3.4.1 Models based on loss indicators of performances

The general theoretical functionality curve and the corresponding polygons based on the loss indicator (i) of performance (j) used as the figure-of-merit for assessing resilience, robustness and vulnerability of an airport before, during and after the impact of a given disruptive event are shown in Fig. 3 [64].

• • Resilience, robustness

Figure 3. Functionality recovery curve and the corresponding polygons based on loss indicator (i) of performance (j) as figure-of-merit for estimating resilience, robustness and vulnerability [64].

Cumulative resilience and robustness of the given airport based on the loss indicator (i) of performance (j) before, during, and after the impact of the given disruptive event is estimated as the ratio between the darker-shaded part and the total area of the polygon AEFD in Fig. 3 as follows [Reference Bocchini, Frangopol, Ummenhofer and Zinke1, 64]:

(5a) \begin{align} & R{E_{L/ij}}\left( {{T_4} - {T_1}} \right) = R{B_{L/ij}}\left( {{T_4} - {T_1}} \right)\nonumber\\& = \left[ {\begin{array}{*{20}{c}}{1,\;t \lt {T_1}}\\[5pt]{\dfrac{{\mathop \smallint \nolimits_{{T_1}}^{{T_2}} {\alpha _{ij}} \cdot tdt + \mathop \smallint \nolimits_{{T_1}}^{{T_4}} [FO{M_{0/ij}} - {\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right)]dt + \mathop \smallint \nolimits_{{T_3}}^{{T_4}} {\beta _{ij}} \cdot tdt,for\;{T_1} \lt t \lt {T_4}}}{{FO{M_{0/ij}} \cdot \left( {{T_4} - {T_1}} \right)}}}\\[10pt]{1,t \ge {T_4}}\end{array}} \right] \nonumber\\[5pt]& = \left[ {\begin{array}{*{20}{c}}{1,\;t \lt {T_1}}\\[5pt]{\dfrac{{\dfrac{1}{2} \cdot {\alpha _{ij}} \cdot {{\left( {{T_2} - {T_1}} \right)}^2} + [FO{M_{0/ij}} - {\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right) \cdot \left( {{T_4} - {T_1}} \right)] + \dfrac{1}{2} \cdot {\beta _{ij}} \cdot {{\left( {{T_4} - {T_3}} \right)}^2}}}{{FO{M_{0/ij}} \cdot \left( {{T_4} - {T_1}} \right)}},for\;{T_1} \lt t \le {T_4}}\\[10pt]{1,t \gt {T_4}}\end{array}} \right]\end{align}

The time-dependent resilience and robustness of the given airport based on the loss indicator (i) of performance (j) before, during and after the impact of the given disruptive event along the line ABCD in Fig. 3 is estimated as follows [Reference Janić18, 64, Reference Henry and Ramirez-Marquez65]:

(5b) \begin{align}r{e_{L/ij}}\left( t \right) = r{b_{L/ij}}\left( t \right) = \left[ {\begin{array}{*{20}{c}}{1\;,\ for\;t \lt {T_1}}\\[5pt]{1 - \dfrac{{{\alpha _{ij}} \cdot t}}{{FO{M_{0/ij}}}},\ for\;{T_1} \lt t \lt {T_2}}\\[14pt]{1 - \dfrac{{{\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right)}}{{FO{M_{0/ij}}}},\ for\;{T_2} \lt t \le {T_3}}\\[14pt]{1 - \dfrac{{{\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right) + {\beta _{ij}} \cdot t}}{{FO{M_{0/ij}}}},\ for\;{T_3} \lt t \le {T_4}}\\[14pt]{1,\,f\,or\,t \gt {T_4}}\end{array}} \right]\end{align}

• • Vulnerability

The cumulative vulnerability of the given airport based on the loss indicator (i) of performance (j) before, during and after the impact of the given disruptive event is estimated as the ratio between the lighter-shaded area of the polygon ABCD and the total area of the polygon AEFD in Fig. 3 as follows [Reference Bocchini, Frangopol, Ummenhofer and Zinke1, 64]:

(5c) \begin{align}V{B_{L/ij}}\left( {{T_4} - {T_1}} \right) & = \left[ {\begin{array}{*{20}{c}}{0,\;t \lt {T_1}}\\[5pt]{\dfrac{{\mathop \smallint \nolimits_{{T_1}}^{{T_2}} {\alpha _{ij}} \cdot tdt + \mathop \smallint \nolimits_{{T_2}}^{{T_3}} [{\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right)]dt + \mathop \smallint \nolimits_{{T_3}}^{{T_4}} {\beta _{ij}} \cdot tdt}}{{FO{M_{0/ij}} \cdot \left( {{T_4} - {T_1}} \right)}},\ for\;{T_1} \lt t \lt {T_4}}\\[10pt]{0,t \ge {T_4}}\end{array}} \right] \nonumber\\[5pt]& = \left[ {\begin{array}{*{20}{c}}{0,\;t \lt {T_1}}\\[5pt]{\dfrac{{\dfrac{1}{2} \cdot {\alpha _{ij}} \cdot {{\left( {{T_2} - {T_1}} \right)}^2} + \left[{\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right) \cdot \left( {{T_3} - {T_2}} \right)\right] + \dfrac{1}{2} \cdot {\beta _{ij}} \cdot {{\left( {{T_4} - {T_3}} \right)}^2}}}{{FO{M_{0/ij}} \cdot \left( {{T_4} - {T_1}} \right)}},\ for\;{T_1} \lt t \le {T_4}}\\[10pt]{0,t \gt {T_4}}\end{array}} \right] \end{align}

The time-dependent vulnerability of the given airport based the loss indicator (i) of performance (j) before, during and after the impact of the given disruptive event along the line ABCD in Fig. 3 is estimated as follows [Reference Janić18, 64, Reference Henry and Ramirez-Marquez65]:

(5d) \begin{align}v{b_{L/ij}}\left( t \right) = \left[ {\begin{array}{*{20}{c}}{0,\ for\;t \lt {T_1}}\\[5pt]{\dfrac{{{\alpha _{ij}} \cdot t}}{{FO{M_{0/ij}}}},\ for\;{T_1} \lt t \lt {T_2}}\\[14pt]{\dfrac{{{\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right)}}{{FO{M_{0/ij}}}},\ for\;{T_2} \lt t \le {T_3}}\\[14pt]{1 - \dfrac{{{\alpha _{ij}} \cdot \left( {{T_2} - {T_1}} \right) + {\beta _{ij}} \cdot t}}{{FO{M_{0/ij}}}},\ for\;{T_3} \lt t \le {T_4}}\\[14pt]{0,t \gt {T_4}\begin{array}{*{20}{c}}{} \end{array}}\end{array}} \right]\end{align}

where

i

is the loss indicator of performance (j) of the given airport (i = 1,2,., N ^j );

j

is the performance of the given airport (j = 1, 2,., N);

N

is the number of loss performances of the given airport affected by the given disruptive event;

N _j

is the number of loss indicators of performance (j);

T ₁

is the time when the impact of the indicator (i) of performance (j) starts by the given disruptive event;

T ₂

is the time when the impact of the indicator (i) of performance (j) ends by the given disruptive event;

T ₃

is the time when the recovery of the indicator (i) of performance (j) starts;

T ₄

is the time when the indicator (i) of performance (j) fully recovers;

t

is the time during the observed period;

FOM _0/ij

is the reference (planned/regular) value of the loss indicator (i) of performance (j);

$\alpha_{ij}$

is the rate of deterioration of the loss indicator (i) of performance (j); and

$\beta_{ij}$

is the rate of recovery of the loss indicator (i) of performance (j).

In Equation 5(a, c) and (b, d), the cumulative and time-dependent resilience, robustness and vulnerability can vary between 0 and 1 during the observed period (T ₁ , T ₄ ). They change during the impact of the disruptive event depending on the values of the indicator (i) of performance (j), FOM _ij (t) compared to the reference (planned/regular) value FOM _0/ij (T ₄ – T ₁ ). The value of FOM _ij (t) can even be 0 when the given indicator of performance is completely deteriorated. The latter happens when the airport is closed and all flights are cancelled. If the rate of deterioration of the given indicator of performance (α _ij ) is constant as it is in the given case, the end of deterioration of the corresponding performance will happen at time: (T ₂ – T ₁ ). Consequently, the term (α _ij ·t) indicates the current value of the deteriorated indicator (i) of performance (j) at time (t) (t ε T ₁ , T ₂ ). For example, this happens when severe weather causes decrease of the airport’s regular/planned capacity and/or the main airlines start to perceive long delays of their flights. In case of a lasting airport closure, all affected flights are cancelled, the indicator (i) of performance (j) drops to zero, and the corresponding resilience and robustness become minimal and the vulnerability becomes maximal. After reopening of the airport, the indicator (i) of performance (j) starts to recover due to a rather gradual resumption of the previously cancelled flights. If the recovering rate $(\beta_{ij})$ is constant, the time of its full recovery up to the reference (regular/planned) state prior the impact of the disruptive event will be equal to: T ₄ = T ₃ + [FOM _0/ij – α _ij ·(T ₂ -T ₁ )]/ $\beta_{ij}$ . In this case, the term ( $\beta_{ij}$ ·t) represents the restored indicator (i) of performance (j) at time (t) (t ε (T ₃ , T ₄ ). Consequently, the corresponding resilience and robustness recover towards their full value, while the vulnerability gradually drops to zero.

3.4.2 Models based on savings indicators of performances

The general theoretical functionality recovery curve and the corresponding polygons based on the savings indicator (k) of performance (l) used as figure-of-merit for estimating resilience, robustness and vulnerability of the given airport before, during and after the impact of the given disruptive event are shown in Fig. 4 [64].

• • Resilience, robustness

Figure 4. Functionality recovery curve and the corresponding polygons based on savings indicator (k) of performance (l) as figure-of-merit for estimating resilience, robustness and vulnerability [64].

The resilience and robustness of the given airport based on the savings indicator (k) of performance (l) before, during and after the impact of the given disruptive event can be quantified as the ratio between the area of the brighter-shaded polygon ABCD and the area of polygon ADEF in Fig. 4 as follows [Reference Bocchini, Frangopol, Ummenhofer and Zinke1, 64]:

(6a) \begin{align} R{E_{S/kl}}\left( {{T_4} - {T_1}} \right) & = R{B_{S/kl}}\left( {{T_4} - {T_1}} \right) = \left[ {\begin{array}{*{20}{c}}{1,\;t \lt {T_1}}\\[5pt]{\dfrac{{\mathop \smallint \nolimits_{{T_1}}^{{T_2}} {\gamma _{kl}} \cdot tdt + \mathop \smallint \nolimits_{{T_2}}^{{T_3}} {\gamma _{kl}} \cdot \left( {{T_2} - {T_1}} \right)dt + \mathop \smallint \nolimits_{{T_3}}^{{T_4}} {\delta _{kl}} \cdot tdt}}{{FO{M_{0/kl}} \cdot \left( {{T_4} - {T_1}} \right)}},for\;{T_1} \lt t \lt {T_4}}\\[15pt]{1,t \ge {T_4}}\end{array}} \right]\nonumber\\[5pt]& = \left[ {\begin{array}{*{20}{c}}{1,\;t \lt {T_1}}\\[5pt]{\dfrac{{\dfrac{1}{2} \cdot {\gamma _{kl}}{{\left( {{T_2} - {T_1}} \right)}^2} + {\gamma _{kl}}\left( {{T_2} - {T_1}} \right) \cdot \left( {{T_3} - {T_2}} \right) + \dfrac{1}{2} \cdot {\delta _{kl}}{{\left( {{T_4} - {T_3}} \right)}^2}}}{{FO{M_{0/kl}} \cdot \left( {{T_4} - {T_1}} \right)}},for\;{T_1} \lt t \lt {T_4}}\\[15pt]{1,t \ge {T_4}}\end{array}} \right]\quad\quad \end{align}

The time-dependent resilience and robustness of the given airport based on the savings indicator (k) of performance (l) before, during and after the impact of the given disruptive event along the line ABCD in Fig. 3 can be estimated as follows [Reference Janić18, 64, Reference Henry and Ramirez-Marquez65]:

(6b) \begin{align}r{e_{S/kl}}\left( t \right) = r{b_{S/kl}}\left( t \right) = \left[ {\begin{array}{*{20}{l}}{1,\;\,for\;t \lt {T_1}}\\[7pt]{\dfrac{{{\gamma _{kl}} \cdot t}}{{FO{M_{0/kl}}}},\,for\;{T_1} \lt t \lt {T_2}}\\[10pt]{\dfrac{{{\gamma _{kl}}\left( {{T_2} - {T_1}} \right)}}{{FO{M_{0/kl}}}},\,for\;{T_2} \lt t \le {T_3}}\\[10pt]{\dfrac{{{\gamma _{kl}}\left( {{T_2} - {T_1}} \right) + {\delta _{kl}} \cdot t}}{{FO{M_{0/kl}}}},\,\,for\;{T_3} \lt t \le {T_4}}\\[10pt]{1,\begin{array}{*{20}{c}}{\,for\;\;t \gt {T_4}} \end{array}}\end{array}} \right]\end{align}

• • Vulnerability

The cumulative vulnerability of the given airport based on the savings indicator (k) of performance (l) before, during and after the impact of the given disruptive event as the area of the darker-shaded polygon AEFD in Fig. 4 can be quantified as follows [Reference Bocchini, Frangopol, Ummenhofer and Zinke1, 64]:

(6c) \begin{align}V{B_{S/kl}}\left( t \right) & = \left[ {\begin{array}{*{20}{c}}{0,\;t \lt {T_1}}\\[5pt]{1 - \;\dfrac{{\mathop \smallint \nolimits_{{T_1}}^{{T_2}} {\gamma _{kl}} \cdot tdt + \mathop \smallint \nolimits_{{T_2}}^{{T_3}} {\gamma _{kl}} \cdot \left( {{T_2} - {T_1}} \right)dt + \mathop \smallint \nolimits_{{T_3}}^{{T_4}} {\delta _{kl}} \cdot tdt}}{{FO{M_{0/kl}} \cdot \left( {{T_4} - {T_1}} \right)}},for\;{T_1} \lt t \le {T_4}}\\[10pt]{0,t \gt {T_4}}\end{array}} \right] \nonumber\\[5pt]& = \left[ {1 - \begin{array}{*{20}{c}}{0,\;t \lt {T_1}}\\[5pt]{\dfrac{{\dfrac{1}{2} \cdot {\gamma _{kl}}{{\left( {{T_2} - {T_1}} \right)}^2} + {\gamma _{kl}}\left( {{T_2} - {T_1}} \right) \cdot \left( {{T_3} - {T_2}} \right) + \dfrac{1}{2} \cdot {\delta _{kl}}{{\left( {{T_4} - {T_3}} \right)}^2}}}{{FO{M_{0/kl}} \cdot \left( {{T_4} - {T_1}} \right)}},for\;{T_1} \lt t \le {T_4}}\\[10pt]{0,t \gt {T_4}}\end{array}} \right]\end{align}

The time-dependent vulnerability of the given airport based on the savings indicator (k) of performance (l) before, during and after the impact of the given disruptive event along the line AEFD in Fig. 3 can be estimated as follows [Reference Janić18, 64, Reference Henry and Ramirez-Marquez65]:

(6d) \begin{align}v{b_{S/kl}}\left( t \right) = \left[ {1 - \begin{array}{*{20}{l}}{0,\;\,for\;t \lt {T_1}}\\[5pt]{1 - \dfrac{{{\gamma _{kl}} \cdot t}}{{FO{M_{0/kl}}}},\,for\;{T_1} \lt t \lt {T_2}}\\[10pt]{\dfrac{{{\gamma _{kl}}\left( {{T_2} - {T_1}} \right)}}{{FO{M_{0/kl}}}},\,for\;{T_2} \lt t \le {T_3}}\\[10pt]{1 - \dfrac{{{\gamma _{kl}}\left( {{T_2} - {T_1}} \right) + {\delta _{kl}} \cdot t}}{{FO{M_{0/kl}}}},\,for\;{T_3} \lt t \le {T_4}}\\[10pt]{0,\,for\;t \gt {T_4}}\end{array}} \right]\end{align}

where

k

is the savings performance of the given airport (k = 1, 2,…, M);

l

is the indicator of savings performance (k) of the given airport (k = 1,2,., M _k );

M

is the number of savings performances affected by disruptive events;

M _k

is the number of savings indicators of performance (k);

FOM _0/kl

is the regular/planned value of the savings indicator (k) of performance (l);

γ _kl

is the rate of deterioration of the savings indicator (k) of performance (l); and

δ _kl

is the rate of recovery of the savings indicator (k) of performance (l).

Other symbols are analogous to those in Equation 5(a–d).

In Equation 6(a, c) and (b, d), the resilience, robustness and vulnerability of the given airport based on the savings indicator (k) of performance (l) can vary between 0 and 1 during the observed period (T ₁ , T ₄ ). They change during the impact of the disruptive event depending on the values of the indicator (k) of performance (l), FOM _kl (t) compared to the reference (planned/regular) value FOM _0/kl (T ₄ – T ₁ ). The value FOM _kl (t) can even be 0 when the corresponding indicator is completely deteriorated, i.e. when the maximum savings are made. The latter happens when the airport is closed, all flights are cancelled and consequently not making any costs/externalities. If the rate of reducing the given impact (γ _kl ) is constant as in the given case, the time of achieving maximum savings in the corresponding indicator (impact) happens after time (T ₂ – T ₁ ). In addition, the term (γ _kl ·t) indicates the current value of the indicator (k) of performance (l) at time (t) (t ε T ₁ , T ₂ ). For example, this happens when the airport’s planned regular/capacity decreases due to severe weather and the main airlines start to gradually cancel their planned flights as they expect rather long delays. In the case of airport closure and consequent cancellation of all flights, for example during the period (T ₃ – T ₂ ), the indicator (k) of performance (l) increases to its maximum reference value FOM _0/kl . Consequently, the corresponding resilience and robustness will be maximal and the vulnerability minimal. If the recovery of the indicator (k) of performance (l) starts just after the end of the impact of the disruptive event, the time (T ₃ – T ₂ ) will represent the recovery time. This appears realistic because although the affected airport instantly declares returning to the planned/regular operating regime, the airlines usually need some time to restore the previously long-delayed and/or cancelled flights. If the recovering rate to the full scale of the given impact (δ _kl ) is constant, the time of full recovery of the given indicator up to its reference value prior to the impact of the disruptive event will be equal to: T ₄ = T ₃ + (γ _kl /δ _kl )·(T ₂ – T ₁ ). In this case, the term (δ _kl ·t) represents the restored indicator (k) of performance (l) at time (t)(t ε T ₃ , T ₄ ). Consequently, the corresponding resilience and robustness decrease towards zero and the vulnerability increases to one, i.e. when this savings indicator reaches its reference value as it used to be before the impact of the disruptive event.

4.2.1 LHR airport

LHR (London Heathrow) airport (UK) is the largest among five London airports (the other four are: Gatwick, Stansted, London City, and London Luton). The scheme of the airport layout is shown in Fig. 5.

Figure 5. Layout of LHR (London Heathrow) airport [67].

Under planned/regular conditions, the airport operates two parallel runways in the segregated mode (one exclusively for arrivals and the other for departures) due to the noise cap of 57 dBA L _eq and 55 dBA L _eq during the day and night, respectively. Consequently, the annual declared runway capacity was 480·10³ ATMs/year. In the year 2019, LHR airport was connected to 217 destinations – 8 domestic (4%) and 209 international (96%). The average market share of ATMs of three world’s regions was about 79%, i.e. North America – 18.3%; Europe (UK, EU, Non-EU) – 50.1%, and Asia Pacific – 10.6% [68]. The market share of three airline alliances – Oneworld, Star Alliance, and SkyTeam – was 84% [69]. In the year 2019, the airport handled: N _0/11 = 473·10³ ATMs, 81·10⁶ passengers, and 1.6·10⁶ ton of air cargo [67, Reference Janić70–72].

Table 3 gives the estimated indicators of the above-mentioned performances in the year 2019 relevant for particular actors/stakeholders and used as reference figures-of-merit for assessing resilience, robustness, and vulnerability during the impact of COVID-19 pandemic disease – Period: January 2020-July 2021.

Table 3. Indicators of performances as figures-of-merit for assessing resilience, robustness and vulnerability: Case of LHR (London Heathrow) airport (UK)

${}^{(1)}$ Averages – Period: 2019 [73]; ${}^{(2)}$ Average over the period: 2019 $($ before tax $)$ [71]; ${}^{(3)}$ Based on 11.14 USD/pax and 170 pax/atm $($ 20 year average $)$ [75]; ${}^{(4)}$ Based on: 13.25 $($ MTOW/50 $)$ ^0.7 $($ MTOW – Maximum Take-Off Weight $)$ $($ tons $)$ [78]; ${}^{(5)}$ GDP1 – With spending of tourists; GDP2 – Without spending of tourists [75, 76, 77]; ${}^{(6)}$ Refs [67, 71, 74, 79]; GBP = 1.317 USD $($ GBP – British Pound; USD – US dollar [80]; ${}^{(7)}$ Implies reduction by −3dB during 30 years, 0.1 dB/year or 0.16 $\%$ /year [67]; ${}^{(8)}$ Heathrow airport: Period: 1962–2018–11 fatal accidents and 17.763·10⁶ ATM; 1 GBP = 1.317 USD [78, 81]; ${}^{(9)}$ Refs [78, 82–85].

4.2.2 NYC JFK (John F. Kennedy) airport

NYC JFK (John F. Kennedy) airport (US) is the largest among three main New York airports. The other two are LGA (La Guardia), mainly handling domestic, and EWR (Newark International) airport, mainly handling international flights. The simplified airport layout of JFK airport is shown in Fig. 6.

Figure 6. Layout of NYC JFK (John F. Kennedy) airport [86].

The airport operates two pairs of parallel runways with the annual declared capacity of 735.8 · 10³ (84 ATMs/h) (two runways used for arrivals and one for departures) and 788.4·10³ (90 ATMs/h) (two runways used for departures and one for arrivals). Under planned/regular operating conditions, the airport was connected to 174 destinations: 70 – North America (40%), Europe 30 (17%), and Asia Pacific 16 (9%), which was 66% of the total. In addition, the airline capacity was split to 56.1% domestic and 43.9% international ATMs. The average market share of ATMs of the above-mentioned three regions was about 88.6%, i.e. North America – 66.6%; Europe-Transatlantic – 18%, and Asia Pacific – 4% [87]. The market share of the three airline alliances – Oneworld, Star Alliance, and SkyTeam – was 64% [88]. In the year 2019, the airport handled: N _0/11 = 355.514·10³ scheduled passenger ATMs, 62.5·10⁶ passengers, and 1.4·10⁶ ton of air cargo [89, 90]. Table 4 gives the estimated indicators of the above-mentioned performances relevant for particular actors/stakeholders in the year 2019 used as reference figures-of-merit for assessing resilience, robustness and vulnerability during the above-mentioned impact of COVID-19 pandemic disease during the observed period.

Table 4. Indicators of performances as figures-of merit for assessing resilience, robustness, and vulnerability: Case of NY JFK (John F. Kennedy) airport (US)

⁽¹⁾Averages – Period: 2019 [90]; ⁽²⁾Averages – Period: 2019 (before tax) [91]; ⁽³⁾ Refs (92, 93); ⁽⁴⁾ Ref. [94]; ⁽⁵⁾ GDP1 – With spending of air visitors; GDP2 – Without spending of air visitors [95–97]; ⁽⁶⁾ Ref. [98]; ⁽⁷⁾ Ref. [Reference Wolfe, Malina, Barrett and Waitz99]; ⁽⁸⁾Period: 2000–2019 [100]; ⁽⁹⁾ Refs. [83–85, 101].

4.2.3 Some characteristics of the impact of the given disruptive event

The given disruptive event – the COVID-19 pandemic disease – affected the global air transport system indirectly by requiring almost simultaneously enforcement of various contingency/restrictive measures at the global (national and international) scale. Most measures embraced stricter checking and screening of air passengers at the airports, post travel quarantines, but also completely constraining the access to the airports and airline services. Figure 7 shows the introduction of particular contingency/restrictive measures at the global scale – in the three above-mentioned regions during the observed period (January 2020-March 2021).

Figure 7. Simplified scheme of introducing contingency/restrictive measures in the air transport system affected by COVID-19 pandemic disease (Period: January 2020-March 2021) [102].

As can be seen, in the three above-mentioned regions, North America, Europe and Asia-Pacific, the increased screening (Level 1 measure) of air passengers at airports, quarantining arrivals from the high-risk regions (Level 2 measure) and closing arrivals to/from some regions (Level 3 measure) were successively applied during the first quarter of the year 2020 (until April 2020). With some variations within the same and between different above-mentioned regions, the measures around Level 3 were in place until the end of the observed period. Since under regular operating conditions LHR and NYC JFK airports had substantial shares of traffic to/from these three regions, contingency/restrictive measures both in these regions and domestically have considerably affected both airports.

4.3.1 Operational performances

• • ATMs (Air Transport Movement(s)) at airports

Figure 8(a, b) shows the number of ATMs (air transport movements) at both airports, representing the loss indicator of their operational performances and the corresponding time-dependent resilience, robustness and vulnerability during the observed (disrupting) period.

Figure 8. Operational performances – Number of ATMs (Air Transport Movement(s)): Case of LHR (London Heathrow) and NYC JFK (John F. Kennedy) airport – Impact of COVID-19 pandemic disease (Period: January 2020–July 2021). (a) Time-dependent number of ATMs, (b) Time-dependent functionality – resilience, robustness and vulnerability.

Figure 8(a) shows that during the first quarter of the year 2020, the number of ATMs at LHR airport decreased from 35,328 to 4,873 ATMs (−86%). During the same period, the number of ATMs at NYC JFK airport decreased from 27,235 to 3,125 ATMs (−89%). During the next six months (period: April–October 2020), the number of ATMs at LHR airport gradually increased to 18,026 ATMs (−50%) and at NYC JFK airport to 10,790 ATMs (−40%). Later on, during the following five months (period: October 2020-February 2021) the number of ATMs at LHR again decreased to 7,785 (−78%). During the same period, the number of ATMs at NYC JFK airport increased to 11,516 ATMs (– 61%). Furthermore, during the period February-June 2021, the number of ATMs increased at both airports – to 13,255 ATMs (– 62%) at LHR and 24,779 ATMs (−16%) at NYC JFK airport.

Figure 8(b) shows that at the beginning of the observed period (the first quarter of the year 2020), the resilience and robustness of both airports were sharply decreasing during March 2020 and reached their minimum in April 2020 of about: re _L/11 (4) = rb _L/11 (4) $\approx$ 0.10 (i.e. 10%) compared to the reference value of: re _L/11 (0) = rb _L/11 (0) = 1.0 (i.e. 100%) in the year 2019. The rate of their decrease was about: α _L/11 $\approx$ 22.5 %/month. Consequently, the vulnerability of both airports was increasing at approximately the same rate: β _L/11 = 22.5 %/month and reached its maximum in April 2020 at about: vb _L/11 (4) $\approx$ 0.90–0.95 (i.e. 90%–95%). Such developments were mainly driven by an increased impact of the COVID-19 disease, which increasingly prevented the access of air passengers to the airports and airlines there. For example, at the beginning of March, the dominant airline, British Airways, cancelled most of its international short-haul (UK and European) and long-haul intercontinental flights at LHR airport. At the same time, foreign airlines from similarly affected countries cancelled most of their medium-haul (continental European) and long-haul intercontinental flights to LHR airport (the UK and most of these countries were under conditions of full or close-to-full lock-down) [103]. At the same time, NYC JFK airport was also affected by different forms of impact of the COVID-19 pandemic disease. One was the US travel restrictions imposed on 26 European countries (announced on 12 March 2020). Airlines such as Lufthansa and Air France-KLM had to cancel their flights between the above-mentioned European (Schengen area) countries and the US, including those to/from NYC JFK airport. Flights from the UK and Ireland were exempted. The other form was the COVID-19 pandemic infection of the staff at 17 US ATC control centres including that of the NYC (New York City) area. Consequently, American Delta and United airlines cancelled about 90% of their domestic and international short-haul, medium-haul, and long-haul flights to/from the increasingly affected New York City area, including that to/from NYC JFK airport. On the contrary, JetBlue airline tried to consolidate its presence there under the given conditions [104, 105].

Later on, due to the partial relaxation of access conditions to air transport services, the resilience and robustness of LHR airport were recovering during the sub-period April-October 2020 at an average rate of: β _L/11 $\approx$ 5.8 %/month up to the level: re _L/11 (10) = rb _L/11 (10) $\approx$ 0.45 (i.e. 45%). However, with the repeated tightening of the access-restrictive measures, the resilience and robustness were deteriorating over the sub-period October 2020-February 2021 at the rate of: α _L/11 $\approx$ 6.25 %/month to about: re _L/11 (14) = rb _L/11 (14) $\approx$ 0.20 (i.e. 20%). Finally, with further relaxation of the access-restrictive measures, the resilience and robustness were recovering again during the last sub-period February-June 2021 at the rate of: $\beta_{11}$ $\approx$ 3.25 %/month to the level: re _L/11 (18) = rb _L/11 (18) $\approx$ 0.33 (i.e. 33%). The corresponding vulnerabilities at the end of the above-mentioned sub-periods were: vb _L/11 (10) $\approx$ 0.55 (i.e. 55%), vb _L/11 (14) $\approx$ 0.80 (i.e. 80%), and vb _L/11 (18) $\approx$ 67 (i.e. 67%), respectively.

The resilience and robustness of NYC JFK airport over the sub-period April 2020-February 2021 were also recovering due to the relaxation of demand-access restrictions mainly throughout the US. The resilience and robustness were recovering with some rather slight variations at an average rate of: β ₁₁ $\approx$ 3 %/month from the level: re _L/11 (4) = rb _L/11 (4) $\approx$ 0.09 (i.e. 9%) to the level: re _L/11 (14) = rb _L/11 (14) $\approx$ 0.39 (i.e. 39%), and again during the sub-period February 2021-June 2021 at the rate of: β ₁₁ $\approx$ 11.25 %/month to the level: re _L/11 (18) = rb _L/11 (18) $\approx$ 0.84 (i.e. 84%) by the end of the observed period (June 2021). The corresponding vulnerabilities at the end of the above-mentioned sub-periods were: vb _L/11 (14) $\approx$ 0.61 (i.e. 61%) and vb _L/11 (18) $\approx$ 0.16 (i.e. 16%), respectively.

The total number of ATMs, which would have been carried out at LHR and NYC JFK airports under planned/regular operating conditions during the observed period (January 2020-June 2021), would be: N _0/11 = 713,808 and N _0/11 = 533,268 ATMs, respectively (based on the average reference monthly number in the year 2019 of: N _0/11 = 39,656 ATM/month at LHR and N _0/11 = 29,626 ATM/month at NYC JFK airport). The actual number of cancelled ATMs during the same period was: n ₁₁ = 459,910 ATMs at LHR and n ₁₁ = 280,917 ATMs at NYC JFK airport. Consequently, the cumulative resilience, robustness and vulnerability of LHR airport were: RE _L/11 (1,18)= RB _L/11 (1,18) = 0.356 and VB _L/11 (1,18) = 0.644, respectively. Those of NYC JFK airport were: RE _L/11 (1,18)= RB _L/11 (1,18) = 0.473 and VB _L/11 (1,18) = 0.527. These indicate that the robustness and resilience of NYC JFK airport were higher than their counterpart values for LHR airport by about 33%. The vulnerability of LHR airport was higher than that of NYC JFK airport by about 22%. This indicated that under the given conditions the resilience and robustness of NYC JFK airport were higher and the vulnerability was lower than that of LHR airport by about 33% and 20%, respectively.

4.3.2 Economic performances

• • Airport and aviation industry’s profits

Figure 9(a, b) shows the time-dependent and cumulative profits of both airports and related aviation industries as the loss indicators of economic performances during the observed (disrupting) period (January 2020–June 2021). Since these profits directly depend on the number of ATMs, the corresponding time-dependent resilience, robustness, and vulnerability are not explicitly shown because they are equivalent to those based on the number of ATMs.

Figure 9(a) shows that the airport and aviation industry’s profits were substantively affected by the cancellation of ATMs at both airports and actually changed in line with the changes of the cancelled ATMs during the observed period. As can be seen, the losses of profits of LHR airport and the related aviation industry were maximal in April 2020, −111.3 and −173.6 million USD, respectively, and again in February 2021, 125.4 and 194 million USD, respectively. In the meantime, they were following the changes of the cancelled ATMs. In addition, the maximum loses of profits of NYC JFK airport and the aviation industry there were also incurred in April 2020, −29.3 and 79.0 million USD. During the remainder of the observed period, these profits were gradually increasing due to the recovering number of ATMs. Figure 9(b) shows that cumulative losses of airport and aviation industry’s profits of LHR airport were about −1.47 and −2.3 billion USD, respectively, and those of NYC JFK airport about −0.31 and −0.83 billion USD, respectively. The cumulative resilience, robustness, and vulnerability of LHR airport and the aviation industry during the observed period were the same as those of ATMs: RE _L/21/22 (1,18)= RB _L/21/22 (1,18) = 0.356 and VB _L/21/22 (1,18) = 0.644, respectively. Those of NYC JFK airport were: RE _L/21/22 (1,18)= RB _L/21/22 (1,18) = 0. 479 and VB _L/21/22 (1,18) = 0.521.

• • Contribution to GDP

Figure 9. Economic performances – Airports and aviation industries’ profits: Case of LHR (London Heathrow) and NYC JFK (John F. Kennedy) airport – Impact of COVID-19 pandemic disease (Reference period: Average month in 2019; Period: January 2020 – July 2021). (a) Time-dependent profits of airports and related aviation industries, (b) Cumulative losses of profits of airports and aviation industries.

Figure 10(a, b) shows the time-dependent and cumulative contribution to GDP (Gross Domestic Product) as the loss indicators of economic performances during the observed (disrupting) period (January 2020–June 2021). As in the case of airport and aviation industry’s profits, the corresponding time-dependent resilience, robustness and vulnerability are not explicitly shown since they are again equivalent to those based on the number of ATMs.

Figure 10. Economic performances – Contribution to GDP (Gross Domestic Product): Case of LHR (London Heathrow) and NYC JFK (John F. Kennedy) airport (GDP1 – With spending of tourists/air visitors; GDP2 – Without spending of tourists/air visitors) – Impact of COVID-19 pandemic disease (Reference period: Average month 2019; Period: January 2020–July 2021). (a) Time-dependent contribution to GDP, (b) Cumulative losses of contribution to GDP.

Figure 10(a) shows that the contribution of both airports to GDP was changing in line with the changes in the number of cancelled ATMs during the observed period. The maximum losses of the contribution by LHR airport were in April 2020 (GDP1 – 2.45 billion USD with spending of tourists and GDP2 – 1.76 billion USD without spending of tourists) and again in February 2021 (GDP1 – 2.74 billion USD with spending of tourists and GDP2 – 1.97 billion USD without spending of tourists). The maximum losses of the contribution by NYC JFK airport were in April 2020 (GDP1 – 0.85 billion USD with spending of air visitors and GDP2 – 0.59 billion USD without spending of air visitors). During the rest of the observed period (until June 2021), the losses of contribution to GDP were decreasing due to the gradual decrease in the number of cancelled ATMs. Figure 10(b) shows that the cumulative losses of contribution to GDP during the observed period (January 2020–June 2021) by LHR airport were −32.4 billion USD (GDP 1 with spending of tourists) and −23.4 billion USD (GDP2 without spending of tourists). Those by NYC JFK were −8.95 and −6.16 billion USD, respectively. The corresponding cumulative resilience, robustness and vulnerability of both airports were similar to those in the case of losses of profits of the airports and related aviation industries, i.e. for LHR airport: RE _L/23 (1,18)= RB _L/23 (1,18) = 0.356 and VB _L/23 (1,18) = 0.644, respectively, and for NYC JFK airport: RE _L/23 (1,18)= RB _L/23 (1,18) = 0. 479 and VB _L/23 (1,18) = 0.521.

4.3.3 Environmental and social performances

• • Costs/externalities

Figure 11(a, b, c) shows the time-dependent and cumulative costs/externalities, representing the savings indicator of social and environmental performances and the corresponding cumulative resilience, robustness, and vulnerability of both airports during the observed (disrupting) period.

Figure 11. Social and environmental performances – Costs/externalities: Case of LHR (London Heathrow) and NYC JFK (John F. Kennedy) airport – Impact of COVID-19 pandemic disease (Reference period: Average month 2019; Period: January 2020–July 2021. (a) Time-dependent savings in costs/externalities, (b) Cumulative savings in costs/externalities, (c) Cumulative resilience, robustness and vulnerability.

Figure 11(a) shows that the monthly savings in the costs/externalities were generally higher at LHR than at NYC JFK airport and changed in line with the number of cancelled ATMs during the entire observed period. The main reasons for such difference were the higher number of cancelled ATMs at LHR airport and the higher average costs/externalities per atm. The highest positive difference in favour of LHR airport of about 49% was at the end of the first quarter of the observed period (April 2020) and then again about 147% at the end of the half of the first quarter in 2021 (February 2021). After that time, the positive gap in favour of LHR airport was continuously increasing by the end of the observed period, and it was mainly driven by the higher rate of recovering ATMs at NYC airport. Figure 11(b) shows that the cumulative savings in cost/externalities were by about 99% higher at LHR than at NYC JFK airport during the observed period. Figure 11(c) shows that the corresponding cumulative resilience, robustness and vulnerability were different at both airports. In the given context, LHR airport was more resilient and consequently less vulnerable than NYC airport under the given conditions by about 19% and 28.5%, respectively.

4.3.4 Net impact

Figure 12 shows the total differences between the losses of airport and aviation industry’s profits and the corresponding contribution to GDP, and the savings in the costs/externalities of both airports impacted by the given disruptive event – COVID-19 pandemic disease during the observed period (January 2020–June 2021).

Figure 12. Differences between the total losses of profits and contributions to GDP and the total savings in costs/externalities: Case of LHR (London Heathrow) and NYC JFK (John F. Kennedy) airport – Impact of COVID-19 pandemic disease (Period: January 2020–July 2021).

As can be seen, these total losses in range of billions of USD were about 4 times higher at LHR than at NYC JFK airport during the observed period. This indicates that generally the savings in costs/externalities based on the current charging of corresponding impacts can only marginally compensate for overall losses of benefits from the cancelled ATMs at the given airports under given conditions.

4.3.5 Some causes of differences in the impact of the same disrupting event between airports

The above-mentioned airport characteristics and the applied contingency/restrictive measures shown in Fig. 7 could be used to explain the differences in the indicators of considered performances and related resilience, robustness and vulnerability of both airports affected by the COVID-19 pandemic disease. The main reasons for these differences are summarised as follows:

• • The number of planned/regular and cancelled ATMs at LHR were higher by about 33% and 64% than that at NYC JFK, respectively.

• • The average airport and aviation industry’s profits and contribution to GDP per ATM were about 2.9, 1.67, 2.18 (GDP1), and 2.39 (GDP2) times higher at LHR than their counterpart values at NYC JFK airport, respectively. The average costs/externalities per ATM were about 1.15 times higher at LHR than those at NYC JFK airport.

• • Based on the differences in the total number of planned/regular and cancelled ATMs and differences in the averages per ATM, the total airport and aviation industry’s profits and contribution to GDP were about 4.8, 2.8, 3.6 (GDP1) and 3.8 (GDP2) times higher at LHR than their counterpart values at NYC JFK airport, respectively, during the observed period. The total costs/externalities per atm were higher about 1.90 times at LHR than that at NYC JFK airport.

• • At both airports, the given disruptive event had a very similar strong impact during the first quarter of the observed period (January–April 2020). During the rest of the observed period, the nature of the impact was different at both airports. Due to the predominantly international ATMs (92%–94%), LHR airport remained highly dependent on the above-mentioned contingency/restrictive measures in the three regions rather than on the measures at the local (UK) scale. Most of the contingency/restrictive measures remained around Level 3, thus causing a slow, modest, and rather fluctuating recovery of the airport ATMs. Thanks to the relaxation of the US contingency/restrictive measures, NYC JFK airport with its generally substantive share of domestic ATMs (66.6%) was modestly but continuously recovering by the end of the observed period. Such recovery was contributing to decreasing losses of the airport and aviation industry’s profits and contributions to GDP on the one hand, and reducing savings in the costs/externalities on the other.