University of Groningen
Taxi-hailing platforms
Sun, Luoyi; Teunter, Ruud H.; Hua, Guowei; Wu, Tian
Published in:
Transportation Research. Part B: Methodological
DOI:
10.1016/j.trb.2020.10.001
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from
it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
2020
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Sun, L., Teunter, R. H., Hua, G., & Wu, T. (2020). Taxi-hailing platforms: Inform or Assign drivers?
Transportation Research. Part B: Methodological
,
142
, 197-212. https://doi.org/10.1016/j.trb.2020.10.001
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.
More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-
amendment.
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 10-08-2022
Transportation Research Part B 142 (2020) 197–212
Contents lists available at ScienceDirect
Transportation Research Part B
journal homepage: www.elsevier.com/locate/trb
Taxi-hailing platforms: Inform or Assign drivers?
Luoyi Sun
a , 1
, Ruud H. Teunter
b , 2
, Guowei Hua
a , ∗
, Tian Wu
c , 3
a
Beijing Jiaotong University, Beijing, China
b
University of Groningen, The Netherlands
c
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
a r t i c l e i n f o
Article history:
Received 27 August 2019
Revised 4 September 2020
Accepted 4 October 2020
Available online 7 November 2020
Keywords:
Sharing economy
Two-sided market
Peer-to-peer market
Ride-sourcing platform
a b s t r a c t
Online platforms for matching supply and demand, as part of the sharing economy, are
becoming increasingly important in practice and have seen a steep increase in academic
interest. Especially in the taxi/travel industry, platforms such as Uber, Lyft, and Didi Chux-
ing have become major players. Some of these platforms, including Didi Chuxing, operate
two matching systems: Inform, where multiple drivers receive ride details and the first
to respond is selected; and Assign, where the platform assigns the driver nearest to the
customer. The Inform system allows drivers to select their destinations, but the Assign
system minimizes driver-customer distances. This research is the first to explore: (i) how
a platform should allocate customer requests to the two systems and set the maximum
matching radius (i.e., customer-driver distance), with the objective to minimize the overall
average waiting times for customers; and (ii) how taxi drivers select a system, depending
on their varying degrees of preference for certain destinations. Using approximate queuing
analysis, we derive the optimal decisions for the platform and drivers. These are applied to
real-world data from Didi Chuxing, revealing the following managerial insights. The opti-
mal radius is 1-3 kilometers, and is lower during rush hour. For most considered settings,
it is optimal to allocate relatively few rides to the Inform system. Most interestingly, if des-
tination selection becomes more important to the average driver, then the platform should
not always allocate more requests to the Inform system. Although this may seem counter-
intuitive, allocating too many orders to that system would result in many drivers opting
for it, leading to very high waiting times in the Assign system.
©2020 Elsevier Ltd. All rights reserved.
1. Introduction
Online platforms have been developed for many industries in recent years, and their popularity and use are rapidly
increasing ( Wang and Yang, 2019 ). For instance, the emergence of Uber, Lyft, and Didi Chuxing has provided passengers
with a new, convenient travel mode. According to the China Online Takeaway Market Monitoring Report for the First Half of
2018 , the market size of food delivery in China alone exceeded 26 billion euros in 2017 ( iiMedia Research, 2018 ).
∗
Corresponding author at: No. 3 Shangyuancun, Haidian District, Beijing, China.
E-mail addresses: luoyisun@bjtu.edu.cn (L. Sun), r.h.teunter@rug.nl (R.H. Teunter), gwhua@bjtu.edu.cn (G. Hua), wutian@amss.ac.cn (T. Wu).
1
No. 3 Shangyuancun, Haidian District, Beijing, China.
2
University of Groningen, PO Box 72, 9700 AB Groningen, the Netherlands.
3
No. 55 East Zhongguancun Road, Haidian District, Beijing, China.
https://doi.org/10.1016/j.trb.2020.10.001
0191-2615/© 2020 Elsevier Ltd. All rights reserved.
L. Sun, R.H. Teunter, G. Hua et al. Transportation Research Part B 142 (2020) 197–212
Different from the one-way value stream from suppliers to consumers for traditional enterprises, platforms’ costs and
benefits come from both ends. That is to say, platforms gain profit by building a communication bridge between suppliers
and customers. Thus, the efficiency of matching supply and demand is the key factor that drives platforms’ operational
efficiency and optimizes resource allocation.
There are basically two main matching systems in use by platforms: the Inform (also referred to as Grab Single) system,
where the platform acts as an information platform only and suppliers decide who to offer their services to; and the Assign
system where the platform itself assigns a supplier to a customer ( Gao, et al., 2016 ; Wang et al., 2016 ; Dai et al., 2017 ; Li and
Wang, 2017 ). For online car hailing platforms, in the Inform system, the first driver to respond (in a certain area) is selected
and matched to the customer. It is a fair system that allows drivers to control their destination area, by only responding to
associated customer requests ( Sina, 2017a , 2017b ). A disadvantage of this system, however, is that the assigned driver might
not be the one closest to the passenger, increasing the time until the customer is picked up ( Dai et al., 2017 ). In the Assign
system, this can be prevented by the platform, which typically selects the closest available driver. However, in this system,
drivers lose their freedom of choice and can’t refuse requests to transport customers to an area that they dislike.
A number of online car hailing platforms, including Didi Chuxing, Shouqi Limousine & Chauffeur and Yidao Yongche,
allow drivers to opt between these two systems. Some other platforms, such as Uber, use one system that can be seen
as a mixture of the two that we consider. Uber inquires nearby drivers in turn, from close to distant, until one agrees to
accept the order. This has the advantage of limiting driving times, whilst still allowing drivers to reject rides. However, this
system cannot reward more flexible drivers by assigning more rides to them. Also, the average matching time will increase,
negatively affecting the average customer waiting time. The pros and cons of a mixed system compared to that with two
separate systems is interesting to analyse. However, that is beyond the scope of this study, which compares the two different
matching systems.
Obviously, how the platform allocates rides to the two systems affects how attractive those systems are to the drivers,
and so affects the driver system selection. Ride allocation should ensure a good matching of supply and demand on both
systems. Besides, to avoid large customer-driver distances and so long en route times, an important control lever is to set a
maximum ‘radius’ ( Castillo et al., 2017 ). Our main goal is to find out what allocation rates and radius minimize the overall
expected waiting time. To the best of our knowledge, we are the first authors to do so.
Not all drivers have the same degree of preference for certain destinations over others. For instance, some drivers may
want to avoid remote areas of a city more than others. Also, not all drivers are equally knowledgeable about different areas.
Some are more experienced and/or have better access to real-time information, allowing them to differentiate better be-
tween good/preferred areas and bad/non-preferred areas. As a result, drivers are expected to be heterogeneous with respect
to their preferences. We will take this heterogeneity into account when analysing the allocation decision for the platform.
To analyse the matching efficiency on the platform with the two described systems and with heterogeneous drivers, we
adopt an M/M/1 queuing approximation for both systems where drivers act as the server. We explore the strategic interac-
tions between the platform and the drivers. In the presence of drivers’ heterogeneity, drivers are offered a choice between
the two operating systems and decide based on their regional preference. The platform sets the maximum customer-driver
distance and decides what fractions of customer requests for good areas to assign to each system, which affects a driver’s
probability to reach to a good area and thereby the system selection decision. In order to avoid congestion, the platform
minimizes the customers’ expected waiting time (i.e. the sum of the matching time and the driver en route time to the
customer), and we derive the optimal distribution rate of rides to good areas over the two systems as well as the optimal
radius. We remark that although we refer to the case of ride-sourcing platforms in this study, our results also apply to other
online platforms where platforms can either assign suppliers itself to a customer request or allow a selection of suppliers
to service the customer.
A key finding is that, based on real life data collected for the Chengdu car hailing market, a radius of 1-3 kilome-
ters is optimal. This provides the optimal balance between ensuring a sufficient number of available drivers to avoid long
matching times and avoiding long en route times (of the driver to the customer). Moreover, the optimal radius is smaller
during rush hour, because of the lower driving speed. Furthermore, for most considered settings, a relatively small frac-
tion of rides (of about 10%) should be allocated to the Inform system, because the Assign system minimizes customer-
driver distances. However, a much higher allocation rate (50%-60%) is optimal when either there is a small proportion
rides to bad destinations under bad traffic conditions, or there is a small proportion of rides to good destinations under
good traffic condition. Also, and most interestingly, if the degree of preference for good rides increases for the average
driver and so the Inform system becomes more popular, then the platform should not always increase the allocation rate to
that system. Otherwise, the Inform system may attract too many drivers, leading to very long waiting times in the Assign
system.
The remainder of the paper is organized as follows: In Section 2 , we review the related literature. In Section 3 , we
present the problem and formulate the model. Section 4 contains the analysis. In Section 5 , we conduct an empirical study
based on the ride-hailing market in Chengdu to derive managerial insights. Finally, Section 6 provides a conclusion.
2. Literature review
Online car hailing platforms are a typical example of two-sided markets in the growing peer-to-peer sharing economy
( Djavadian and Chow, 2017 ; Nourinejad and Ramezani, 2019 ). There is a growing stream of literature that focuses on the
198
L. Sun, R.H. Teunter, G. Hua et al. Transportation Research Part B 142 (2020) 197–212
effective matching of supply and demand for such markets, while keeping search frictions low. As our research also cen-
ters around matching, this is the main focus of our review. We next discuss key contributions on matching in general in
Section 2.1 , before moving on to matching under spatial references in Section 2.2 . Thereafter, in Section 2.3 , we point out
our contribution.
2.1. Matching buyers and sellers
We first discuss studies that primarily focused on matching, as our study is. Yang et al. (2010) introduced an equilibrium
model to explore the bilateral searching and meeting frictions between customers and taxis on road networks. Yang and
Yang (2011) further explored properties of the market equilibrium and the meeting function between customers and taxis
for the traditional taxi market. Their analysis is based on the observation that, in equilibrium, the expected number of
times that a customer randomly encounters a driver and vice versa in some area during a certain period of time (e.g. 1
hour) must be equal. He and Shen (2015) made the first attempt on determining a matching function for online car hailing,
assuming that customers are homogenous with respect to waiting time and that the ride length is constant. Others extended
their work by considering platform profits, social welfare, subsidies strategies, and customer cancellation behaviour when
determining equilibrium matching functions ( Zha et al., 2016 ; Wang et al., 2016 ; Wang and Yang, 2019 ; Wang et al., 2020 ).
To analyse waiting times, many researchers modelled the matching process for the sharing economy as a queuing sys-
tem ( Banerjee et al., 2015 ; Feng et al., 2017 ; Hu and Zhou, 2017b ; Bai et al., 2018 ; Benjaafar et al., 2018 ; Taylor, 2018 ;
Nourinejad and Ramezani, 2019 ; Xu et al., 2020 ), where buyers arrive according to a Poisson process, and sellers function
as servers. Benjaafar et al. (2018) considered car sharing and modelled the matching between car owners and renters by
a multi-server loss queuing system. They further compared two types of platforms based on profit-maximizing and social-
welfare-maximizing, respectively, in terms of general impacts, including ownership, usage, and social welfare. They found
that the transition to a sharing economy can result in either lower or higher ownership and usage levels, with higher owner-
ship and usage levels more likely when the cost of ownership is high. Sun et al. (2019) explored the matching of supply and
demand for ride-sourcing platforms by providing per service price determination for any specific ride request. They derived
the optimal pricing strategy by taking ride details and driver location into account, and found that the optimal pricing struc-
ture for successful matchings includes three parts: (a) a base fare based on the ride length, (b) a rush hour congestion fee,
and (c) an emergency fee. Mo et al. (2020) modelled the matching of drivers and riders in a duopoly competition between
two ride-sourcing platforms to study optimal subsidization of electric vehicles. Their numerical results revealed that when
the returns to scale are significant, the platforms revenue, ride price, and consumer surplus may not be monotone functions
of the subsidy. Using bilateral meeting functions, Wang et al. (2020) modelled the matching rates for ride-sourcing and taxi
markets. They found that the order cancellation rate is negatively correlated with the customer waiting time, as customers
may switch to a taxi whilst waiting to be picked up by a ride-sourcing car. Yang et al. (2020) considered the matching
time interval and matching radius as two decision variables in order to optimize the matching process in a ride-sourcing
platform, considering the matching rate, expected waiting time, and pick-up time. Theoretical and numerical findings both
showed that the matching rate and expected pick-up time increase with the matching radius up to some threshold for that
radius, and then become independent of the radius. Moreover, when the supply is considerably larger than the demand, an
optimal matching time interval can maximize the system performance.
Many matching studies have considered heterogeneity at the demand side, for instance because of customer impatience
under congestion ( Bai et al., 2018 ; Ibrahim, 2019 ) and under time-related uncertainty of demand ( Jiang and Tian, 2019 ;
Hu and Zhou, 2017a ). Some researchers have centered on the heterogeneity at the supply side ( Hu and Zhou, 2017a ;
Ibrahim, 2019 ; Chen et al., 2020 ). For example, Ibrahim (2019) explored the problems of staffing and controlling queuing
systems in sharing economies, taking the randomness in the number of servers into account, where a shortage of supply
creates congestion in the system. Hu and Zhou (2017a) considered matching (for transportation, but also more generally)
between two types of supply and demand during multiple time periods, where the rewards for each potential matched pair
are given and costs are incurred at the end of each period for unmatched supply and demand. Although they allowed supply
to be heterogeneous, they assumed that the number of suppliers of the different types as well as the demand are exogenous
and observed.
2.2. Matching with spatial variability features
A key aspect of our work is that we include spatial preferences on the supply side. Only in the last few years, re-
searchers have started to pay attention to spatial variability when matching supply and demand. Rayle et al. (2016) fo-
cused on the spatial distribution of passengers and drivers, capturing the spatial distribution of trip origins and destina-
tions within San Francisco through a survey. In order to achieve a higher efficiency of matching, they tried to eliminate
the differences between regions through spatial pricing, which provides drivers with an incentive to move to over-demand
zones. Bimpikis et al. (2016) showed that differentiating the price based on customer location can indeed increase profits
for drivers and the platform as well as the consumer surplus. Guda and Subramanian (2019) considered the strategic in-
teraction amongst drivers in their decisions to move between two zones, and found that surge pricing can be profitable
even in a zone where the supply of drivers exceeds demand. They focused on whether a driver will move to another area
due to surge prices, where the remaining customers are lost in congestion. Zha et al. (2018) divided an urban region into
199
L. Sun, R.H. Teunter, G. Hua et al. Transportation Research Part B 142 (2020) 197–212
different geographic zones and further investigated the optimal price in each zone under demand surges. They aimed at
the same profitable level across different regions and determined the corresponding optimal pricing scheme for each region.
Nair et al. (2020) developed a nonlinear-in-parameters multinomial logit (NPMNL) model to forecasting the destinations of
deadheading trips on ride-sourcing, taking location specific characteristics (i.e., the built environment, employment oppor-
tunities, and socio-demographic characteristics) into account. Using publicly available data from Ride Austin, the showed
increased accuracy compared to a multinomial logit (MNL) model.
2.3. Contribution
As is transparent from our literature review, so far studies about matching in sharing economy have mainly focused on
the heterogeneity at the demand side. Studies that did consider heterogeneous supply, develop optimal work schedules in
the presence of self-scheduling suppliers that have the flexibility to choose whether and when to work ( Zha et al., 2018 ;
Gurvich et al., 2019 ; Ibrahim, 2019 ).
We consider the flexibility of workers/drivers from a different and new perspective, by allowing them a choice between
operating systems, motivated by this choice being available in a number of real life car hailing platforms, as discussed in
Section 1 . We model how destination preference affects the choice of a driver between the systems. We derive insights into
how the platform should allocate rides to the two systems and how the platform should set the radius (i.e., the maximum
driver-customer distance), in order to minimize the overall expected waiting time for customers across systems.
3. The model
The model is applicable to platforms that connect supply and demand using two systems, Inform (where the first driver
to respond is assigned) and Assign (where the platform directly assigns a driver), which from now on we will also refer to
as systems I and A , respectively, for notational ease. Furthermore, we classify destinations as good or bad (e.g. central or
remote, respectively) and consider heterogeneity in driver preference between both types of destinations.
In what remains of this section, we first present some model basics ( Section 3.1 ), then discuss platform ( Section 3.2 ) and
driver ( Section 3.3 ) specifics and decisions, and finally describe our approximate queuing approach ( Section 3.4 ).
3.1. Basic considerations
We consider a single period (of e.g. one hour), where the platform decides what fractions of customer requests to allocate
to either system and the maximum driver-customer distance (radius), and drivers determine their system choice. We assume
that drivers are fully informed on how the platform allocates rides, and that drivers make their system decisions based on
the allocation rate announced by the platform at the start of the period. In real life, dependent on changing traffic conditions
and customer request rates, the platform may alter the allocation fraction from one period to the next and drivers may
adjust their system choice accordingly. Analysing such dynamic behaviour over time is of interest, but outside our scope.
This exploratory paper considers a single period, i.e., a snapshot of the system. We also remark that the platform could set
different radiuses for the two systems, but as the main purpose in both systems is to limit the driver-customer distance, it
seems natural to use the same radius for both systems.
We consider an area with known driver density E , i.e., with E taxi drivers per square kilometer. Furthermore, taxi drivers
are uniformly distributed over (parts of) the area. In our analysis in the next section, we will particularly focus on circular
areas around a customer request, because drivers are only interested in and/or considered in a request if their distance to
the customer is not too large. Letting R denote the radius of such an area, r the distance to the customer, and the angle
between a driver and the positive r -axis, the uniform distribution implies that the polar coordinates of a driver, (r , ), follow
the probability density functions:
f
r
(
r
)
=
2 r
R
2
, 0 ≤ r ≤ R, (1)
f
θ
(
)
=
1
2 π
, 0 ≤ ≤ 2 π,
and the corresponding probability distribution function of the distance between any driver in this area and the customer
is
F
r
(
r
)
=
r
2
R
2
, 0 ≤ r ≤ R.
Customer requests arrive according to a Poisson process at a rate of per square kilometer. The corresponding locations
are distributed uniformly over the considered area, i.e., equally likely to occur at any point of that area. Each request is for
a good (destination) area with probability f
g
and so for a bad area with probability f
b
= 1 − f
g
. Thus, customer requests for
good and bad areas ( Z = g, b ) arrive according to Poisson processes with rates
Z
= f
Z
· .
All customers wait for the first taxi that becomes available - so we do not consider a maximum waiting time. In practice,
customers may of course leave the system after a long wait, and probably show heterogeneity in their behaviour. However,
modelling such behaviour is outside the scope of this paper.
200
