The Economics of Crowding in Public Transport e de Palma a Robin Lindsey b Andr´ Guillaume Monchambert a,c,1 a ´ Ecole Normale Sup´ erieure de Cachan b University of British Columbia c KULeuven Railway Operations Research Seminar: ” Put Passengers first ” KUL - May 3rd, 2016 1 guillaume.monchambert@kuleuven.be
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Motivation 2 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Motivation 3 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Modal split - Intuition 1/4 Generalized cost • is the sum of the monetary and non-monetary costs of a journey (travel time, waiting time...), • may depend on the patronage. 4 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Modal split - Intuition 1/4 Generalized cost • is the sum of the monetary and non-monetary costs of a journey (travel time, waiting time...), • may depend on the patronage. Figure 1: Generalized cost of using road as a function of the number of road users 4 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Modal split - Intuition 2/4 The equilibrium on a network is reached when the generalized cost is the same for all modes (Wardrop equilibrium). 5 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Modal split - Intuition 2/4 The equilibrium on a network is reached when the generalized cost is the same for all modes (Wardrop equilibrium). Figure 2: Bi-modal equilibrium with economies of scale in public transport (Mohring effect) 5 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Modal split - Intuition 3/4 Figure 3: Bi-modal equilibrium without economies of scale in public transport 6 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Modal split - Intuition 4/4 Figure 4: Bi-modal equilibrium with diseconomies of scale in public transport (Crowding) 7 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Characteristics of public transport crowding Crowding in public transport have characteristics which are similar to congestion (traffic jam) on road: • a negative externality, • caused by an excess of demand, • which increases with the demand, • which degrades the individual experience of travel, • and which raises the generalized travel cost. 8 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A In the literature • There is an economic theory of road congestion (mainly through the bottleneck model : Vickrey, 1969; Arnott et al., 1990, 1993), • but few works on crowding in public transport. Almost all works study competition between road and public transport including congestion on road but not on public transport (Tabuchi, 1993 ; Danielis et Marcucci, 2002 ; Mirabel et Reymond, 2011 ; Gonzales et Daganzo, 2013 ; Tian et al., 2013...). = ⇒ Fill this gap in the literature. 9 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Goals of this work • Develop a dynamic model of public transit usage that includes crowding ( PTM model ). • Derive: - User equilibrium - System (i.e., social) optimum - Optimal fares: uniform and time-varying - Optimal service • Timetable, no. trains, train capacity • Dependence on fare regime • Comparisons with bottleneck model of road traffic congestion (the most widely adopted road congestion model in the economic literature). • Application to a segment of RER A transit line in the Paris Region. 10 / 37
Outline 1. Literature review 2. Hypothesis of the model 3. PTM Model 4. Capacity adjustment 5. Application to RER A 6. Conclusions
Outline 1. Literature review 1.1 Empirical microeconomic evidences 1.2 Empirical macroeconomic valuations 2. Hypothesis of the model 3. PTM Model 4. Capacity adjustment 5. Application to RER A 6. Conclusions
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Empirical microeconomic evidences Mircoeconomic valuations of crowding cost: • Fixed penalties, about 2,5$US/trip (Pepper et al., 2003 ; Hensher et al., 2011) • Time multipliers - Whelan and Crockett, 2009 ( next slide) . - Wardman and Whelan, 2011 : standing = 2,32 ; seating = 1,32. - Kroes and al., 2013 : • Seating when all seats are occupied = 1,1. • Standing when the vehicle is full = 1,6. - Haywood and Koning, 2015 ( next slide ). 12 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Figure 5: Time multipliers as a function of the in-vehicle density - Source: Haywood and Koning, 2015. 13 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Table 1: Times multipliers as a function of the trip characteristics - Source : Whelan and Crockett, 2009. 14 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Empirical macroeconomic evidences Valuations of crowding cost at a city scale: • Prud’homme et al., 2012 : From 2002 to 2007, an 8% increase in ridership on the Paris subway system caused a welfare loss due to extra crowding of at least e 75M/year. • Veicht et al., 2013 : In 2011, welfare loss of over-crowding in Melbourne: $280M. • de Palma, Monchambert and Picard, 2015 : crowding cost in Paris Region public transport reaches from 11 to 15 millions euros per working day. 15 / 37
Outline 1. Literature review 2. Hypothesis of the model 2.1 Bottleneck theoretical framework 2.2 Specific to public transport 2.3 Crowding cost function 3. PTM Model 4. Capacity adjustment 5. Application to RER A 6. Conclusions
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Bottleneck theoretical framework Hypothesis from Arnott et al., 1990, 1993 : • N identical individuals commute from A to B every day. • All individuals have the same preferred arrival time, t ∗ . • The strategic variable is the departure time, t : individuals trade-off between schedule delay cost and congestion cost (extra travel time on road and crowding for public transport). • Individuals incur a schedule delay cost if they do not arrive at t ∗ , denoted δ ( t ) δ ′ ( t ) < 0 � si t < t ∗ δ ( t ∗ ) = 0 , δ ′ ( t ) > 0 si t > t ∗ . 16 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Specific to public transport • A PT line connects A and B with no intermediate stops. • Travel time is fixed (and normalized to zero). • The public transport authority operates m trains, indexed by departure time k = 1 , ..., m (train m leaves last). • Train k leaves (and arrives) at t k . • Users know the timetable. • Departure time decision is discrete. • There is no upper limit to train capacity. 17 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Crowding cost function Linear form: g ( n ) = λn s where • n is the number of users in the same train, • s > 0 is a measure of the train capacity (might be m 2 ), • and λ is a scale parameter. 18 / 37
Outline 1. Literature review 2. Hypothesis of the model 3. PTM Model 3.1 Equilibrium - graphical intuition 3.2 Inefficiency of equilibrium 3.3 Social optimum 4. Capacity adjustment 5. Application to RER A 6. Conclusions
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Equilibrium - graphical intuition User private cost t ∗ = t 5 t 1 t 2 t 3 t 4 t 6 t 7 t Arrival time of PT Figure 6: Equilibrium distribution of departure times when m = 7 . 19 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Equilibrium - graphical intuition User private cost Scheduling cost SDC t ∗ = t 5 t 1 t 2 t 3 t 4 t 6 t 7 t Arrival time of PT Figure 6: Equilibrium distribution of departure times when m = 7 . 19 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Equilibrium - graphical intuition Crowding cost User private cost Scheduling cost c e SDC t ∗ = t 5 t 1 t 2 t 3 t 4 t 6 t 7 t Arrival time of PT Figure 6: Equilibrium distribution of departure times when m = 7 . 19 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Inefficiency of equilibrium In equilibrium, the pattern of departure times is sub-optimal (the marginal social cost of a trip is higher than the private cost). Crowding is a negative externality. It implies two distorsions: • There are too many users using the facility (if the demand is elastic). • Ridership is not optimally distributed over trains. ( Presumption: riders are too concentrated on ”timely” trains ). 20 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Social optimum - Graphical intuition Figure 7: Equilibrium cost and pattern of departure times 21 / 37
Introduction Literature review Hypothesis PTM Model Capacity Application to RER A Social optimum - Graphical intuition Figure 8: Optimal private and marginal social costs 22 / 37
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