The key message of Section 3 is that due to the lack of reliable empirical estimates of key cost parameters, it is difficult to find the optimal occupancy rate during Covid-19. It is more likely that public transport operators (will) need to follow external social distancing rules in daily operations. The third objective of this paper is to investigate what demand management methods might be available to comply with such rules, how efficient they are according to various criteria, and what practical difficulties may hinder their implementation.
Throughout this section we assume that social distancing can be ensured by controlling the flow of passengers into the public transport system. The system boundary is at station entrances and exits (e.g. fare gantries) in case of rail services and at the doors of vehicles in case of buses. Based on the frequency and interior capacity of vehicles, one can derive the upper bound of ridership that can be served without exceeding the critical occupancy rate. Naturally, if headways are irregular and the distribution of passengers is uneven within the vehicles and on platforms, then social distancing requires that the planned occupancy rate remains lower than the external regulation. We assume that operators have sufficient knowledge and data to determine the necessary correction factor, and thus the section’s focus is on the regulation of system inflows.
Inflow control with queueing
Inflow control implemented with a queueing system is the simplest demand management method which is already applied in several large urban rail networks, primarily to avoid station overcrowding and the associated safety risk. Inflow control is implemented by physically restricting the flow of passengers entering the metro station, and storing the excess flow in a physical queueing system. In large networks inflow controls might have to be applied at numerous stations to achieve the demand management objective. Thus, the optimisation of the inflow control policy includes the determination of (i) which stations should be controlled, and (ii) the upper bound of inflows at each station.
Conceptually, the idea of inflow control is rooted in the literature of highway ramp metering, which is a closely related problem in road traffic management. The literature of highway ramp metering dates back to the 1960’s (see e.g. May
1965; Wattleworth
1967); its primary purpose is to keep traffic flows under a pre-estimated threshold by limiting the number of vehicles entering the highway at on-ramps. In case of road traffic, this critical flow is determined by the point where the road section reaches its capacity, and additional traffic would deteriorate its total throughput due to hypercongestion (Daganzo
1997). The control problem is not trivial, because inflows can be restricted at any on-ramp upstream to the active bottleneck on the highway, and new (downstream) bottlenecks can also emerge as a result of the intervention. Users might re-optimise their travel after the interventions, thus increasing the complexity of this two-level control problem (Yang et al.
1994).
The literature of ramp metering is hallmarked by repeated efforts to improve the optimisation heuristics based on a known, time dependent demand matrix of each on-off ramp pair along the highway. The objective function of the problem is normally to minimise the total time spent in the system, or minimise queueing delay at on-ramps subject to the critical flow restriction on the main highway. Lovell and Daganzo (
2000) develop a general non-anticipative heuristic appropriately representing the temporal dynamics of the problem, i.e. that the effect of control measures at upstream stations is realised at the bottleneck with a time lag. They point out two important characteristics of inflow control, from a practical implementation point of view. First, they discuss the potential importance of whether inflows can be differentiated at a given origin by destination. This is impossible with traditional signalised ramp metering technology, but they hint that differentiation would make the system more efficient. Second, they note that “the question of where to store excess demand to a congested system can be very political”. Locally, extensive queueing at on-ramps may spill back to the urban road network, inducing external costs for residents, while on a system level politics might be involved in the determination of which on-ramps should be controlled the most. Very similar challenges might appear in a public transport application: queueing requires space, and controlling inflows at a limited number of stations can be perceived unfair.
Is a full time-dependent OD demand matrix required to optimise a ramp metering policy? This question is especially relevant in the context of social distancing in public transport, as demand patterns change regularly and often unpredictably during a pandemic scenario. Zhang and Levinson (
2004) argue that OD demand data are hard to estimate, and do not even exist in reality, as demand levels are endogenous with respect to the supply-side interventions themselves. They develop a heuristic control logic based on simple intuition, which can be explained using the network layout in Figure
1. Assume again that social distancing would be violated on line section BC in the absence of intervention. The operator may limit inflows at Station A or B, or both. Zhang and Levinson (
2004) show the general principle that inflows should be controlled as close to the bottleneck as possible, in this case at Station B only. The reason is that restrictions at Station A would affect the AB market as well, while they actually do not contribute to demand in the bottleneck. Based on this principle, they develop a heuristic to solve the inflow control problem. The only data requirement of their method is the share of off-ramp exit percentages, which is equivalent to the ratio
\(q_{ab}/(q_{ab}+q_{ac})\) in the present public transport application. They argue based on descriptive data analysis that off-ramp exit percentages are relatively stable over time, and therefore their algorithm requires substantially less data collection effort than the estimation of time dependent OD matrices.
Zhang and Levinson (
2004) discuss some of the equity aspects of their general solution to ramp metering as well. They acknowledge that the most efficient metering regime is also the least spatially equitable one, as it implicitly minimises the number of metered on-ramps along the highway. They enlist a couple of practical remedies to relax the potential equity concerns. One of them is a maximum queue restriction combined with minimum/maximum metering rates: this is equivalent to setting an upper bound to the time that individual passengers would have to wait at entry stations. A similar result can be achieved by defining an increasing function for the unit cost of queueing time, which eliminates excess queueing in the policy optimisation process. In a follow-up paper Zhang and Levinson (
2005) propose an advanced heuristic which distributes queueing costs among a predefined number of entry points in the most efficient way, thus balancing spatial equity and efficiency in the system.
The ramp metering literature has inspired several public transport applications. The benefits of boarding control have been recognised in the literature of operational control strategies,
4 focusing mainly on headway regularity, bus bunching, and the associated degradation of user experience. Delgado et al. (
2009,
2012) investigate boarding limitations in combination with more traditional bus holding strategies in a rolling horizon optimisation framework suitable for real-time operations. They show in a numerical simulation that if headways are short (under 10 minutes) and demand is close or above the physical vehicle capacity, then boarding control can achieve an extra 6.3% expected waiting time savings relative to the already substantial benefits of optimal bus holding. In addition, boarding control evens out bus occupancy rates, thus reducing the crowding inconvenience experienced by the average user, which might not be achieved even if headways are perfectly regular (Ceder
2001).
Passenger inflow control has gained more attention in recent years in the context of urban rail systems. The following studies showcase diversity in terms of the objective function of their control mechanisms:
-
Guo et al. (
2015) minimise the sum of queueing time and waiting on platforms subject to a station capacity constraint determined by safety regulation. Trains can be used up until physical capacity. Their solution method is particle swarm optimisation with a fixed OD demand matrix.
-
Bueno-Cadena and Muñoz (
2017) combine passenger trip times with operator costs stemming from energy consumption and minimise the resulting social cost function through three measures: speed control, train holding and boarding limits. They apply a standard numerical solver to optimise the model.
-
Jiang et al. (
2018) apply a queueing and waiting time based objective function similar to Guo et al. (
2015), but the unit value of wait time increases exponentially, especially if the passenger fails to board more than two trains. Their primary motivation is also to avoid overcrowding in stations for safety reasons. The solution method is reinforcement learning, previously applied in traffic flow control (see Walraven et al.
2016).
-
Shi et al. (
2018) contribute to the literature by jointly optimising train timetables and station inflows to avoid platform overcrowding and minimise passenger wait time at station halls and on platforms. They propose an integer linear programming model and solve it with a hybrid heuristic based on a standard integer solver and local search.
-
Zou et al. (
2018) develop a feedback-based bottleneck elimination strategy to optimise inflow controls on a network level. They associate station inflows with section flows using a traffic assignment model, and establish a heuristic inflow control algorithm to eliminate the bottleneck(s) where the predicted demand exceeds the available capacity limit. This study lacks an explicitly defined objective function, but several practical considerations are built into the control algorithm. The heuristic itself is similar to the ramp metering method of Zhang and Levinson (
2005) in the sense that they intend to control a given number of upstream stations directly preceding the bottleneck section.
A common limitation of the literature reviewed above is that they assume fixed (inelastic) OD demand matrices. This assumption is neither realistic nor helpful when the aim of inflow control is to reduce aggregate travel demand. With the user cost minimising objective one cannot differentiate the value of individual trips based on willingness to pay or any other criteria, and therefore the allocational performance of the demand management method cannot be evaluated either. This is a major limitation for social distancing applications.
Queueing might take a considerable share of the total travel time, and a bulk of empirical evidence proves that travel demand is sensitive with respect to trip duration (Wardman
2012). Practically speaking, if the queues are very long in front of the station entrance, some passengers may look for alternative means of transport, or reschedule their trips, or decide not to travel at all. Under the more realistic
elastic demand assumption, queueing achieves an allocation of the available transport capacity based on passengers’ sensitivity with respect to travel time. Queueing prioritises those (i) for whom the trip delivers substantial personal benefits, and (ii) whose travel time valuation is relatively low. As these two characteristics might be inversely proportional (people with high value of time may find it more important to travel), the economic efficiency of this allocation method is questionable. In addition, the time lost in queues is a foregone resource for society, which is a huge disadvantage compared to other allocation methods such as pricing, in which case fare revenues can be recycled and utilised elsewhere within society. Nevertheless, queueing is generally considered as
fair policy, because passengers at a given entry location have to spend the same amount of time in the first in, first out (FIFO) system. In addition, if low income groups have lower travel time valuation, then queueing is inefficient but progressive from a distributional point of view.
Practical applicability
Queueing systems are frequently used when entering crowded public venues such as museums, concert halls and tourist attractions. Passengers might see it inevitable that queueing is introduced when demand exceeds the capacity enabled by social distancing rules. The inefficiency of inflow control might not be visible for individuals in the short run, as the distribution of inflow rates set by the public transport operator at various entry stations is not known by users. This makes inflow metering with queueing in front of stations an evident solution to ensure the functioning of public transport under social distancing constraints.
It is important to note, however, that queueing might be a source of infection risk in itself. Queueing with sufficient physical distancing requires a lot of space which might not be available in or outside busy stations. Even if the required space is available, human assistance might be needed to ensure that potentially impatient passengers keep the safety distance at all times. Thus, the management of queueing systems during the pandemic would be more resource intensive than usual.
Lovell and Daganzo (
2000) and subsequent authors have pointed out that the efficiency of inflow control is substantially higher if users can be differentiated by destination, or more importantly on the basis of whether they will travel through active bottleneck(s). Differentiation is hardly feasible in regular highway ramp metering. However, smart card technology in public transport provides ex-post information on the destination of travellers. This opens up the possibility of establishing multiple queues at entry stations depending on trip destination. Queues for OD pairs leading through bottlenecks are expected to be longer, but violations of the differentiated queueing systems could be identified and fined by cross-checking the entry gate data with the destination station in smart card data records. Again, the practical limitation of this idea is that destination-differentiated entry queues require even more space at entry stations.
Differentiated pricing
Pricing in public transport is an often debated subject in the policy arena, as it is the main determinant of how affordable public transport is, and to what extent public budgets have to contribute to deficit financing through subsidies. The economics literature promotes the principle of marginal social cost pricing in public transport. Theory suggests that social welfare is maximised if the fare equals the gap between the marginal
social cost and marginal
personal cost of travelling (see Figure
2), in which case only trips with a non-negative net welfare effect will be realised.
Pricing techniques have advantageous theoretical properties in achieving both quantitative and allocative demand management goals simultaneously. Pricing enables that the personal cost of travelling can be set to any desired level between the unpriced equilibrium and the highest willingness to pay along the inverse demand curve. With advanced monetary transfer techniques even negative payments might be possible to incentivise travelling, in the form of a direct subsidy for public transport use. Pricing allocates the available capacity based on passengers’ willingness to pay for the service: assuming rational consumer behaviour, the sum of the monetary fare and non-pecuniary user costs form the lower bound of personal benefits among the actual travellers who opt for using the service in equilibrium. The main advantage of pricing as a demand management tool is that monetary payments remain within society, so that the amount by which the personal travel cost is raised can be later on redistributed among members of society, as opposed to the time lost in queues, for example.
The primary goal of the pricing literature has been to derive the net non-personal cost of the marginal trip in plausible models of public transport operations. This incremental welfare effect is determined by the following (sometimes off-setting) mechanisms.
1.
Direct social costs and benefits without capacity adjustment
-
Crowding disutility, as an externality (Tirachini
2013; Hörcher
2018).
-
Delay costs during boarding and alighting (Jansson
1980; Oldfield and Bly
1988; Jara-Díaz and Gschwender
2003).
-
Substitution with underpriced car use (Parry and Small
2009; Basso and Silva
2014).
-
Wider economic benefits, including agglomeration economies (Venables
2007; Hörcher et al.
2020).
2.
Additional welfare effect due to responsive capacity, i.e. adjustments in service frequency and vehicle size
-
User cost savings, the Mohring effect (Mohring
1972,
1976).
-
Marginal cost of public funds (Kleven and Kreiner
2006; Proost and Dender
2008).
-
Density economies in operating costs (Anupriya et al.
2020b).
If an operator’s goal is to achieve social distancing with pricing, the regular supply optimisation problem has to be extended with an additional constraint on the equilibrium occupancy rate. This requirement adds a shadow price to the marginal social cost of travelling if the social distancing constraint is binding, and therefore the optimal fare is expected to be higher than its unconstrained equivalent. Eventually, the fare should raise the generalised price of travelling to the marginal willingness to pay at the demand threshold (see
\(d_1(Q''_1)\) if Figure
2). In other words, a critical precondition of enforcing an efficient allocation under social distancing with pricing is the availability of precise information on the inverse demand functions in all spatio-temporal markets of the network. Given that the demand function fluctuates over time while the demand threshold remains constant or non-binding, the optimal fare system might also have to be differentiated by time periods.
Another branch of the literature develops dynamic models of public transport demand in which travellers’ departure time choice is endogenous, but their desired arrival time is clustered in a narrow time window. Conceptually, these dynamic models resemble the traditional bottleneck problem of road traffic management and pricing (see recent reviews by Small
2015; Li et al.
2020). In public transport, the purpose of the dynamic fare is to replace the user cost of queueing with a payment. An optimised time-dependent fare schedule would essentially achieve the same temporal distribution of departures without queueing, by setting the fare equal to the monetary value of queueing time loss in the unpriced equilibrium (Huang
2000; Kraus and Yoshida
2002; Small and Verhoef
2007). Even though bottleneck models are normally governed by the physical capacity of the infrastructure, social distancing can be implemented assuming that an exogenous occupancy rate must not be exceeded in any line section, even if physical capacity would allow for it.
Practical applicability
Achieving social distancing with pricing tools seems to be a challenging task from a methodological point of view. Most of the theoretical models in the literature rely on explicit demand functions, and in case of dynamic models also on the distribution of desired departure or arrival times. Such demand information would also have to be disaggregate both spatially and temporally to control demand in a large network continuously.
The road pricing literature offers several algorithms to solve the optimal pricing problem without explicit demand functions. The intuitive idea behind trial-and-error based pricing schemes comes from Downs (
1993) and Vickrey (
1993), which is then formalised by Li (
2002) in a bisection toll adjustment method. Yang et al. (
2004), Han and Yang (
2009) and later on Wang and Yang (
2012) enhance this approach for a general road network, and prove its global convergence properties. Guo et al. (
2016) develop a practical method to restrain demand under a predetermined flow level, which may not be equivalent to the welfare maximising flow; this resembles the case of social distancing. Guo et al. (
2020) extend this line of research to a bimodal operational scheme in which bus fares as well frequencies are responsive on a day-to-day basis. Purely public transport related applications of the trial-and-error pricing methods are rare in the literature. The study of Wang et al. (
2018) is an exception, but they adopt this iterative approach for a very specific demand management task: to redirect passengers from busy central stations to neighbouring ones by adopting as little fare differentials as necessarily required.
A common property of the aforementioned pricing methods is that they make two key assumptions: (1) The unknown demand function is stable over time, and even if demand is in disequilibrium temporarily, it converges to a steady state eventually, and (2) the speed at which travellers react to price adjustments is known, and in principle it happens instantaneously. Unfortunately, the travel demand functions might not remain stable on a day-to-day basis in a pandemic scenario. Recent experience suggests that in parallel with rapidly changing disease control rules and fluctuating economic performance, travel demand may oscillate unpredictably on a day-to-day basis, even in the absence of supply-side interventions. Also, not every traveller is informed about price adjustments instantaneously,
5 and even if they are, their behavioural reaction may take longer than expected. Relying on an iterative pricing tool under such circumstances can be hazardous, because the realised demand may easily exceed the desired occupancy threshold on certain days, or the demand control may also be over-insured and therefore too restrictive.
The social acceptance and political implementation of peak pricing is another major challenge of practical applicability. Demand management with pricing involves large financial transfers from public transport users to government, which is generally unpopular. Low income travellers might be especially adversely affected by the policy during a period of economic downturn. The aversion of the public can be limited if the channels of redistribution are transparent. Changes in travel behaviour can be achieved by rewarding, i.e. negative pricing, which is indeed much better perceived in the public opinion (Rouwendal et al.
2012). The downside of extensive reward schemes is the pressure it puts on the public budget at a time when transport operators are already severely financially constrained, and rewarding off-peak travellers might be unfair against those residents/voters who do not travel at all. While some empirical evidence on the success of rewarding does exist in the context of road use (Knockaert et al.
2012), experience in public transport, as documented by Anupriya et al. (
2020a), suggests that the behavioural response might be slower, less intensive, and more expensive than what social distancing during the pandemic would require. On the theoretical front, promising new findings by Tang et al. (
2020a,
b) indicate that the integration of fare-reward schemes with non-rewarding uniform fares may achieve demand management goals revenue neutrally.
Due to the practical limitations above, it is more plausible that time-dependent dynamic pricing could play a complementary role beside physical inflow control, i.e. queueing in front of stations. As soon as such inflow controls are in place, queue lengths are immediately observable and the corresponding user costs are also easy to estimate. Replacing queueing costs with monetary payments, in line with the original dynamic pricing theory of traffic bottlenecks (see Small
2015), seems to be a more manageable goal compared to a purely pricing based demand management policy for social distancing.
Advance booking and slot rationing
The disbenefits of queueing, especially the cost of time loss and its uncertainty, have been recognised in many industries where capacity allocation is organised through reservation systems. Within the transport sector, reservation is mandatory for many low frequency public transport services such as long-distance rail or air, or ferries, because running out of capacity in a given time slot would otherwise cause intolerable user costs. The potential implementation of advance booking on highways has been raised repeatedly by Wong (
1997); Koolstra (
1999); De Feijter et al. (
2004) and Edara and Teodorović (
2008) for unique road sections, and by Zhao et al. (
2010) for a cordon-based downtown area. More recently, Lamotte et al. (
2017) revisited this idea in the context of autonomous vehicles, and Menelaou et al. (
2018) propose a reservation based demand management method for entire urban road networks. Interestingly, urban public transport related applications are sparse in the literature.
The basic rationale behind slot reservation is to avoid unproductive time loss in queues. Advance booking is a simple quantity control method which prevents more trip plans being made than what is actually feasible in a given time period. Replacing queueing with reservations offers several benefits for both users and the operator. Beside the regained time in the absence of queueing, advance booking makes the trip duration more reliable, saving additional schedule delay costs due to early or late arrivals. This user benefit may be substantial in a morning commuting scenario (see, e.g., Peer et al.
2012). Additionally, advance booking provides important benefits for the operator as well, in the form of much more predictable demand patterns. Prior information on unexpected demand shocks might be extremely valuable for service planning and management, even if the reservation system is not meant to eliminate queues entirely. The advance reservation requirement enables the operator to explicitly reject travel requests before passengers arrive at their trip origin. Whilst this is certainly not a desirable outcome
per se, advance rejection may still cause less harm and annoyance for the passenger than modifying the travel plan after she spent a considerable amount of time in queues.
Ideal demand management under the pandemic serves quantitative as well as allocative goals simultaneously. It is clear that advance booking achieves the quantitative goal very well if no more time slots are made available than what social distancing rules enable. The allocative efficiency of regular reservation tools based on a FIFO principle is more questionable, however. In this case capacity is allocated to those users who make their trip decisions earlier, and last-minute requests are more likely to be rejected. There is no clear connection between the time of booking and the value of trips for society,
6 and therefore the efficiency of the FIFO reservation policy is ambiguous.
Operators might be able to improve the allocational efficiency of the reservation system by setting the price of advance booking in such a way that spare capacity remains available until the end of the booking horizon (i.e. just before the train or bus departure). This strategy would seemingly resemble the pricing strategy of airlines, where fares normally increase in function of the time of booking. The literature suggests that profit maximising firms have two distinct motivations behind this strategy: (i) to handle unexpected demand shocks, and (ii) to apply intertemporal price discrimination, exploiting the fact that last-minute travellers’ willingness to pay tends to be higher than the early bookers’ reservation price (McAfee and Te Velde
2006; Williams
2020). With a social welfare oriented objective, there is no reason to apply price discrimination, but the ability to handle stochastic demand variations might be important, especially in a pandemic environment. Reaction to stochastic demand means that the operator (1) follows the evolution of bookings for each capacity slot over the booking horizon, (2) models the regular pattern of booking requests, and (3) adjusts the price of reservations upwards (downwards) if the booking pattern exceeds (subsides) the regular pattern over time (see the equivalent process described by Williams
2020, in the context of airline pricing). This way the main challenge of regular pricing methods discussed in Section
4.2, namely the difficulty of
ex-ante demand function estimation, can be overcome very effectively.
Finally, a slot reservation system enables the operator to pre-assign capacity to specific groups of travellers. This might be important in order to ensure that key workers can reach hospitals, care homes, schools or other destinations safely and in compliance with social distancing rules. The reservation system is also suitable to give priority to disadvantaged travellers, and adopt price discrimination based on social equity considerations.
Practical applicability
The implementation of an online travel slot reservation system via smartphone applications and other electronic channels is feasible from a technological point of view.
7 Alternative means of advance booking must remain available for disabled passengers, those who experience technical failures on their devices temporarily, and those who do not have access to such devices. The reservation and ticketing system must also comply with the relevant privacy regulations.
The key prerequisite of the successful implementation of a network-wide reservation system is that both passenger and train movements remain punctual. Naturally, if passengers arrive earlier than the pre-booked entry time, they have to wait in front of the station which requires sufficient buffer space locally. Late arrivals cannot be corrected this way, and therefore the system has to be prepared for minor adjustments in individual itineraries. The scheduling problem is even more pronounced in large multimodal networks where late passenger arrivals at entry stations might be caused by unreliability or disruptions on feeder services. If the available capacities are fully booked in a given period of time, disruptions might have a cascading effect throughout the network, as entry queues caused by the delay cannot be reduced rapidly. Nevertheless, the fact that the operator has reliable information on future demand can make disruption management with the use of extra capacity and optimised diversions more effective than usual.
Advanced quantity control techniques
The final group of demand management methods discussed in this paper are also direct quantity control tools with advance booking, but their slot allocation processes are based on bidding mechanisms instead of a FIFO rule. We first discuss permit auctions, followed by an extension to tradeable permit schemes.
An alternative way in which capacity reservations can be organised is an auction system where potential travellers bid for the available capacity. In order for an auction mechanism to reach efficient capacity allocation, an iterative process has to be implemented, primarily to allow the winning bids to approach the optimal market price, and leave sufficient consumer surplus with travellers. In a digital environment, the bidders do not need to be the users themselves; their preferences can be represented by an automated bidding logic, and thus several hundreds of auction iterations can be performed virtually within reasonable computing time (Iwanowski et al.
2003).
Once again, we find more road use related applications in the literature. In a recent contribution, Su and Park (
2015) develop a highly granular agent-based simulation tool in which travellers’ value of time and preferred arrival time are unique. Their bidding logic performs a blind and greedy search among the available travel time intervals on a highway, with varying bid levels, in a series of consecutive iterations. They show the convergence of the bidding process and its effectiveness in guaranteeing congestion-free travel on the simulated highway section. This auction algorithm has not yet been adapted for public transport.
After an auction or a direct initial allocation of travel permits, their holders may also be allowed to resell their right to travel on secondary markets, thus implementing a tradeable travel permit scheme.
8 The concept of tradeable credit mechanisms as an alternative to congestion pricing has been present in the road traffic management literature since Verhoef et al. (
1997) and Goddard (
1997), and in-depth reviews of this emerging literature are provided by Fan and Jiang (
2013), Grant-Muller and Xu (
2014) and Dogterom et al. (
2017).
The main benefit of a tradeable permit scheme, in comparison with pure pricing techniques, is on the equity and social acceptance side. The essence of such schemes is that travel credits are distributed among all residents according to a predetermined rule, and then those who actually intend to travel regularly must buy additional credits from those who do not. Thus, the scheme achieves an efficient allocation of the available capacity, but those who would be priced off public transport when capacity is limited receive a direct monetary payment. Potential users with low or zero willingness to pay can earn a net income from the scheme. It is well known that the social acceptance of usage-based transport pricing depends heavily on how the revenues are redistributed (Parry and Bento
2001) – the tradeable permit scheme is in fact an auction where revenues are immediately redistributed to non-users, thus making all groups of society interested in the implementation of the policy, and avoiding large monetary transfers to the government. The initial allocation of quotas can be uniform among the population, or non-uniform according to the regulator’s distributional objective. Brands et al. (
2020) raise a word of caution: The initial allocation of permits is also susceptible to corruption. This threat could make the social acceptance of permit schemes less trivial in many emerging economies.
Practical applicability
Even though the theoretical advantages of capacity auctions and tradeable credit schemes are consensual in the literature, their implementation with the aim of achieving social distancing in public transport may be challenging. The challenges stem from the spatially and temporally unstable nature of demand, which requires that capacity, which is perishable, has to be defined individually for each line section and time period. In broad terms, this highly disaggregate product can be auctioned and traded in multiple ways:
(A)
Each spatio-temporial block of capacity has to be associated with a unique set of permits, which are then auctioned/traded prior to its period of validity, individually.
(B.1)
Travel credits are used as a dedicated currency for travelling with their own market value, and the operator or regulator determines how many credits have to be paid for using a spatio-temporal segment of capacity, depending on how stringent the capacity constraint is. Users exchange the credits directly, as part of an online bargaining process or brokerage. The volume of credits is constant.
(B.2)
Travel credits are used as tokens with a time-varying credit charge function, but the credits have to be bought or sold from or to a centralised bank, which controls their price. Thus, the volume of credits may vary over time.
(C)
Travel credits are associated with a given amount of transport consumption. In road transport, this is often measured by vehicle miles travelled (Verhoef et al.
1997; Yang and Wang
2011), the days of week when access is unlimited (Goddard
1997), or the number of individual trips to be taken (Fiorello et al.
2010). Restrictions may apply though on the geographical area and time of day that the credit can be used.
Options B.1, B.2 and C offer several practical benefits in general transport capacity allocation problems, but their usefulness for the specific case of social distancing in public transport appears to be limited. To implement B.1 and B.2, the same amount of demand-side information would be required when setting the credit price of capacity segments as what differentiated pricing requires (see Section
4.2), to ensure that demand never exceeds the critical occupancy rate. This version of the tradeable credit scheme is in fact equivalent to a revenue neutral monetary surcharge-reward scheme proposed by Kalmanje and Kockelman (
2004) for road pricing, and more recently adapted to public transport by Tang et al. (
2020b). Moreover, Bao et al. (
2019) show that option B.1 might lead to an unstable equilibrium in the standard bottleneck model, and therefore the welfare gain it provides is also uncertain.
In option C, permits would allow travelling a predetermined distance in the public transport system. Given that demand can be heavily imbalanced both spatially and temporally, controlling the total passenger miles within the system does not guarantee that social distancing is not violated anywhere and anytime.
This leaves us with option A, if the goal is to keep vehicle occupancy rates below an exogenous level. This can be considered as the public transport equivalent of the road demand management scheme proposed by Akamatsu and Wada (
2017). Verhoef et al. (
1997), Yang and Wang (
2011) as well as Fan and Jiang (
2013) raise concerns about the practical implementation of this approach, as “the [roadway] network may produce a tremendous number of distinct permits for every [roadway] link, at each time interval”, which makes trading “practically inconceivable” (Fan and Jiang
2013). Akamatsu and Wada (
2017) defend their position by proposing that “the implementation of these [time-space specific tradeable permits] would become feasible with advanced vehicles in which an agent software is installed to automatically trade permits based on users’ preferences”. The behavioural and travel demand implications of automated permit trading has not yet been shown in the literature, to the best of our knowledge.
Despite considerable efforts in the past 25 years aimed at understanding the theoretical properties and economic performance of travel demand management with tradeable permits, practical implementations are rarely reported in the literature. Brands et al. (
2020) document the first such experiment we are aware of, in which a small sample of participants tested a virtual parking permit application. Off-the-shelf methods for tradeable permit schemes are not yet available for implementation in public transport.