promising capacity state, i.e. the capacity optimum:
!
!
! !
dg ¼ gradðqÞ ¼ VS qð S Þ
(4)
The capacity dynamics vector shows the direction in which capacity changes most quickly. At any point, it describes the measure of the capacity slope: steepness, fall or incline. Some measure of the magnitude of this capacity change can be represented by a scalar. Let the 2-norm represent this measure. The 2-norm of a vector ! v ¼ ðv1 ; .; vi ; .; vn Þ corresponds to the rffiffiffiffiffiffiffiffiffiffi P 2ffi vi . In particular, the Euclidean length and is defined as k! vk ¼ 2 i
magnitude dg of the capacity change represented by the capacity ! dynamics vector dg is defined as,
! dg ¼ dg
(5)
The capacity dynamics gradient also indicates how capacity changes in directions other than the direction of the largest change. It provides the airport planner with a quantification of the inclination of the field of capacity change potential at any point along a given trajectory of change, i.e. the magnitude of capacity dynamics indicates to airport planners and decision-makers how fast capacity changes in a given planning direction. Indeed, given the surface representing the field of capacity change potential, and given a unit vector on that surface, the inclination or grade of the surface in a particular direction is the dot product of the capacity dynamics with that vector. By analogy, consider a walker who attempts to reach the top of a hill, but who does not set off to climb a mountain. The gradient, at the point where the walker stands, points at the direction of the steepest slope. For instance,
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assume the magnitude of the gradient is 30 in the uphill direction, i.e. relatively hard to climb. Rather than using the 30 slope road which goes directly uphill, the walker takes a path under an angle of 60 with the uphill direction when projected onto the horizontal plane. Then, the slope of the road followed by the walker is reduced to 15 , which is 30 times the cosine of 60 . In summary, the magnitude of capacity dynamics dotted with a unit vector gives the slope of the capacity change potential in the direction of that vector. In such a way, the directional derivative of capacity leads to what we term directional capacity dynamics. A further possible use of the directional capacity dynamics concept is the smooth implementation of capacity enhancement, through its ability to show other directions rather than the direction of largest change. Based on Eq. (4), directional capacity dynamics enables the identification of intermediate capacity states to be considered for smooth implementation of capacity enhancement action plans. 3. Definition and interpretation of capacity stability Predictability of capacity degradation can be a key measure of the intrinsic quality of planning. Capacity fluctuation has a major impact on the accuracy of slot allocation and slot scheduling. To ensure planning accuracy of any economic system, there is a need to measure the robustness of its capacity. A useful question then becomes, ‘‘How robust is airport capacity, given all the various factors that may affect it due to their fluctuations?’’ The more capacity fluctuates, the less accurate airport planning will be, unless the risks associated with fluctuation can be rigorously quantified and controlled with appropriate mitigation plans (Desart et al., 2002). In general, stability measures how robust a system is with respect to external forces and how resistant it is to potential change in the variables of interest. The stability concept, also called constancy or persistence in other fields, provides a measure of the system’s response to some perturbation. Stability is often related to both resistance, that is a measure of how little a given variable of interest changes in response to stress or external pressures, and inertia that represents a change at some rate that is relatively constant in response to external fluctuation. Stability can therefore be understood as the resistance to capacity degradation, driven by a hostile perturbation of its affecting factors. A skyscraper with ball-and-socket joint foundations is robust because it can resist earthquakes. Similarly, capacity is intuitively robust if it can resist the fluctuation of its affecting factors. If so, capacity can be considered as being stable. With capacity dynamics, it is possible to measure how robust capacity is, against potential disruptions. The capacity stability mg with respect to a set F ¼ ff1 ; .; fi ; .; fn g of capacity disrupters, noted mg ðf1 ; .; fi ; .; fn Þ, is a performance indicator that can be formulated as the inverse of the magnitude of capacity dynamics with respect to a set of influencing factors,
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order to keep this formulation as clear as possible, assumptions of traffic demand constancy and fleet homogeneity need to be made. First, the characteristics of local air traffic demand for airport access and service constitutes, after weather conditions, the most dynamic factor influencing airport capacity. The capacity dynamics with respect to traffic pattern is intrinsically dependent on the time horizon during which this factor can remain in a relatively stable state. The shorter the time horizon, the more dynamic the traffic pattern seems to be, especially when those shorter periods are related to peaks; hence, making capacity planning more difficult. Traffic demand is especially dynamic at airports accommodating charter flights or low-cost carriers. Airports accommodating high level of scheduled traffic are less subject to traffic pattern fluctuation, especially if subject to International Air Transport Association slot scheduling meetings. In order to stabilise operations, minimise delay and optimise air traffic and capacity management, those airports are co-ordinated or schedule-facilitated (European Commission, 2004). Based on these considerations, the traffic demand constancy assumption is based on the fact that traffic demand and, therefore, accommodated traffic are statistically representative over a relatively long period of time. Consequently, the average inbound and outbound fleet mixes are relatively constant. Second, fleet homogeneity is assumed, that is all aircraft types form a single class, characterised by an average performance, weighted by a fleet mix representation. Based on these two assumptions, capacity g can be formulated as the reciprocal of the arithmetic mean of the time intervals s between successive movements,
.
þ gðsÞ : Rþ 0 /R0 : s/gðsÞ ¼ 1 s
½movements per unit of time
ð7Þ
The primary formulation reported in Eq. (7) is sufficiently generic for it to be applied to both arrival and departure capacity. In this relationship, capacity approaches infinite values when spacing between successive events (movements) tend toward infinitesimal numbers, whilst capacity tends to zero for large values of spacing. The function has, therefore, two asymptotes: a vertical one that is expressed by lim gðsÞ ¼ N, and a second one that is horizontal and s/0
defined by lim gðsÞ ¼ 0, as represented in Fig. 1. The capacity s/N
function is a rectangular hyperbola. Capacity is expressed in terms of number of movements (arrivals, departures or mix of both) per unit of time (usually per hour). Capacity dynamics is based on differentiation of the capacity function. Based on Eqs. (3) and (7), the capacity dynamics dg with respect to spacing s results in
g 1 dg :Rþ 0 /R0 : s/dg ¼ s2 ¼ s ½capacity unit per unit of time
ð8Þ
1 1 ¼ ! jdg ðf1 ; .; fi ; .; fn Þj kdg ðf1 ; .; fi ; .; fn Þk (6)
The image of the first-order differentiation of capacity is the set of negative and non null real numbers, noted R 0 . As represented in Fig. 1, the capacity dynamics dg with respect to spacing s also includes two asymptotes: a vertical one expressed by
Hence, capacity stability measures the inertia of capacity to change, i.e. its robustness regarding changes. The more stable the capacity, the less its responsiveness to disruption.
gs lim d ð Þ ¼ N, and a second that is horizontal and defined as s/0 ds gs lim d ð Þ ¼ 0. As with capacity, capacity dynamics is theoretically s/N ds
mg ðf1 ; .; fi ; .; fn Þ ¼
4. Primary formulation of capacity dynamics and stability To be useful to airport planners and modellers, the concepts of capacity dynamics and stability needs to be further formulated. In
a rectangular hyperbola, but negative. This second horizontal asymptote is however theoretical only; in practice, the minimum level of capacity dynamics depends upon the relative accuracy of the capacity influencing factors. Roughly speaking, it cannot be expected that the output of a system will be more precise than the
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Fig. 1. The capacity dynamics and stability functions.
accuracy of its inputs, and its dynamics to be smaller than the natural fluctuation of the factors influencing that system. A recent study on the average distance-based separation and landing capacity shows that 144 s in-trail spacing is, on average, a representative separation for 6 NM (Eurocontrol, 2005b); this corresponds to an average speed of 150 Kts, which is a common operational value for instrument-based final approaches in Europe. Referring to Eq. (7) and (8), 144 s in-trail spacing results in 25 arrivals/h and any marginal change (increase or decrease) of intrail spacing by 1 s leads to a capacity fluctuation of 0.17 arrivals/ h/s. This is illustrated in the zoom view of Fig. 1 by the two points (143:25.17) and (145:24.83). Based on Eqs. (6) and (7), the capacity stability mg with respect to spacing s is synthesised as, þ 2 mg :Rþ 0 /R0 : s/mg ¼ s ¼
s g
½unit of time per capacity unit
ð9Þ
Capacity stability being the positive inverse of capacity dynamics can be expressed in terms of unit of time per capacity unit: arrival capacity stability at 144 s in-trail spacing is 5.76 s per arrivals/h whilst it decreases to 1.44 s per arrivals/h, for 72 s in-trail spacing, as represented in Fig. 1.
5. The capacity/stability paradox The purpose of operating an economic system, whatever it may be (e.g. an airport, telecommunications, productive industry, etc), is to maximise outputs over inputs. To do this, it needs to be operated at optimal capacity. On one hand, systems may be under-operated and slack capacity is created, enabling good quality of service and few delays. However, this is inefficient in terms of profitability. On the other hand, economic systems may be saturated causing delays with associated service quality problems and costs. As a result, any economic system needs to be operated with an acceptable level of delay to maximise profits (Janic, 2000, 2003). This requires finding the optimum trade-off between throughput and quality of service. To determine this, capacity stability is a key component: pulling the capacity ‘rope’ almost to breaking point. The art of capacity planning resides to some extent in the identification of this breaking point. As illustrated in the zoom view of Fig. 1, any marginal change of in-trail spacing by 1 s in the vicinity of 144 s leads to an arrival capacity fluctuation of 0.17 arrivals per h. As confirmed by Eurocontrol (2005b), a decrease of distance-based separation from 6 to 3 NM leads to a decrease of in-trail spacing to 72 s, resulting in an increase of capacity to 50 arrivals per h. However, the same 1 s marginal change around 72 s in-trail spacing results in a capacity
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fluctuation of 0.69 arrivals/h, that is to say that the impact is four times more significant than around 144 s in-trail spacing. Paradoxically, reducing in-trail spacing from 6 NM to 3 NM enables capacity to be doubled, but also entails capacity to be four times more sensitive to the same marginal fluctuation of in-trail spacing, and consequently four times less stable (see Eq. (8) and Fig. 1). Indeed, arrival capacity stability at 144 s in-trail spacing is 5.76 s per arrivals/hr whilst it decreases to 1.44 s per arrivals/hr for 72 s in-trail spacing. Vice-versa, doubling spacing divides capacity by a factor of two, but leads to a magnitude of potential change of capacity divided by four, and to a capacity four times more robust. This is what we term the capacity/stability paradox. Put simply, this states that the higher an airport is performing from a capacity perspective, the more sensitive is its capacity to potential fluctuation of some of its disrupters, and therefore the less stable it becomes. In other words, from a capacity perspective, an airport becomes less stable the higher its level of performance. Two important implications arise as a result of this paradox. First, the problem of airport capacity allocation lies in the ability to select the appropriate capacity value from the given arrival/ departure ratio ranges to best satisfy traffic demand, bearing in mind the possible dynamic variation of this demand. The objective therefore consists of maximising the use of available capacity to be allocated to traffic demand subject to allocation criteria, in order to achieve specified objectives like, for instance, minimisation of queues, delays and associated costs (Janic, 2004). In a similar way, Gilbo (1993) describes the capacity allocation problem as the evaluation of decision variables, airport capacities, in accordance with predefined optimisation criteria. Gilbo identified two types of criteria to determine the operational effectiveness of traffic accommodation over a given time period: first, the number of flights in the queue; and, second, the delay time of the accommodated traffic (i.e. waiting time in the arrival, stack, and departure queues). These two criteria are strongly correlated: the larger the queues, the longer the delays. An optimal solution that minimises the flights in the queue is also expected to provide favourable conditions to minimise delays. However, the choice of the appropriate optimisation criterion mainly depends on the type of input data available and the relative complexity of calculating the solutions. Setting criteria for the size of the queues may be preferred at the strategic airport planning level, when aggregated data are available (e.g. demand per 15 min or one-hour time intervals). In contrast, delay time may be preferred for tactical planning purposes, when flight-by-flight data are available. Based on an acceptable level of stability defined by appropriate risk analysis, the capacity/stability paradox definitely constitutes one valid criterion to be considered in the scope of capacity allocation. Second, with the same airport planning methodology, planning is more robust if it is related to a low-performing system than to a high-performing system, because the latter is subject to less stability. This constitutes a paradox because the more a system is used close to saturation, the better it should perform and, consequently, the more accurate planning is needed. The capacity/ stability paradox, therefore, raises serious questions about the constant capacity maximisation and questions the ultimate goal of
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capacity enhancement with respect to stability. Capacity stability should be part of risk quantification of airport planning. 6. Conclusions This paper has examined capacity dynamics and stability as one approach to planning for capacity fluctuation and degradation. Experience shows that unpredictability of capacity degradation challenges both airport planners’ and modellers’ intuition. The capacity dynamics concept provides an indication of how quickly capacity can change in response to fluctuations brought about by one or more influencing factors, whilst capacity stability provides airport planners with a measure of capacity robustness. Both concepts enable the rigorous quantification of the degradation impact. In contrast to conventional approaches based on trial-anderror, these two concepts contribute to a better a priori understanding of the airport system because of enhanced quantification of the impact and sensitivity assessment of factors affecting it. These two concepts have unravelled a capacity/stability paradox: the better an airport is performing from a capacity perspective, the more sensitive is its capacity to potential fluctuation in some influencing factors; consequently the less stable it becomes, the more likely it is to experience increasing delays. In brief, by highlighting potential risks of capacity degradation that could not have been identified otherwise, the capacity dynamics and stability concepts offer a new dimension to airport planning. References Caves, R.E., Gosling, G.D., 1999. Strategic Airport Planning. Pergamon, Elsevier Science, Amsterdam. Cook, A., 2007. The Management and Costs of Delay. In: Cook, A. (Ed.), European Air Traffic Management. Ashgate, Aldershot. Desart, B., Caves, R.E., Gillingwater, D., Hirst, M., 2002. Robustness of slot allocation for multiple runway-use configurations: a formulation of the capacity instability problem. Proceedings of the ATRS Conference. Seattle. Eurocontrol, 2004. Challenges to Growth 2004 Report. European Organisation for the Safety of Air Navigation, Brussels. Eurocontrol, 2005a. Performance Review Report 2005. European Organisation for the Safety of Air Navigation, Brussels. Eurocontrol, 2005b. European Wake Vortex Mitigation Benefits Study; High-level Benefits Analysis and Systemic Analysis, WP3 Deliverable. European Organisation for the Safety of Air Navigation, Brussels. European Commission, 2004. European council regulation 793/04 on common rules for the allocation of slots at community airports, Brussels: Official Journal of the European Union, Luxembourg. Gilbo, E.P., 1993. Airport capacity: representation, estimation, optimization. IEEE Transactions on Control Systems Technology 1, 144–154. Janic, M., 2000. Air Transport System: Analysis and Modelling. Gordon & Breach, Amsterdam. Janic, M., 2003. A model for assessment of the economic consequences of large scale disruptions of an airline network. Proceedings of the 82nd TRB Annual Conference. Washington DC. Janic, M., 2004. Air traffic flow management: a model for tactical allocation of airport capacity. Proceedings of the ATRS Conference. Istanbul. Krollova, S., 2004. Dynamic climatological processing of flight weather hazards data at airports. Proceedings of the 1st International Conference on Research in Air Transportation (ICRAT 2004). Zilina. SESAR, 2006. Air Transport Framework – The Performance Target, SESAR Definition Phase Deliverable 2, DLM-0607-001-02-00. SESAR Consortium, Brussels. Stamatopoulos, M.A., Zografos, K.G., Odoni, A.R., 2003. A decision support system for airport strategic planning. Transportation Research C 12, 91–117.