Survival analysis of new intra-European scheduled air services
R. Klophausa,*, M. Viehmanna
aCompetence Center Aviation Management (CCAM), Worms University of Applied Sciences, Germany
klophaus@hs-worms.de, viehmann@hs-worms.de* Corresponding author

Extended abstract submitted for presentation at the 11th Triennial Symposium onTransportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

March 31, 2022
Keywords: Airline network management, air services, survival analysis, Cox regression

1INTRODUCTION

Year after year, airlines offer new air services, some of them in route competition with othercarriers. Planning and launching scheduled air services requires time and money of the operating
carrier but also at the served airports. There might be substantial support through tax payers’
money as well. Nevertheless, new air services are often abandoned within the first years. Some arediscontinued shortly after the start even without exceptional events such as the COVID pandemic,
although the respective carrier as a whole continues to operate or competing services by othercarriers sustain on a given route. Accordingly, the important question for airlines, airports andother stakeholders arises as to the key factors of service survival. The present paper addresses thisquestion. We analyze the survival of direct services on intra-European routes opened from 2013 to2018. Our aim is to examine how airline, airport, route and service attributes affect the probabilityof service survival over time. Covariates include the airline business model and route competition.
Our empirical analysis ends in 2019, the last regular year for the aviation industry before theCOVID crisis led to an exceptionally high number of suspended services (Suau-Sanchez et al.,2020).
Research on airline competition and market entry following the deregulation of passenger airlinemarkets (e.g., Borenstein, 1992) do not consider the survival probability of individual direct
services. Same holds for applications of graph theory to airline networks (e.g., Roucolle et al.,2020). With a case study approach, Lohmann & Vianna (2016) examined how aviation and nonaviation factors affected route suspension in Australia between 2008 and 2013. de Wit & Zuidberg(2016) estimated discrete choice models of route termination in the networks of the four largest
European low-cost carriers. They found that distance, the number of seats offered, market share,seasonality and route age have a significant effect on the chance of route termination. Calzada &Fageda (2019) mainly investigated route expansion in the European air transport market in theperiod 2002 to 2013, but also considered a sample of active routes and the factors determining
their discontinuity using a logit model. More recently, Manello et al. (2021) linked route closures
to the economic development of European regions using socio-economic and airport
characteristics, however, without specification of airline or service attributes.

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R. Klophaus and M. Viehmann

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Our aim is to fill a gap in the literature by estimating probabilities of service survival on intraEuropean routes with a set of airline, airport, route and service characteristics. We estimate
variants of a Cox proportional hazard model with data from the OAG airline schedules database.
Among other findings, we derive a significant dependence of the service survival rate on theairline business model. Our results should be of particular interest for airline and airport managers
not to invest time and money in the launch of scheduled air services that are more likely to failthan others.

2METHODOLOGY

2.1

Model Formulation

The Cox proportional hazards model (Cox, 1972) makes a parametric assumption concerning theeffect of the covariates on the hazard function, but no assumption regarding a particular form of
the hazard function itself. This approach suits us as we are primarily interested in the effects of thecovariates, not in the shape of the hazard function itself. The hazard function for the Cox
proportional hazards model can be specified as:λ(t|X) = λ0 (t) exp(Xβ) = λ0 (t) exp(β1 X1 ) ⋯ exp(βk X k )(1)

This expression provides the hazard function for air services at time 𝑡 dependent on the covariate
vector 𝑋 of 𝑘 explanatory variables. The hazard function denotes the rate or probability of an event(termination of a service) in the interval of infinitesimal length [𝑡, 𝑡 + Δ𝑡] conditional on thecovariates 𝑋. The model assumes multiplicative effects of the covariates on the baseline hazard
function 𝜆0 (𝑡), i.e., the baseline hazard function that is time-dependent does not depend on thecovariates itself. The influence of the covariates is expressed by the hazard ratios exp(𝛽𝑗 ) that are
assumed to be constant over time. If 𝛽𝑗 is estimated close to 0, the hazard ratio exp(𝛽𝑗 ) ≈ 1, i.e.,the covariate 𝑗 is predicted to have no significant influence on the hazard rate. Similarly, 𝛽𝑗 > 0
results in a hazard ratio exp(𝛽𝑗 ) > 1 and the predictor increases the risk of an event. For acovariate predicted to decrease the risk or increase survival probabilities, 𝛽𝑗 < 0 or exp(𝛽𝑗 ) < 1.
The Cox model is a standard method, e.g. in medical studies to analyze the effects of different
covariates such as different treatments or physical characteristics. The subjects in our case are nonstop air services between two airports provided by a specific airline. The subjects are followed up
regularly during the study with their status and their characteristics being recorded. We areinterested in the event of termination of the air service by the respective carrier. After the event,
the subjects are no longer followed-up. Hence, we do not consider services interrupted for morethan one year. We check for the first week in October each year whether a service is continued orterminated. In order to exclude the special effects of the ongoing COVID crisis, we only recordschedule data until 2019. We are therefore making censored observations, as we cannot observe
the further survival of the services that were still active in October 2019. As we examine new airservices opened from 2013 to 2018, truncation is of no relevance.
We calibrate different models to evaluate model quality and potential differences in termination
risk stemming, for example, from business models or specifics of individual airlines. First, we fit asingle model including all business models (mainline and low-cost) and analyze effects of thecovariates commonly shared between different carriers (Model 1). We expect the airlines’
particularities to influence the risk but also expect differences due to the airlines’ business models.
In a stratified model, a common extension to standard Cox models, we estimate separate baseline
hazards 𝜆0,1 (𝑡), 𝜆0,2 (𝑡), … for each level of the stratification variable:

TRISTAN XI Symposium

Original abstract submittal

R. Klophaus and M. Viehmann

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where 𝜆𝑠 (𝑡|𝑋) is the hazard function for subjects belonging to stratum 𝑠. While the baseline
hazard depends on the stratum, the proportional hazards do not. Hence, we model specifics of thehomogeneous group in a stratum in the baseline hazard and assume that effects of the covariatesinfluence the hazard independently of the stratum. We build models that include the businessmodel and the carriers as stratification variables (Model 2 and Model 3). In order to analyze
potentially different effects of the predictors, we continue to build separate models that only
contain subsets of a single business model (Model 4 / mainline and Model 5 / low-cost). To
account for effects particular to individual airlines, we further stratify the airlines in each subset in
Model 6 (mainline) and Model 7 (low-cost).

2.2

Data and Covariates

Our data contains 18,836 records of 5,820 distinct intra-European city pairs (non-directional),
which are operated by 100 airlines in continuous operation during the entire study period up to theyear 2019. 18 of these airlines are categorized in the OAG database as airlines with a low-costbusiness model (3,753 city pairs), while the other 82 airlines are classified as mainline carriers(2,587 city pairs). Table 1 provides an overview of the covariates analyzed.
Table 1 – Description of Covariates
Description
Airline business model (mainline or low-cost)
Airline size as available seat kilometers offered world-wide (ASKs, in
AirlineSizemillions)Distance
Route distance in NM
Frequency
Service frequency offered by respective airline
CapacityShare
Market share of the respective carrier on city pair by seat capacity
ArrApFreq
Airline presence at the arrival airport (# frequencies)
DepApFreq
Airline presence at the departure airport (# frequencies)
ArrApFreqShare
Airline relative presence at the arrival airport (share of all frequencies)
DepApFreqShare
Airline relative presence at the departure airport (share of all frequencies)
LargerApFreqTotal Airport size in terms of total frequencies (world-wide) for the larger airport
SmallerApFreqTotal Airport size in terms of total frequencies (world-wide) for the smaller airport
Variable
BusModel3RESULTS AND DISCUSSION

The results of the different models are detailed in Table 2. We state the proportional hazards
estimated and additionally provide the significance levels. Model 1 shows a significantly increased
likelihood of service termination when airlines follow a mainline instead of a low-cost businessmodel. This is a rather surprising result, considering that low-cost carriers’ footloose strategieshave been emphasized in the academic literature (e.g., Graham, 2013). Mainline carriers may close
unprofitable new services early before they become established with increasing demand. Airline
size is not a differentiator, a somewhat counter-intuitive finding as well. However, this mightlargely depend on our assumption to only examine new air services by carriers with ongoing
operations. Due to modal competition, increasing route distance has a positive impact on thesurvival probability, a finding in line with de Wit & Zuidberg (2016) and Manello et al. (2021).
Frequency has a positive impact as well. Route competition between carriers measured by capacity
shares, decreases termination risk only in Model 5, i.e., for low-cost carriers. Hubbing effects formainline carriers strongly increase service survival as shown in airlines’ relative presence at either
endpoint. Effects of the absolute size of the respective arrival and destination airports are limited.

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R. Klophaus and M. Viehmann

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Table 2 – Estimated Proportional Hazards
VariableBusModel
AirlineSize
DistanceFrequency
CapacityShare
ArrApFreq

Model 1
1.9634(***)
1.0000(*)
0.9995(***)
0.9405(***)
0.9503Model 2NA

Model 3NA

Model 4NA

1.0000(**)
0.9995(***)
0.9406(***)
0.9542NA

1.00000.9995(***)
0.9339(***)
0.96110.9995(***)
0.9465(***)
1.05360.9992(***)
0.9992(***)
0.8186(**)
0.91740.9992(***)
0.9992(***)
0.8145(**)
0.91460.9993(***)
0.9992(***)
0.9264Model 5NA
00.9999(***)
0.9996(***)
0.9304(***)
0.8154(**)
0.9990(***)
0.9984(***)
1.4594(**)
2.6031(***)
1.0002(***)
1.00010.9994(***)
DepApFreq
0.9996(***)
ArrApFreqShare
0.5249(***)
DepApFreqShare
1.18820.4248(***)
LargerApFreqTotal
1.00011.00011.00010.9999
(***)
(***)
(**)
(***)
SmallerApFreqTotal
1.00001.00001.00000.9998(**)
Observations
18,836
18,836
18,836
7,178
11,658
Events
2,697
2,697
2,697
1,393
1,304
Significance levels shown in parentheses, p<0.01 (***), p<0.05 (**), p<0.1 (*)

Model 6NA

Model 7NANANA

0.9995(***)
0.9358(***)
0.96730.9995(***)
0.9330(***)
0.94480.9996(***)
0.9996(***)
0.6924(**)
0.6818(**)
1.00000.9989(***)
0.9985(***)
1.21590.9998
(***)
7,178
1,393

1.9685(***)
1.0001(***)
1.0001
11,6581,304

REFERENCES
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Original abstract submittal