Modeling the decision of ridesourcing drivers to park and wait at trip ends: a comparison between Perth, Australia and Kolkata, India

Abstract

It is often difficult for the ridesourcing drivers to get a trip immediately after dropping off a passenger. The main objective of the drivers is to increase their income by serving more trips. The most prominent options available to the drivers after reaching passengers’ destinations are: (a) park and wait in and around their drop-off location, (b) cruise in and around their drop-off location and (c) drive to another location to receive trip requests quickly. Previous studies were conducted to understand the driver behaviour in a taxi and other similar services. However, the perception of ridesourcing drivers on parking and waiting after dropping off passengers is yet to be explored. The drivers’ decision on waiting can affect users’ waiting time, the number of matched trips by the TNCs, and parking spaces in the city. Moreover, drivers’ waiting time tolerance can also impact other drivers’ total number of trips, total earnings, total distance travelled in the city, and fleet size. The aim of this study is to understand the influence of drivers’ characteristics on drivers’ decision to park and wait after dropping off a passenger. This study estimates and compares the waiting time tolerance of the ridesourcing drivers using a zero-inflated cox spline model between Perth and Kolkata. It is observed that drivers in Kolkata have higher waiting time tolerance than Perth drivers. Moreover, the drivers in both the cities are more likely to wait at high-demand areas urging the urban authorities to determine spatio-temporal parking demand to design the parking infrastructure for such areas.

Introduction

The Transportation Network Companies (TNCs) (e.g., Uber, Ola, or DiDi) use a pool of drivers to address the ride requests generated by the users. The drivers play a significant role as one of the primary stakeholders to fulfill the supply needs catering to the demand for On-Demand En-Route Ride (OnERide) services (Chakraborty et al. 2020), popularly known as rideosurcing services. As the demand for ridesourcing services is spatio-temporal, it is often difficult for the drivers to get a trip immediately after dropping off a passenger. The time spent by a driver without a passenger is often referred to as the ‘idle time’ of the driver. The driver either waits at a specific location or drives to another location to receive trip requests quickly during this period.

The drivers of OnERide services need to make decisions on several aspects, like, schedule and area of operation, acceptable pick-up time, acceptance of incoming requests, and activities to undertake when they do not have passengers on board. Once a driver completes a trip, the driver can decide to wait or adopt other available options based on exogenous factors like available information on hotspots, traffic condition, weather, availability of parking in and around their current location, and their personal experience. The drivers’ decision on waiting can directly impact the number of trips served, thereby influencing their income.

Although studies like Zheng et al. (2018) and Zhang et al. (2018) have explored drivers’ tactical and operational decisions in China and United States respectively, study on ridesourcing drivers’ waiting strategy is yet to be explored. The drivers' waiting time tolerance depends on time and location and is also related to their experience, driving behaviour, and socioeconomic characteristics. For example, the drivers are more likely to reduce their idle time during their working hours when they receive back-to-back trip requests. Currently, limited studies have been conducted to quantify the impact of various factors on drivers’ idle time decisions. Furthermore, the driving behaviour and characteristics of ridesourcing drivers are different from the traditional taxi services. Besides, the driver characteristics observed in the U.S. (Hall and Krueger 2016) and Chile (Fielbaum and Tirachini 2020) had certain similarities and dissimilarities. To the best of our knowledge, no studies have been conducted to compare the park and wait decisions adopted by the drivers during their idle time between developed and developing nations.

The study compares the influence of drivers’ characteristics on drivers’ decision to park and wait after dropping off a passenger between different ridesourcing market using two case studies in Perth, Australia, and Kolkata, India. The study adopted one of the survival analysis, a zero-inflated cox spline model, to estimate the waiting time tolerance of the ridesourcing drivers (Cox and Oakes 1984; Tian and Olshen 2015; Zhang 2005). This study can provide valuable insights to the TNCs regarding the characteristics of drivers who are willing or not willing to wait. Moreover, this study will also help the TNCs to understand the waiting time duration of these drivers. The TNCs can use the study’s outcome to set up their back-to-back application for better relocation strategies for the drivers and devise efficient pricing strategies. The drivers’ willingness to wait at a specific location can also estimate the parking requirement for the city authorities, enabling the urban authorities to design an efficient parking infrastructure and formulate parking policies for the ridesourcing services.

Literature review

Existing literature on the drivers of OnERide services is quite limited. Ridesourcing, one of the OnERide services have certain similarities with the taxi market regarding hiring of personal drivers, non-stop service between start and destination, exclusive hiring for users and queuing mechanisms. Therefore, research on taxi services can also provide valuable insights regarding the characteristics and behaviour of the drivers. Research on the drivers focus on different aspects like drivers’ characteristics (Hall and Krueger 2016), their wage and income (Chou 2002; Farber 2005; Henao and Marshall 2017; Sheldon 2016; Sun et al. 2019), various behavioural patterns (Kooti et al. 2017; Leng et al. 2016; Yang et al. 2010a; Yang and Wong 1998; Zheng et al. 2018), job satisfaction (Fielbaum and Tirachini 2020), safety & security (Schwendau 2017) and impacts of regulation on market entry and fare structure (Yang et al. 2002). Some studies have also explored the differences in drivers’ operation between taxi and ridesourcing services (Angrist et al. 2017; Liu et al. 2018).

It must be noted that the drivers in taxi and ridesourcing market get their riders based on street hailing and assignment algorithms respectively. However, the drivers in both the markets tend to increase their earnings by maximising their trips. So, the drivers would be eager to stay at location where they can get higher number of passengers. In this regard, the drivers may adopt different decisions to meet their next passenger as shown in Yang and Wong (1998) for the taxi market. Yang et al. (2010b) modelled such decisions of the drivers using a fixed-point algorithm with embedded logit models. The taxi and ridesourcing drivers may also choose to drive to different location if they are not able to get a passenger at their current location. Such decision to drive to a specific location depend on factors like travel distance and perceived profit that can be modelled using multinomial logit models (MNL) as found in Wong et al. (2014b). The study was further extended to model various decisions of taxi drivers on driving to a taxi stand using a sequential logit model based on 258 observations collected through a stated-preference (SP) survey. In addition to travel distance and profit, the research also found congested road condition to be a significant variable influencing drivers’ decision on driving to taxi stands (Wong et al. 2014a, b). Although designated ridesourcing stands are uncommon, the ridesourcing drivers may choose to drive to hotspots either based on the recommendation provided by the TNCs or their individual experience.

Apart from understanding the factors influencing drivers’ decision on passenger-search, Zhang et al. (2018) also formulated a latent class model using the detailed trip data of 13,000 taxis in New York City to investigate drivers’ behaviour outside downtown areas and found that the destination preference to search passengers varied significantly across the drivers. Such preference for destination may also be prevalent among the ridesourcing drivers since the ridesourcing drivers are assigned with the riders within their proximity. Different decisions adopted by the drivers related to passenger search may be affected based on the recommendations provided for both taxi and ridesourcing market. Szeto et al. (2019) investigated various factors influencing the drivers’ decisions on recommended areas through a sequential binary logistic regression (SBLR). They analysed 6705 observations and found that “taxi-calling signals” informing drivers about passengers played a significant role in affecting drivers’ decisions. Apart from recommendation, drivers can modify their activities based on their past experiences. Such anticipatory behaviour of the drivers at airports was simulated using a Bayesian updating technique in Zheng et al. (2018). The drivers in taxi and ridesourcing market may also need to decide on accepting an incoming request. Leng et al. (2016) and Xu et al. (2018) found that economic incentives significantly influence drivers’ response behaviour to a request in taxi markets.

The decision on the time taken by the drivers to reach passengers’ location (pick-up times) can affect their income. Such decisions are common for both taxi and ridesourcing market. Rong et al. (2017) found a positive correlation of pick-up times with the total income of the taxi drivers. Income in taxi and ridesourcing market is directly related to trip frequency of the drivers. The daily trips made by the drivers depend on their individual characteristics as shown in Kooti et al. (2017) who used logistic regression to determine a group of ridesourcing drivers having higher trip frequency.

Individual characteristics tend to affect drivers’ behaviour (Wang et al. 2016). Researchers highlighted various socio-economic as well as operational characteristics of the ridesourcing drivers. These characteristics can affect drivers’ decisions during their idle time. Existing literature highlighted that the drivers’ characteristics for ridesourcing services can be defined in terms of age, gender, education, vehicle ownership, working schedule, service duration, time and day of operation (Chen et al. 2017; Chen and Sheldon 2015; Fielbaum and Tirachini 2020; Hall and Krueger 2016; Kooti et al. 2017; Wang and Smart 2020). Studies on ridesourcing drivers also highlighted drivers’ preferences related to work schedules and car ownership (Chen and Mahmassani 2015; Wang and Smart 2020).

Other studies on drivers of ridesourcing and similar services explored the effects of regulation on drivers’ entry to the market (Yang et al. 2002), comparison of distinct characteristics of taxi and ridesourcing drivers (Angrist et al. 2017; Liu et al. 2018), prediction of drivers’ location (Rossi et al. 2020; Yuan et al. 2011), safety issues encountered by the drivers and security provided to them from the TNCs (Schwendau 2017), and assessment of satisfaction of the drivers while working with the TNCs (Fielbaum and Tirachini 2020).

With reference to the above studies, it is observed that the drivers’ decisions related to passenger search has been examined by the researchers mostly for the taxi market. However, drivers’ decisions related to waiting for both taxi and ridesourcing market are yet to be explored. It must be noted that the taxi drivers enjoy more flexibility in searching passengers compared to the ridesourcing drivers. Unlike taxi drivers, the ridesourcing driver may get a request immediately in peak hours and the ridesourcing drivers also have less freedom in case of pre-determined trip chains. But in many cases the request for next ride request is not immediate due to spatio-temporal demand variation. Besides, the taxi drivers are subjected to penalties in case of trip rejections (NYCTLC 2016). Such penalties are yet to be implemented in the ridesourcing market and ride rejections of the ridesourcing drivers have often been reported (Romanyuk 2017). Moreover, studies have highlighted that many taxi drivers have shifted to the ridesourcing market (Kashyap and Bhatia 2018; Peticca-Harris et al. 2020). Therefore, it is essential to investigate drivers’ decision on waiting for the ridesourcing market. Moreover, the research on the significance of spatial locations on drivers’ decision is also quite limited. While Zheng et al. (2018) highlighted the importance of the arrival time of the flights on drivers’ decisions, Zhang et al. (2018) mentioned the difference in customer searching behaviour between inside and outside of central city areas. Both the studies emphasised the influence of spatial locations on drivers’ behaviour. This implies that the drivers’ decisions at different spatial locations will be unique and must be recorded separately. Hence, this study has focused on the drivers’ decision on waiting after dropping off passengers at certain areas.

The time spent by the drivers after dropping off a passenger before receiving the subsequent request is referred to as the idle time of the drivers (Martinez et al. 2015). The drivers can park their car and wait at a certain location or cruise to other locations. Therefore, the idle time will take both the waiting and cruising time of the drivers into consideration. This study defines the waiting time of the drivers as the total time spent by the driver in waiting along with a parked vehicle. The main research focus of this study is to determine the drivers’ waiting time tolerance at certain locations. Waiting time tolerance can be defined as the maximum threshold time after which the driver re-examines his decision of park-and-wait. To the best of our knowledge, a study on drivers’ waiting time is yet to be explored. This study has considered two aspects related to drivers’ decision on waiting based on field observations, (a) decision of the driver to wait at a location after dropping off a passenger, and (b) how long the driver is likely to wait. This study also attempts to understand the difference in drivers’ characteristics in the context of two different ridesourcing markets and its impact on driving behaviour with respect to their decision to park-and-wait.

Researches having similar objective as the current study used survival analysis to understand transit users’ response behaviour using accelerated failure time (AFT) models (Rahimi et al. 2019), assess user waiting time on information interfaces through Kaplan–Meier estimator (Asthana et al. 2015) and estimated waiting time of the graduates for their first employment opportunity using Cox Proportional Hazard (PH) and AFT model (Getie Ayaneh et al. 2020). The analysis of time to drivers’ change in decision to park-and-wait is also similar to the fundamental theory of survival analysis. Therefore, this study determines the perceived waiting time tolerance of the drivers through survival models. The zero-inflated cox spline regression used for analysis is discussed in detail in “Methodology” section.

Study areas and data collection

Study areas

The operation of the ridesourcing services is governed by the government regulations, dispatching algorithms, and human behaviour. So, the nature of ridesourcing market tend to vary across locations. Hence, this research has included two different areas across continents to study the impact of varying nature of ridesourcing market on drivers’ behaviour. These areas are, Perth in Australia and Kolkata in India.

Perth, one of the major cities of Australia, is considered as the fourth most automobile-dependent city with one of the urban areas with lowest population density (1210 persons per km²) across the globe. The ridesourcing services were introduced in Perth in July 2014 (McNeill 2016). Although ridesourcing was launched in Perth much later compared to other Australian cities, the highest adoption rate of these services was observed in the state of Western Australia where 23.9% of its residents used Uber to reach their destination (McNeill 2016; Roy Morgan Research 2017). The Transport (Road Passenger Services) Act 2018 enables regulations of the on-demand transport services like ridesourcing in Perth. As per the Transport (Road Passenger Services) Regulations 2020, the on-demand service providers (TNCs) must be an authorised provider that enforce them to provide a safety management system, an updated database for the drivers and bookings, and an efficient complaint redressal mechanism (Western Australia 2020). Besides, the drivers driving under TNCs also need to obtain a Passenger Transport Vehicle (PTV) On-Demand Charter (OD-C) authorisation.

Kolkata,1 one of the highly dense metropolises (7978 persons per sq. km) located in the eastern part of India, has nearly 12 different public transit modes (Basu 2022) to cater to the requirements of the commuters. The ridesourcing services were launched in Kolkata in late 2012 by a TNC based in India. Soon, other global TNCs also began their operation by 2014. The ridesourcing services soon gained popularity among the users in Kolkata with nearly 13% of the population using ridesourcing as their mode of travel (Chin et al. 2018). Initially, strict enforcements were absent for ridesourcing services in Kolkata. With growing concerns over surged fares during peak hours, the transport department of the State of West Bengal enforced a cap of 45% to surge fares for ridesourcing services in 2018 (Bandyopadhyay 2018). Very recently, in March 2022, the State issued a notification based on Motor Vehicles Aggregators Guidelines, 2020 to regulate the maximum and minimum limit of the fare and impose a penalty on the drivers for cancelling rides (Anonymous 2022a). The State Government has also decided to bring a law to regulate the exorbitant fares charged by the TNCs (Anonymous 2022b).

Survey design

Pilot surveys were conducted in both cities for the drivers to test the questionnaire. The final survey was distributed online to the Uber drivers2 with the help of a Market Research Company in Perth between April and June 2019 similar to the approach adopted in research related to ridesourcing drivers (Fielbaum and Tirachini 2020; Hall and Krueger 2016). However, online survey could not be conducted in Kolkata due to limitations of technical know-how of the drivers. A paper-based offline survey was conducted in Kolkata during the month of January and February 2020 among Uber and Ola drivers. The samples for both cities were estimated using the sample size formula given by (Moore and McCabe 1999),

$$n={\left(\frac{z}{m}\right)}^{2}p\left(1,-,p\right)$$ 1

where z represents the z-value, m refers to the margin of error and p refers to the response rate.

Based on the pilot survey, the response rates for Perth and Kolkata were found to be 0.85 and 0.75 respectively. With the z-value for 90% confidence interval (CI) and 5% margin of error, the sample sizes for Perth and Kolkata were calculated as 138 and 202 respectively. The number of samples collected for Perth was 180 which accounted for nearly 3.6% of the registered Uber drivers in Perth (Deloitte 2015). The registered drivers for Uber and Ola in Kolkata were unknown to the authors. So, a total of 353 samples were collected for Kolkata from drivers waiting at Sector V (Salt Lake), Sealdah Station, Howrah Station and near Garia bazar area. The location of the collected samples for Perth and Kolkata have been provided in “Appendix”.

Sample size interpolated based on sample size tables for multiple regression analysis provided in Cohen (1988) is 146 for 40 independent variables. Number of completed and valid responses obtained from the drivers in Perth is 152 which is 3.04% of the registered Uber drivers in Perth (Deloitte 2015). Similarly, for Kolkata the number of responses included in the analysis is 302. So, the number of samples included in the analysis for both Perth and Kolkata are more than the minimum requirement to understand the socio-demographic and individual characteristics of the drivers.

The following group of questions were asked to the drivers in both the cities:

1. Socio-demographic characteristics of the drivers concerning their age, gender, education, income, and employment.

2. The operational characteristics of the driver considering the reason for driving, vehicle ownership, experience as a taxi driver, time of day they are driving, day of the week they are working as drivers, number of working hours as driver, driving frequency and duration of driving with the TNCs.

3. The perception of the drivers regarding ride requests received across various locations in both cities. For example, the drivers were asked to rate commercial areas on a scale of 1 to 5 (5 being ‘very high’ and 1 being ‘very low’) based on their experience of receiving trip requests in such areas per month.

4. The maximum time a driver is willing to park his/her vehicle and wait at a specific location before his/her change in mind. The driver was asked to record his/her time as ‘0’ if he did not wait. The waiting time tolerance was recorded for four-time slots, morning, afternoon, evening, and night. The tolerance was also recorded for high demand and low demand locations for each time slot.

Sample characteristics

The ridesourcing drivers in Perth drivers are mostly young, educated males who either drive part-time or full-time with Uber making additional monetary contributions to their families. On the other hand, ridesourcing drivers of Kolkata are young males with basic education choosing ridesourcing services as the only option to earn their livelihood to fulfil the necessities of their families.

The preference of the Perth drivers to work as part-time drivers is also reflected in their preferred driving hours per day. Nearly 78% of the drivers drive below 8 h per day on average. Driving being the sole occupation for the drivers in Kolkata, almost 98% of the drivers are found to work over 8 h per day on average. Moreover, the majority of the drivers are observed to work over 14 h per day which raises serious health and safety concerns for the drivers. The sample characteristics of Perth and Kolkata have been summarised in Tables 1 and 2 respectively.

Table 1.

Description of driver characteristics in Perth

Category	Count	Percentage	Category	Count	Percentage
Socio-demographic variables
Sex			Personal income (monthly)
Male	113	72.0	$1–$1999	17	10.83
Female	44	28.0	$2000–$3999	37	23.57
Age			$4000–$5999	53	33.76
21–24	23	14.65	$6000–$7999	15	9.55
25–34	69	43.95	$8000–$9999	13	8.28
35–44	50	31.85	$10,000–$11,999	8	5.10
45–54	12	7.64	$12,000 or more	10	6.37
55–64	2	1.27	Prefer not to answer	4	2.55
65 or older	1	0.64	Household Income (Monthly)
Education			$1–$1999	14	8.92
University (postgraduate or higher)	60	38.22	$2000–$6999	45	28.66
			$7000–$11,999	52	33.12
University (undergraduate)	58	36.94	$12,000–$16,999	20	12.74
			$17,000–$21,999	7	4.46
Diploma	14	8.92	$22,000–$26,999	6	3.82
Vocational or Technical	9	7.64	$27,000–$31,999	4	2.55
Senior high School	12	5.73	$32,000 or more	4	2.55
Primary or some secondary	4	2.55	Prefer not to answer	5	3.18
Employment Status			Jobs apart from Uber
Full-time worker (more than 30 h/week)	116	73.88	Yes	73	46.5
Part-time worker (8–30 h/week)	41	26.11	No	84	53.5
Operational variables
Uber driver status			Owns the vehicle
Full-time driver	67	42.68	Yes	141	89.8
Part-time driver	90	57.32	No	16	10.2
Duration of driving with Uber			Hours of driving per day
< 1 year	51	32.48	< 4 h	40	26.32
1 year to 2 years	37	23.57	4 to 6 h	57	37.50
2 years to 3 years	44	28.03	6 to 8 h	26	17.11
3 years or beyond	25	15.92	More than 8 h	34	22.37
Frequency of driving			Drove taxi
< 3 days	35	23.03	Yes	79	50.31
3 to 5 days	70	46.05	No	78	49.68
Daily	52	34.21

Table 2.

Description of driver characteristics in Kolkata

Category	Count	Percentage	Category	Count	Percentage
Socio-demographic variables
Age			Education
21–24	18	5.96	graduate or higher	31	10.26
25–34	152	50.33	Higher secondary	47	15.56
35–44	95	31.46	Secondary	105	34.77
45–54	28	9.27	Middle	72	23.84
55–64	9	2.98	Primary	26	8.61
65 or older	0	0.00	Literate but below primary	21	6.95
Personal income (monthly)			Household income (monthly)
Less than or equal to 10,000 INR	17	5.63	Less than or equal to 10,000 INR	12	3.97
10,001–20,000 INR	166	54.97	10,001–20,000 INR	151	50.00
20,001–30,000 INR	77	25.50	20,001–30,000 INR	84	27.81
30,001–40,000 INR	20	6.62	30,001–40,000 INR	25	8.28
40,001–50,000 INR	10	3.31	40,001–50,000 INR	14	4.64
50,001–60,000 INR	5	1.66	50,001–60,000 INR	6	1.99
More than 60,000 INR	1	0.33	More than 60,000 INR	4	1.32
Prefer not to answer	6	1.99	Prefer not to answer	6	1.99
Employment status
Full-time worker (more than 30 h/week)	273	90.39
Part-time worker (8–30 h/week)	29	9.61
Operational variables
Owns the vehicle			Drove taxi
Yes	149	49.34	Yes	146	48.34
No	153	50.66	No	156	51.66
Duration of driving with TNCs			Hours of driving per day
< 1 year	52	17.22	< 8 h	6	1.99
1 year to 2 years	46	15.23	8 to 12 h	31	10.26
2 years to 3 years	67	22.19	12 to 14 h	63	20.86
3 years or beyond	137	45.36	> 14 h	202	66.89
Frequency of driving
< 3 days	6	1.99
3 to 5 days	86	28.48
Daily	210	69.54

Drivers’ perception of high demand and low demand areas

The spatial demand for ridesourcing depends on density, design, diversity and transit variables (Brown 2019; Yu and Peng 2020). The density variables found significant in generating more ridesourcing trips are population density (Alemi et al. 2018; Clewlow and Mishra 2017; Goodspeed et al. 2019; Mitra et al. 2019; Wang and Mu 2018; Yu and Peng 2019), employment density (Alemi et al. 2018; Brown 2019; Goodspeed et al. 2019; Yu and Peng 2020, 2019), and household density (Alemi et al. 2019; Dias et al. 2017). The design aspects that can distinguish between a high and low demand area for ridesourcing are road network density (Brown 2019; Goodspeed et al. 2019; Wang and Mu 2018; Yu and Peng 2019), walkability of neighbourhoods (Clewlow and Mishra 2017; Goodspeed et al. 2019; Yu and Peng 2019), parking space counts (Brown 2019) and regional accessibility (Alemi et al. 2018). The diversity of a neighbourhood can also identify the high demand and low demand areas for ridesourcing trips that can be measured with proportions of various landuse within a neighbourhood (Alemi et al. 2018; Clewlow and Mishra 2017; Goodspeed et al. 2019; Yu and Peng 2020). High and low demand areas for ridesourcing can also be identified based on transit connectivity (Alemi et al. 2018; Clewlow and Mishra 2017; Goodspeed et al. 2019; Mitra et al. 2019; Yu and Peng 2019) and transit stop density (Brown 2019; Wang and Mu 2018).

The factors affecting the spatial demand for ridesourcing must be estimated for specific locations using disaggregated datasets for Traffic Analysis Zones (TAZ) to determine high and low demand areas. Such datasets can either be obtained from the TNCs (Wang and Mu 2018) or through household surveys (Goodspeed et al. 2019). It is difficult to obtain proprietary data from the TNCs and household surveys require substantial time and funding. The drivers were found to have better perception about the demand due to their driving knowledge mostly in the taxi market (Haggag et al. 2017; Zheng et al. 2010). Earlier studies have highlighted the importance of perception to understand various decisions and actions of individuals (Sharma et al. 2020; Wood 1970). It is important to consider the psycho-milieu of the drivers since they are continuously interacting with the ridesourcing market and are well aware about the market that is constantly at disequilibrium. The knowledge about demand among the ridesourcing drivers was also confirmed during the pilot survey conducted for this research. It was also identified during this study that the drivers tend to associate their ride requests with specific areas. Earlier studies highlighted a strong relationship between landuse and the ridesourcing demand (Alemi et al. 2018; Goodspeed et al. 2019; Rayle et al. 2016; Yu and Peng 2020). So, this research has considered the high and low demand areas based on the drivers’ perception on the intensity of ride requests over a month for different landuse averaged over time.

To obtain the drivers’ perceptions, eight prominent areas defining different landuse were listed. The drivers were then asked to rank these areas based on the intensity of receiving ride requests over a month. These areas are, airports/railways/bus terminals, commercial areas, offices, shopping centres, educational institutions, hospitals, recreational areas like hotels/restaurants and the residential areas. It must be noted that spatial characteristics of Perth is quite different from Kolkata. While Perth is a planned city with low population density and segregated landuse having a centrally located business district, Kolkata is a partially planned city with high population density and mixed landuse. Accordingly, the high demand and low demand areas as perceived by the drivers might be different for both the cities. The drivers were asked to rate the above areas based on their experience of receiving ride requests in these areas during a month on a scale of 1 (very low) to 5 (very high). Almost 75% of the Perth drivers felt that they receive maximum ride requests in a month from major transport terminals like airports, or railway stations. Similar trend was also observed among the Kolkata drivers with 94% stating the prominence of the transport terminals regarding ride requests. Although bus terminals were included in the first category, the drivers of both the cities are found to be more optimistic about airports and railway stations. The commercial areas, office spaces and hotels/restaurants in Perth are mostly located in the Central business district (CBD). This is the reason why the perception of the drivers regarding these areas is quite similar. The majority of the drivers feel that the probability of receiving ride requests is relatively high in commercial areas (63.5%), offices (63.5%) and hotels/restaurants (64.1%). In Kolkata, however, the drivers feel that the probability of receiving ride requests at office locations (72%) are higher compared to the commercial areas (58%). Besides, the majority of the drivers (41%) felt that the ride requests received at hotel/restaurants were quite low. Nearly 67% of the Perth drivers thought the shopping centres to be one of the prominent locations with high number of ride requests. Almost half of the drivers in Kolkata also shared the same view. The drivers of both the cities also perceived that getting ride requests at educational institutions and hospitals is quite low. The drivers shared a different opinion regarding the residential areas. While 55% of the Perth drivers perceived residential areas as low demand areas, nearly 45% of the drivers of Kolkata rated residential areas to be an area with high intensity of ride requests. Such difference can be attributed to the prominence of mixed landuse in Kolkata. The results on drivers’ perceptions have been summarised in Fig. 1. The high demand and low demand areas mentioned in this paper represents the areas identified based on the drivers’ perception.

Fig. 1.

Drivers’ Perception on ride requests received across different areas on an average month, a Perth, b Kolkata. (Color figure online)

Methodology

Research design

Classification of parameters

Each socio-economic or operational parameter, to be considered for analysis, has been classified in this section. This research has considered ‘age’, ‘educational qualification’ and ‘monthly income’ as socio-economic characteristics of the driver. In this chapter ‘age’ has been categorised as follows, ‘21 to 24’ (very young), ‘25 to 34’ (young), ‘35 to 44’ (middle-aged) and ‘45 or above’ (seniors) for Perth where the senior age category has been used a reference category for analysis. In Kolkata, a dummy variable representing drivers above 35 years has been used who are referred to as ‘seniors’ for Kolkata. The drivers outside this category have been referred to as ‘young’ drivers in Kolkata. ‘Educational qualification’ of the drivers has been categorised as, ‘Senior School’, ‘Diploma’, ‘Undergraduate’ and ‘Postgraduate’ for Perth where the ‘Senior School’ represents the lowest educational qualification and ‘Postgraduate’ represents the highest educational qualification of the drivers. A dummy variable ‘Education till higher Secondary’ has been considered to represent the lowest educational qualification of the drivers in Kolkata. The monthly income of the drivers has been represented as ‘Income greater than $6000’ for Perth and ‘Income greater than 40,000 INR’ for Kolkata. The drivers falling in both the categories have been referred to as wealthy drivers. The driving experience of the drivers is expressed using ‘taxi driving experience’, ‘total duration of association with the TNCs’, and ‘full-time driving experience’. The duration of drivers’ association with the TNCs is represented by the parameter ‘duration < 1 year’. Drivers qualifying under this parameter has been referred as ‘new drivers’ in this research. Full-time (30 h in a week) driving is a function of average daily driving hours and driving frequency. Apart from the effect of ‘average daily trips per driver’, the author expects to obtain positive or negative effect of drivers’ driving preference defined by ‘day of driving’, ‘time of driving’, ‘driving frequency’, ‘daily driving duration’ and ‘vehicle ownership’ on their waiting time tolerance. ‘Day of driving’ has been classified as weekday, weekend, or both. ‘Time of driving’ has been categorised as morning (6 a.m.–12 p.m.), afternoon (12 p.m.–6 p.m.), evening (6 p.m.–12 a.m.) and night (12 a.m.–6 a.m.). ‘Driving frequency’ has been categorised as ‘< 3 days a week’, ‘3 to 5 days a week’ and ‘daily’ for Perth where ‘< 3 days a week’ has been considered as the base category. The drivers either driving ‘daily’ or ‘3 to 5 days a week’ have been considered as ‘frequent’ drivers otherwise they have been referred to as ‘infrequent’ drivers. In Kolkata, ‘Driving frequency’ has been represented using the parameter ‘> 5 days a week’. The drivers in Kolkata qualifying under this parameter have been considered as ‘frequent’ drivers. ‘Daily driving duration’ has been classified as ‘< 4 h’, ‘4 to 6 h’, ‘6 to 8 h’ and ‘> 8 h’ where ‘> 8 h’ has been considered as the reference category for Perth. The drivers who belong to the categories of ‘> 8 h’ and ‘6 to 8 h’ have been referred to as ‘active’ drivers. The drivers belonging to other categories have been referred to as ‘passive’ drivers. In Kolkata, the categories for ‘average driving duration’ have been redefined as follows, ‘< 8 h’, ‘8 to 12 h’,’12 to 14 h’ and ‘> 14 h’ where ‘< 8 h’ is considered as base category. The drivers qualifying for categories like ‘< 8 h’ and ‘8 to 12 h’ have been mentioned as ‘active drivers’ otherwise they have been referred to as ‘passive drivers’. All other parameters used in the model have been mentioned in Tables 1 and 2.

Scope of investigation

The goal of this paper is to assess the effects of drivers’ characteristics and spatial demand on their waiting time tolerance. After dropping off a passenger, the driver takes decision on parking their car to wait at certain areas. In this regard, the drivers need to take decision on two fronts, whether they will wait and for how long they will wait. It is assumed that the socio-economic and operational characteristics like driving experience, preferences on driving and average daily trips per driver will have finite effect on drivers’ decision to wait and waiting time tolerance. Therefore, this research has attempted to investigate the effects of each parameter, mentioned in 5.1.1, on drivers’ decisions on waiting.

Modelling technique

The most popular technique in survival analysis to model duration data is the proportional hazards approach (Cox 1972). This study attempts to understand the waiting time tolerance of the drivers before they receive their next passenger request. After dropping off a passenger, the driver takes decision on parking their car to wait at certain locations. They may or may not wait. Here, we are interested in the waiting time of the driver after dropping passenger to his/her destination.

The waiting time is a non-negative random variable denoted by $T_{\mathit{area}}$ for a specific area. As mentioned in “Survey design” section, the driver was asked to mention the maximum time he was willing to park his/her car before considering other options. The drivers who did not wait recorded their time as ‘0’. Therefore, the waiting time response variable, i.e., $T_{\mathit{area}}$ is a semi-continuous variable. The variable can either assume a zero value with a discrete probability or follow a continuous distribution of positive values greater than zero. Besides, the duration data for the drivers was recorded for four time slots for both high and low demand areas. In this research, separate waiting time tolerance over four time slots have not been considered as the focus is on the aggregated ridesourcing operations over a day. The average waiting time tolerance over a 24-h period has been considered. From the perspective of urban infrastructure planning, aggregated operations data over a day is desirable. So, it is required to determine an average waiting time normalised over 24 h from the data of four-time windows. The normalisation can be achieved by,

$$t^{{}^{\prime }}=\frac{t-{\mathit{min}}_F}{{\mathit{max}}_F-{\mathit{min}}_F}\left({new\_max}_F,-,{new\_min}_F\right)+{new\_min}_F$$ 2

where $\mathit{t}$ represents the waiting time of drivers, ${\mathit{t}}^{{}^{\prime }}$ represents the waiting time of drivers after normalisation, min_F represents the minimum waiting time observed in a specific time window, max_F represents the maximum waiting time observed in a specific time window, new_min_F denotes the minimum waiting time observed across time-windows, new_max_F denotes the maximum waiting time observed across time-windows. The above equation was calibrated for high demand and low demand areas of both the cities based on the following values (Table 3).

Table 3.

Maximum and minimum waiting time values observed in Perth and Kolkata

City	High demand area		Low demand area
	new_minF	new_maxF	new_minF	new_maxF
Perth	0	30	0	25
Kolkata	0	60	0	35

Once the waiting time is normalised, the mean of the waiting time across four-time windows, ${\mathit{T}}_{\mathit{a}\mathit{r}\mathit{e}\mathit{a}}$ is determined for each observation given by,

$$T_{\mathit{area}}=\frac{{\sum }_{i=1}^N{t}_i^{{}^{\prime }}}{N}$$ 3

where N represents the total number of time slots. The conditional distribution of the semi-continuous response variable $T_{\mathit{area}}$ with zero-valued observations can be modelled using a zero-inflated model, expressed as (Braekers and Paul 2007),

$$G\left(t,|,x,,,z\right)=P\left(T_{\mathit{area}},\le t|X=x,Z=z\right)=\pi \left(x\right)+\left(1,-,\pi ,\left(x\right)\right)G_{T_{\mathit{area}}>0}(t|z)$$ 4

where the non-zero positive part of the response variable is represented by the continuous conditional distribution $G_{T_{\mathit{area}}>0}$, the probability of a driver not waiting is represented by $\pi \left(x\right)$ and X and Z represent the vector of covariates in discrete and continuous distribution respectively. Let us assume a parametric model for the latter, i.e., $\pi \left(x\right)$, $\alpha$ represents the finite dimensional vector of the model coefficients. The logistic regression model for $\pi \left(x\right)$ can be generalised as (Braekers and Paul 2007),

$$\ln \left(\frac{\pi \left(x\right)}{1-\pi \left(x\right)}\right)={\alpha }^T\mathit{X}$$ 5

Let us assume that $T_{\mathit{area}}>0$ follows a cumulative distribution function (CDF), $\mathit{f}(\mathit{t})$ and a probability density function (PDF), denoted by $\mathit{F}(\mathit{t})$ which is also known as ‘failure function’. $\mathit{F}(\mathit{t})$ is the probability that a randomly selected driver will not wait and look for other options before time t. Using the law of total probability, the survival function $\mathit{S}(\mathit{t})$ can be derived from the failure function $\mathit{F}(\mathit{t})$ (Eq. 4) (Borovkova 2002; Cox and Oakes 1984).

$$F\left(t\right)={\int }_0^{t}f\left(t\right)dt$$ 6

$$S\left(t\right)=P\left[T_{\mathit{area}},\ge ,t\right]=1-F\left(t\right)$$ 7

The literature in survival analysis deals with the instantaneous rate of failure also known as hazard rate or hazard function denoted as ${\mathit{h}}_{\mathit{T}}\left(\mathit{t}\right)$ (Kleinbaum and Klein 2010). The hazard function can be defined as the conditional probability of the driver exhausting the waiting time threshold within the interval [t, t + Δ], given that the event is yet to occur prior to time t. The hazard rate can be expressed as follows (Cox and Oakes 1984):

$$h_T\left(t\right)=\underset{\mathrm{\Delta }\to 0+}{\lim }\frac{P(t\le T_{\mathit{area}}<t+\mathrm{\Delta }|T_{\mathit{area}}\ge t)}{\mathrm{\Delta }}$$ 8

The baseline hazard function of a semi-parametric CPH model is considered as a “high-dimensional nuisance and erroneous parameter” (Royston and Parmar 2002). So, the effect of covariates on average waiting time tolerance can be quantified efficiently using flexible parametric form of CPH models. Such flexible methods can be developed based on splines without making strict assumptions on the parametric form of the baseline hazard. The generalised proportional hazard spline model, where ${\gamma }^T$ represents the vector of coefficients of the spline function, $\mathit{v}\left(x\right)$ represents the vector of linear basis function, can be written as (Herndon and Harrell 1995),

$$\ln H\left(t,;,\mathit{z}\right)={\alpha }_0+{\gamma }^T\mathit{v}\left(x\right)+{\beta }^T\mathit{z}$$ 9

where $\mathit{v}\left(x\right)={\left(x,,,v_1,\left(x\right),,,\cdots ,.,,,v_m,(x)\right)}^T,\dim \left(\gamma \right)=m+1$, and m is the number of distinct internal knots. Replacing $x=\ln t$, Eq. (9) can further be modified as (Heinzl and Kaider 1997; Royston and Parmar 2002),

$$\ln H\left(t,;,\mathit{z}\right)={\alpha }_0+{\gamma }_0\ln t+\sum _{i=1}^m{\gamma }_m{v}_m(\ln t)+{\beta }^T\mathit{z}$$ 10

Based on Eq. (10), a cox’s spline regression model can be considered for $G_{T_{\mathit{area}}>0}(t|z)$, the conditional distribution of the non-zero waiting time of the drivers, and is expressed as using Eqs. (7), (9) and (10) (Braekers and Grouwels 2016),

$$G_{T_{\mathit{area}}>0}(t|z)=1-\exp \left(-,H,\left(t,;,\mathit{z}\right)\right)=1-e^{-e{\beta }^T\mathit{z}{e}^{{\alpha }_0+{\gamma }_0\ln t+{\sum }_{i=1}^m{\gamma }_m{v}_m(\ln t)}}$$ 11

In order to analyse the duration data, it is assumed that the driver will cease to wait if the time is less than or equal to the time mentioned in the data. Such data is said to be left censored. Therefore, a random variable C is assumed to be the detection limit such that C > 0. For the conditional distribution of the non-zero part, let us consider Y = max(T,C) and δ = I(T ≥ C), where Y refers to the maximum number between the recorded value and the detection limit, and δ is a binary variable detecting whether the response variable exceeds the detection limit (Braekers and Paul 2007). The parameters of the model can be estimated using maximum likelihood techniques. The likelihood function of Eq. (4) can be constructed as follows (Braekers and Paul 2007):

$$\begin{array}{cc}\hfill L& =\prod _{i=1}^n{\left[\frac{\partial }{\partial t}P\left(T\le t,\delta =1|X=x_i,Z=z_i\right){|}_{t=t_i}\right]}^{{\delta }_i}{\left[P(T\le d,{\delta }_i=0|X=x_i,Z=z_i\right]}^{1-{\delta }_i}\hfill \\ \hfill & =\prod _{i=1}^n{\left[\left(1-\pi \left(x_i\right)\right)g_{T>0}(t_i|z_i)\right]}^{{\delta }_i}{\left[\pi \left(x_i\right)+\left(1-\pi \left(x_i\right)\right)G_{T>0}(d|z_i)\right]}^{1-{\delta }_i}\hfill \\ \hfill \end{array}$$ 12

$$L=\prod _{i=1}^n{\left[\frac{h_0\left(t_i\right)e^{{\beta }^T{z}_i}{e}^{-e^{{\beta }^T{z}_i}{e}^{{\alpha }_0+{\gamma }_{0}ln{t}_i+{\sum }_{i=1}^m{\gamma }_m{v}_m\left(ln{t}_i\right)}}}{1+e^{{\alpha }^t{x}_i}}\right]}^{{\delta }_i}{\left[\frac{e^{{\alpha }^t{x}_i}+1-e^{-e^{{\beta }^T{z}_i}{e}^{{\alpha }_0+{\gamma }_{0}lnd+{\sum }_{i=1}^m{\gamma }_m{v}_m\left(lnd\right)}}}{1+e^{{\alpha }^t{x}_i}}\right]}^{1-{\delta }_i}$$ 13

The log-likelihood can be determined by taking logarithm of Eq. (13) expressed as follows (Braekers and Paul 2007),

$$\begin{array}{cc}\hfill logL& =\sum _{i=1}^n{\delta }_i\left[log\left(h_0\left(t_i\right)\right)+{\beta }^T{z}_i-e^{{\beta }^T{z}_i}{e}^{{\alpha }_0+{\gamma }_{0}ln{t}_i+\sum _{i=1}^m{\gamma }_m{v}_m\left(ln{t}_i\right)}-log\left(1+e^{{\alpha }^t{x}_i}\right)\right]\hfill \\ \hfill & +\sum _{i=1}^n(1-{\delta }_i)\left[log\left(e^{{\alpha }^t{x}_i}+1-e^{-e^{{\beta }^T{z}_i}{e}^{{\alpha }_0+{\gamma }_{0}lnd+\sum _{i=1}^m{\gamma }_m{v}_m\left(lnd\right)}}\right)-log\left(1+e^{{\alpha }^t{x}_i}\right)\right]\hfill \\ \hfill \end{array}$$ 14

The parameters of the models for both high and low demand areas are estimated by maximising the above log-likelihood function using lifelines, a toolbox to estimate survival models in python (Davidson-Pilon 2019).

Results

The effect on waiting time with the variation in parameters in the zero inflated fitted model for high demand and low demand areas has been discussed in this section. While the logistic part of the model describes drivers’ probability of not waiting, hazard part highlights upon the waiting time tolerance of the driver once he/she decides to wait. The parameters that are found to be significant (having 90% confidence interval) for either logistic or hazard part have been considered in the fitted model. The parameters found significant for the fitted models of high and low demand areas have been analysed for both Perth and Kolkata.

Waiting time tolerance in high demand and low demand areas

The variation in parameters along with their statistical inference for high and low demand areas has been summarised in Tables 4 and 5 for Perth and Kolkata respectively. The coefficients of parameters with p-value lower than 0.1 for either logistic or hazard part or both have been shown in the table. All other coefficients have been left blank. A p-value lower than 0.1 highlights statistical significance of the parameter. The negative value of the coefficient represents lower hazard probability indicating a higher waiting time and positive value represents higher hazard probability indicating lower waiting time.

1. Effect of age—For the logistic part, the effect of age is statistically insignificant for low demand areas which implies that there is no effect of age on the decision for not waiting in Perth. However, in the hazard part the coefficients are found to vary with age in low demand areas. Very young drivers are less tolerant to waiting time compared to the seniors in Perth. Similar effect of age is observed in high demand areas in Kolkata for the hazard part only.

2. Effect of educational qualification—The drivers with higher education have lower tolerance for waiting time in high demand areas in Perth. But they are observed to decide in favour of waiting for low demand areas in Perth. A contrasting effect for higher education is observed in Kolkata for both high and low demand areas in the logistic part of the model. This implies that the drivers with lower educational qualification are more likely to wait after completing their trip. The highly educated drivers have a stable source of income from other jobs apart from driving. This factor is likely to influence their decision on waiting. It is also observed that this parameter has no effect on the waiting duration except for the high demand areas of Perth. This is in conformity with the strict parking regulations in the high demand areas of Perth.

3. Effect of income—The wealthy drivers in Perth tend to be less tolerant in taking decisions to wait in low demand areas in Perth. Such drivers are also less tolerant to waiting time in low demand areas. The wealthy drivers in Kolkata are less likely to wait in high demand areas. Both the observations confirm the findings of an earlier study on this aspect for the taxi market (Chou 2002). No effect of income has been observed for the hazard part of the model in Kolkata.

4. Effect of full-time driving experience—While the logistic part is observed to have significant effect on full-time drivers in high demand areas of Perth, the hazard part has significant effect in low demand areas. This implies that the full-time drivers are less likely to wait in high demand areas in Perth. These drivers tend to wait more at low demand areas compared to part-time drivers. Although no effect on decisions on waiting time is observed in low demand areas in Kolkata, the full-time drivers tend to wait for longer duration in high demand areas in Kolkata.

Table 4.

Results for zero-inflated cox spline regression model in high and low demand areas of Perth

Characteristics	Parameters	High demand areas		Low demand areas
		Coefficient (S.E.)*	p-value	Coefficient (S.E.)*	p-value
		Logistic part		Logistic part
Socio-demographic	Age_21–24	–	–	1.2295 (0.78)	0.1277
	Age_25–34	–	–	0.4223 (0.75)	0.5777
	Age_35–44	–	–	1.2059 (0.82)	0.1542
	Education_University (undergraduate)	1.1936 (0.89)	0.1882	− 1.4098 (0.76)	0.0725
	Education_University (postgraduate or higher)	1.9700 (1.21)	0.1061	− 1.8924 (0.64)	0.0061
	Month_Inc_ > $6000	–	–	3.2090 (0.78)	< 0.005
Driving/operational	Emp_Full-time driver (more than 30 h/week)	2.6917 (0.84)	< 0.005	− 0.2820 (0.61)	0.6464
	Drove Taxi_Yes	0.4838 (0.83)	0.5655	1.0517 (0.56)	0.0748
	Duration_ < 1 year	− 1.1337 (0.82)	0.1798	− 3.9456 (1.12)	< 0.005
	Freq_3–5 days a week	2.5727 (1.07)	0.0220	− 2.1200 (0.74)	0.0077
	Freq_Daily	2.9639 (1.16)	0.0155	− 4.2091 (1.02)	< 0.005
	Drivingday_both Weekdays and Weekends	− 2.3466 (0.97)	0.0210	− 1.2059 (0.51)	0.0250
	Drivingday_Weekdays	− 1.0604 (0.84)	0.2159	− 1.4330 (0.54)	0.0129
	Hours_ < 4 h	5.1470 (1.07)	< 0.005	–	–
	Hours_4–6 h	4.5319 (1.27)	< 0.005	–	–
	Hours_6–8 h	4.1940 (1.25)	< 0.005	–	–
	Daily trips/driver	0.1098 (0.05)	0.0367	–	–
	Driv_time_Morning	− 1.6934 (0.76)	0.0337	–	–
	Driv_time_Afternoon	− 0.9068 (0.50)	0.0819	–	–
	Driv_time_Night	− 1.6323 (0.83)	0.0566	–	–

Characteristics	Parameters	High demand areas		Low demand areas
		Coefficient (S.E.)*	p-value	Coefficient (S.E.)*	p-value
		Hazard part		Hazard part
Intercept	${\gamma }_0$	− 5.66 (0.94)	< 0.005	− 6.37 (1.03)	< 0.005
	${\gamma }_1$	3.78 (0.59)	< 0.005	3.46 (0.63)	< 0.005
	${\gamma }_2$	0.69 (0.80)	0.01	0.58 (1.19)	0.16
	${\gamma }_3$	− 1.24 (0.64)	0.04	− 1.29 (1.25)	0.24
Socio-demographic	Age_21–24	–	–	1.73 (0.54)	< 0.005
	Age_25–34	–	–	1.20 (0.32)	< 0.005
	Age_35–44	–	–	0.82 (0.24)	< 0.005
	Education_University (undergraduate)	1.40 (0.42)	< 0.005	− 0.21 (0.39)	0.34
	Education_University (postgraduate or higher)	1.18 (0.39)	< 0.005	− 0.11 (0.22)	0.41
	Month_Inc_ > $6000	–	–	0.43 (0.23)	0.08
Driving/operational	Emp_Full-time worker (more than 30 h/week)	0.33 (0.25)	0.21	− 0.75 (0.30)	0.02
	Drove Taxi_Yes	0.56 (0.23)	0.02	0.51 (0.28)	0.08
	Duration < 1 year	− 0.51 (0.24)	0.04	− 1.35 (0.33)	< 0.005
	Freq_3–5 days a week	0.27 (0.26)	0.37	− 0.10 (0.31)	0.75
	Freq_Daily	0.34 (0.22)	0.12	− 0.38 (0.25)	0.14
	Drivingday_both Weekdays and Weekends	− 0.28 (0.27)	0.32	− 0.30 (0.32)	0.36
	Drivingday_Weekdays	− 0.26 (0.21)	0.18	− 0.40 (0.25)	0.13
	Hours_ < 4 h	0.74 (0.30)	0.23	–	–
	Hours_4–6 h	0.39 (0.23)	0.50	–	–
	Hours_6–8 h	0.19 (0.25)	0.59	–	–
	Daily trips/driver	0.14 (0.78)	0.75	–	–
	Driv_time_Morning	− 0.36 (0.20)	0.17	–	–
	Driv_time_Afternoon	− 0.12 (0.21)	0.68	–	–
	Driv_time_Night	− 0.43 (0.21)	0.17	–	–
Log_likelihood		− 612.059		− 542.00
AIC		1296.118		1144.00

^*Standard errors (S.E.) of the coefficients are provided in the parentheses

Table 5.

Results for zero-inflated cox spline regression model in high and low demand areas of Kolkata

Characteristics	Parameters	High demand areas		Low demand areas
		Coefficient (S.E.)*	p-value	Coefficient (S.E.)*	p-value
		Logistic part		Logistic part
Socio-demographic	Age greater than 35 years	− 0.2352 (0.44)	0.5995	–	–
	Education till Higher Secondary	− 1.9318 (1.04)	0.0707	− 1.6298 (0.91)	0.0881
	Month_Inc_ > 40,000 INR	1.7263 (0.87)	0.0568	–	–
Driving/operational	Emp_Full-time driver (more than 30 h/week)	− 0.9875 (1.17)	0.4053	–	–
	Vehicle_Ownership_Yes	0.3342 (0.42)	0.4368	0.0660 (0.89)	0.9417
	Drove_Taxi_Yes	–	–	− 0.9352 (0.98)	0.3520
	Duration_ < 1 year	− 2.1714 (1.02)	0.0421	− 0.1114 (1.24)	0.9297
	Freq_ > 5 days a week	− 0.1301 (0.11)	0.2279	1.0034 (0.455)	0.0375
	Drivingday_both Weekdays and Weekends	− 1.0502 (0.62)	0.1018	–	–
	Hours_8–12 h	− 0.4363 (0.28)	0.1395	–	–
	Hours_12–14 h	− 0.7454 (1.40)	0.5981	–	–
	Hours_ > 14 h	− 0.8631 (2.67)	0.7485	–	–
	Daily trips/driver	–	–	0.0404 (0.08)	0.6301
	Driv_time_Morning	0.1125 (1.02)	0.3958	− 0.1843 (0.11)	0.1032
	Driv_time_Afternoon	− 0.4841 (1.19)	0.3664	− 0.2461 (0.15)	0.1049
	Driv_time_Night	− 0.1951 (0.91)	0.3892	− 0.3914 (0.38)	0.2339

Characteristics	Parameters	High demand areas		Low demand areas
		Coefficient (S.E.)*	p-value	Coefficient (S.E.)*	p-value
		Hazard part		Hazard part
Intercept	${\gamma }_0$	− 7.84 (0.90)	< 0.005	− 5.50 (0.95)	< 0.005
	${\gamma }_1$	2.98 (0.32)	< 0.005	1.97 (0.31)	< 0.005
	${\gamma }_2$	0.78 (0.25)	0.02	− 0.93 (1.54)	0.55
	${\gamma }_3$	− 1.21 (0.31)	< 0.005	1.35 (1.71)	0.44
Socio-demographic	Age greater than 35 years	− 0.16 (0.07)	0.04	–	–
	Education till Higher Secondary	− 0.24 (0.14)	0.10	− 0.03 (0.14)	0.84
	Month_Inc_ > 40,000 INR	0.29 (0.41)	0.49	–	–
Driving/operational	Emp_Full-time driver (more than 30 h/week)	− 0.65 (0.33)	0.06	–	–
	Vehicle_Ownership_Yes	0.16 (0.08)	0.06	0.33 (0.13)	0.02
	Drove_Taxi_Yes	–	–	− 0.17 (0.06)	0.01
	Duration_ < 1 year	− 0.27 (0.11)	0.02	− 0.38 (0.17)	0.04
	Freq_ > 5 days a week	− 0.19 (0.10)	0.09	0.04 (0.05)	0.49
	Drivingday_both Weekdays and Weekends	− 0.25 (0.10)	0.02	–	–
	Hours_8–12 h	− 0.06 (0.03)	0.05	–	–
	Hours_12–14 h	− 0.24 (0.14)	0.10	–	–
	Hours_ > 14 h	− 0.45 (0.19)	0.03	–	–
	Daily trips/driver	–	–	0.03 (0.01)	0.01
	Driv_time_Morning	0.22 (0.12)	0.08	− 0.19 (0.09)	0.05
	Driv_time_Afternoon	− 0.72 (0.19)	< 0.005	− 0.37 (0.15)	0.02
	Driv_time_Night	− 0.51 (0.14)	< 0.005	− 0.53 (0.18)	< 0.005
Log_likelihood		− 935.15		− 898.13
AIC		1938.3		1840.26

*Standard errors (S.E.) of the coefficients are provided in the parentheses

The average daily driving hours for full-time and part-time drivers in Perth is nearly 7 h and 5 h respectively. The full-time drivers are more likely to be active drivers who have better ratings. Such ratings give them higher priority in terms of trip allocation, especially in high demand areas. The part-time drivers tend to maximise their earnings within their duration of driving which motivates them to wait more at high demand areas and less at low demand areas. On the other hand, the average daily driving hours for full-time drivers in Kolkata is 14 h compared to 7 h for part-time drivers. Although the full-time drivers have higher priority over the part-time drivers, the full-time drivers need to wait longer during off-peak periods as their driving duration is 50% higher compared to the part-time drivers.

• (e)Effect of taxi driving—The drivers having prior experience of driving taxis are found to have less waiting time tolerance for both high and low demand areas in Perth. These drivers also tend to have higher probability of not waiting in low demand areas. The decision on waiting is not observed to be significant for both high and low demand areas in Kolkata. However, the drivers who drove taxi before are observed to have higher waiting time tolerance in low demand areas in Kolkata.
• (f)Effect of duration of association with TNCs—In high demand areas, there is no significant impact on the decision to wait for the new drivers in Perth. However, if a new driver decides to wait in a high demand area, he tends to wait for a longer duration. In the low demand areas in Perth, the new drivers are ready to decide in favour of waiting as well as ready to wait for a longer period. Similar observation is made for waiting decision for high demand areas in Kolkata. Besides, the drivers of Kolkata also exhibit similar behaviour for waiting time tolerance for both high and low demand areas. No significant effect on drivers’ decision to wait is observed in low demand areas in Kolkata.
• (g)Effect of driving frequency—The frequent drivers are less likely to wait at high demand areas compared to low demand areas in Perth. Significant effect of this parameter is not observed on their waiting time duration. Unlike Perth, the frequent drivers are less likely to take decision in favour of waiting at low demand areas in Kolkata. These drivers are observed to wait longer in high demand areas in Kolkata.
• (h)Effect of vehicle ownership—No significant effect of this parameter is observed in Perth. Similar observation is also made in Kolkata for both high and low demand areas regarding drivers’ decision to wait. However, drivers driving their own vehicle tend to wait less in both the areas of Kolkata if they decide to wait.
• (i)Effect of day of driving—Compared to the drivers who prefer to drive on weekends, the drivers who drive both on weekdays as well as weekends tend to decide in favour of park and wait for their next customer at both high and low demand areas in Perth. Such effect is found to be similar for the drivers driving during weekdays only in low demand areas of Perth. Significant effect is not observed on drivers’ decision to wait in Kolkata for both high and low demand areas. The drivers driving during both weekdays and weekends have higher waiting time tolerance areas at high demand areas in Kolkata.
• (j)Effect of time of driving—The drivers who prefer to drive during morning or night are more likely to wait at high demand locations compared to drivers who drive during afternoon or evening in Perth. In Kolkata, significant effect of driving time is observed on drivers’ waiting time duration. The drivers tend to wait less during morning and evening at both high and low demand areas compared to the drivers who prefer to drive during afternoon or night. Moreover, the waiting time tolerance at high demand locations is higher at afternoon compared to the night. At low demand areas, the drivers driving at night have higher waiting time tolerance compared to those driving during afternoon.
• (k)Effect of daily driving duration—In case of Perth, the drivers with lower driving duration have lower probability to wait in high demand areas. In case of Kolkata, the drivers’ decision on whether to wait is not significant. But the drivers with higher driving duration have higher tolerance to waiting time in high demand areas of Kolkata.
• (l)Average daily trips per driver—The drivers with higher number of trips are less likely to wait at high demand areas in Perth. There is no significant effect of this parameter on their waiting time duration. On the other hand, the drivers serving more users are less likely to wait for a longer duration in low demand areas in Kolkata.

Based on the observations made from Tables 4 and 5, it is evident that the drivers of Perth and Kolkata consider different aspects related to their waiting time decisions. The drivers in Perth mostly tend to decide whether to wait at a specific location. On the other hand, the drivers in Kolkata are indifferent regarding their decision to wait. They, however, are more likely to take decisions related to their waiting time duration at specific location. Such observation is consistent since the sole occupation of the daily drivers of Kolkata is driving for the TNCs unlike Perth. In Perth, only 43% drivers drive on a full-time basis in contrast to 90% in Kolkata. The cost of operation is a major concern for full-time drivers in Kolkata since driving is their only source of income. Table 6 presents a schematic representation of the variation in effects of the parameters for both Perth and Kolkata. In Table 6, the cells highlighted in green and red represents higher and lower probability respectively. The grey colored cells represents that the corresponding parameter has not been found to have significant effect on drivers' decision to wait or their waiting time duration.

Table 6.

Schematic analysis of effects of parameters on waiting decision for Perth and Kolkata. (Color table online)

HD High Demand, LD Low Demand, None No significant effect, High High Probability to wait, Low Low Probability to wait, More More waiting duration, Less Less waiting duration

Discussions on survival function

The survival curves were estimated based on the coefficients derived for the zero inflated model to understand two aspects, (a) the impact of explanatory variables concerning drivers’ characteristics on the waiting time tolerance of the drivers (b) the mean waiting time tolerance in high and low demand areas for both Perth and Kolkata. The survival probabilities of the concerned response variable can be derived based on the survival function of the hazard part of the zero-inflated cox spline model determined using Eq. (4) and can be expressed as:

$$S_{T>0}\left(t,|,z\right)=exp\left(-,H,\left(t,;,\mathit{z}\right)\right)=e^{-e{\beta }^T\mathit{z}{e}^{{\alpha }_0+{\gamma }_0\mathit{ln}t+{\sum }_{i=1}^m{\gamma }_m{v}_m(\mathit{ln}t)}}\forall m=2$$ 15

The curves generated for the explanatory variables are evaluated at the mean value of both high and low demand areas for both the cities. The mean value estimated for high demand areas and low demand areas is 10 min and 5 min respectively for Perth. In Kolkata, the mean value is relatively higher with 20 min for high demand areas and 15 min for low demand areas. In this section, drivers’ operational characteristics that are found to have significant effect across Perth and Kolkata have been considered to understand the variation in survival probability of the waiting time.

1. Years of association with the TNCs

Figure 2a–b highlights the effect of drivers’ association with the TNCs on their waiting time tolerance in both high and low demand areas of Perth. The new drivers of Perth are observed to have 65% and 285% more waiting time tolerance compared to the old drivers in high and low demand areas respectively. The new drivers of Kolkata are 140% and 277% more tolerant to wait for a longer duration in high and low demand areas respectively as shown in Fig. 3a–b. The new drivers are less acquainted with the market compared to the experienced drivers. The TNCs can provide such drivers with spatio-temporal recommendations to get more trips easily. The TNCs may also consider instructing the new drivers to take a more moderated approach of waiting more at low demand areas and less at high demand areas. Such an approach can improve their chances of getting trips via recommendation system.

• (b)Daily Driving Hours

Fig. 2.

Effect of years of driving with TNCs on survival probability of the waiting time tolerance of the drivers in Perth, a high demand areas, b low demand areas. (Color figure online)

Fig. 3.

Effect of years of driving with TNCs on survival probability of the waiting time tolerance of the drivers in Kolkata, a high demand areas, b low demand areas. (Color figure online)

Longer driving duration can lead to fatigue which in turn can urge the drivers to wait at certain locations. The influence of average daily driving duration on the waiting time tolerance of Perth drivers has been depicted through the curves shown in Fig. 4a–b. It is observed that the drivers driving for more than 8 h have 166% more waiting time tolerance compared to the drivers driving for less than 4 h in high demand areas. These drivers are observed to have 428% more waiting time tolerance in low demand areas. In Kolkata, the drivers driving for more than 14 h have 566% more waiting time tolerance in both high and low demand areas compared to drivers driving for less than 8 h as depicted in Fig. 5a–b. The TNCs can introduce mandatory break periods for drivers with more driving hours and inform them about nearby parking locations. Besides, the urban authorities need to ensure sufficient parking spaces within an urban area especially at high demand locations. The number of parked vehicles at different locations is a function of trip ends, trip origins and number of drivers deciding to wait. The urban authorities can design the parking infrastructure on the basis of real-time data obtained from the TNCs. Moreover, the cities may consider reducing the parking costs and change existing regulations to accommodate the waiting drivers in high demand areas.

• (c)Time of driving

Fig. 4.

Effect of driving hours on survival probability of the waiting time tolerance of the drivers in Perth, a high demand areas, b low demand areas. (Color figure online)

Fig. 5.

Effect of driving hours on survival probability of the waiting time tolerance of the drivers in Kolkata, a high demand areas, b low demand areas. (Color figure online)

Drivers’ preference on driving time also influences their decision on waiting. Figure 6a–d highlights the effect of drivers’ driving time on their waiting time tolerance in both Perth and Kolkata. In Perth, the drivers driving during night tends to wait 183% more than the drivers driving during evening. Moreover, drivers driving during morning also have higher waiting time tolerance compared to afternoon and evening. Such decisions of the drivers of Perth depend mostly on two factors, demand intensity for a specific time period and trip ends and origins. The drivers in Perth receive trips more easily during evening due to higher trip rates compared to other times of the day. Although the trip rates are high during morning and night, the drivers tend to wait at morning at high demand areas since the trips mostly end at such locations. On the other hand, the drivers tend to wait at hotspots during night as the trips mostly generate from such areas during that time period. In Kolkata, the waiting time tolerance of the drivers is quite low during morning and evening compared to other time slots irrespective of the areas they are operating. But it must be noted that the mean value of the waiting time tolerance is higher both in high and low demand areas in Kolkata compared to Perth. As observed earlier, the only profession of ridesourcing drivers in Kolkata is driving which urges them to wait during the off-peak periods. Such drivers with higher tolerance for waiting at off-peak periods must be identified to estimate the number of drivers deciding to wait during those time periods. Such estimation can enable the urban authorities to design the parking infrastructure that can later be used by the TNCs to provide prescriptive information on parking locations to the drivers after trip completion.

Fig. 6.

Effect of time of the day on survival probability of waiting time tolerance of the drivers in, a high demand areas of Perth, b low demand areas of Perth, c high demand areas of Kolkata, d low demand areas of Kolkata. (Color figure online)

Discussion and conclusion

The main objective of this study is to model the decision of ridesourcing drivers to park and wait after the completion of trips. The study was conducted in Perth and Kolkata to understand the drivers’ behaviour in two different ridesourcing markets. This involves the determination of the likelihood of waiting of the drivers at high and low demand areas and the impact of socio-economic and operational characteristics on their waiting time tolerance at various locations. Previous studies were conducted to understand the driver behaviour in the taxi and other similar services. Nevertheless, the perception of ridesourcing drivers on parking and waiting after dropping off passengers is yet to be explored. The operation of ridesourcing services is dependent on the characteristics of the primary stakeholders, i.e., the users and the drivers. The drivers’ decision on waiting can affect the number of matched trips by the TNCs, and parking spaces in the city. Moreover, drivers’ waiting time tolerance can also impact other drivers’ total number of trips, total earnings, total distance travelled in the city, and fleet size.

It must be noted that the drivers’ waiting time decisions can also affect users’ waiting time. For example, a driver nearest to both A and B decides to cruise from location B to A instead of waiting. If a user arrives at location B, his/her waiting time will be more due to the drivers’ decision to cruise to location A. With increase in waiting time of the user, he/she will opt for other modes of transport once the waiting time exceeds beyond his/her tolerance. In such case, the driver will lose a passenger. This will certainly affect the driver’s waiting time and decision on waiting. Therefore, drivers’ decision on waiting and users’ waiting time affect each other mutually.

The waiting time tolerance of the drivers, as observed in the previous sections, varies across different spatial locations. Therefore, the policies mentioned earlier, should be devised to address specific spatial conditions. This research has analysed drivers’ waiting time tolerance after dropping off a passenger based on a zero-inflated cox spline model. The model is comprised of two parts. While the logistic part of the model considers drivers’ decision to wait, the hazard part analyses drivers’ waiting time duration if they decide to wait. However, the logistic part of the model is limited in expressing the probability of a driver not waiting at a location after dropping a passenger. It cannot provide the duration of waiting if the driver decides to wait. The duration of wait must be assessed using the survival analysis, i.e., the hazard part of the model.

While the socio-economic characteristics define the group of drivers who work for ridesourcing services, the operational characteristics of the drivers significantly affect the drivers’ decisions on waiting inside their parked vehicles. The drivers in both cities tend to wait longer if they decide to wait in high-demand areas. However, the waiting time tolerance of the drivers is more in Kolkata than in Perth. The drivers’ decision to wait in high demand areas can affect the waiting time of the users in the low-demand areas. Moreover, such a decision of the drivers will also increase the parking requirement in high-demand areas. The city authorities can collaborate with TNCs to determine an optimal parking requirement in specific high-demand areas. The TNCs may recommend drivers to move to other nearby locations who do not get a parking spot at high-demand locations. Such recommendations will also help the TNCs optimise their users’ waiting time at low-demand locations.

The operational characteristics of the drivers include drivers’ experience and their driving preferences. In Perth, the operational characteristics of the drivers affect whether they will wait at a specific location. On the other hand, the effect of these characteristics is observed on the waiting time tolerance of the drivers in Kolkata. Such observation confirms the difference in the ridesourcing market between Perth and Kolkata.

In Perth, the full-time, experienced drivers (with more than 1 year of experience in ridesourcing) tend to wait less in high-demand locations compared to part-time drivers. While allocating trips to the drivers, the TNCs can prioritise these drivers for matching with the users. Moreover, the TNCs can also relocate the drivers to other hotspots through prescribed information. The part-time drivers tend to wait less in low-demand areas compared to full-time drivers. The TNCs can prioritise such drivers for trip allocation in low-demand areas in Perth. In Kolkata, the newly joined full-time drivers tend to wait more in high-demand areas asserting the need for parking in these areas compared to the experienced drivers. The new drivers tend to wait longer since they are not well acquainted with the market. However, in Kolkata, the experienced drivers who drove taxis before are more likely to wait longer in low-demand areas due to the parking difficulties encountered in high-demand areas compared to drivers who do not have prior experience of driving taxis. Apart from parking issues, the drivers in Kolkata also tend to wait longer in both high and low demand areas to reduce the operating cost.

As observed from the results, the waiting time tolerance of the driver increases with the increase in driving duration irrespective of the cities. The city authorities for both the cities can estimate the number of drivers with higher driving duration who are willing to wait to determine the parking requirement for specific locations. We also observed that the frequent drivers tend to wait more than the infrequent drivers, especially in low-demand areas of Perth. The results also highlight that majority of the drivers usually tend to wait more in the afternoon and night in both Perth and Kolkata compared to morning and evening. While the majority of the Perth drivers prefer to drive during the evening and night, the majority of the Kolkata drivers do not drive at night. This implies that more drivers will be willing to wait at night in Perth, and more drivers will wait in the afternoon in Kolkata. Such diversity in the driving preferences of the drivers cannot be catered to with the existing short-term ridematching strategies of the TNCs. The companies might need to explore different ride-matching strategies for different time frames to increase the efficiency of ridesourcing services. Besides, the urban authorities must determine spatio-temporal parking demand to design the parking infrastructure for ridesourcing services. The urban authorities may also consider curbing existing parking costs and regulations to meet the parking need of the drivers.

This research tried to present a comprehensive understanding of the waiting time tolerance of the drivers for high and low demand areas. It must be noted that different spatial locations have different spatial characteristics. While waiting for passengers at airports or railway stations will depend on the schedule of the concerned transport mode, waiting near hotels or restaurants will depend on the day of the week. Characteristics specific to different areas have not been considered in this study which can be explored in the future. Moreover, it is essential to explore drivers’ decisions once their tolerance level for waiting in the parked vehicle is attained. This will help the researchers to understand drivers’ behaviour with respect to their idle time. As mentioned earlier in “Literature review” section, the idle time is a sum of both waiting time and cruising time. In this paper, the waiting behaviour of the driver has been considered as his decision to wait or not to wait at a specific location after dropping a passenger. It may be noted that the present study intends to get an indication on the requirements of resources for the TNCs and urban infrastructure. The drivers may cruise randomly or cruise to hotspot locations or adopt other suitable strategies if they do not decide to wait. The drivers may also consider these decisions beyond their waiting time tolerance. This research has not considered the cruising behaviour of the drivers. A comparative analysis of waiting and cruising time of the drivers may be investigated in future.

It must be noted that factors affecting traffic conditions like road infrastructure, weather, road maintenance works and accidents will also affect drivers’ tolerance on waiting. Moreover, local regulations may also influence the drivers’ perception on waiting apart from their characteristics. Besides, urban infrastructure like dedicated pick-up/drop-off zones for ridesourcing can also influence drivers’ decision on waiting. Future studies may include factors related to traffic conditions, environment, urban infrastructure & policies, and investigate the influence of such factors on drivers’ perception on waiting. This study has considered the perceived waiting time of the drivers. It is crucial to investigate the decision bias of the drivers based on the comparison with actual waiting time derived from the real-time data recorded by the TNCs. However, the bias of the drivers could not be measured in this research due to limitations in data availability from the TNCs. Moreover, this research has been conducted based on drivers’ waiting time tolerance normalised over 24 h to obtain an aggregated estimate for a specific location. Future research may determine drivers’ waiting tolerance for different time slots. It should be noted that as data for this study were collected before the COVID-19 pandemic, it does not reflect the impact of the outbreak on the drivers' decisions. As different studies reported on the impact of the pandemic on travel behaviour, the effect of the pandemic on different attitudes of the drivers also needs to be explored.

Biographies

Jayita Chakraborty

is a collaborative Ph.D. student at IIT Kharagpur and Curtin University. Her research interests are shared mobility, simulation modelling, and intelligent transport systems.

Debapratim Pandit

is an associate professor at the department Architecture and Regional Planning, IIT, Kharagpur. His research interests are Transportation Planning & Routing Services Public Transportation, Traffic Management & Safety Community & Behavioral Studies in Planning Urban Planning: Utilities, Services IT based Infrastructure, Information System.

Jianhong Xia

is an associate professor at the Department of Spatial Sciences, Curtin University. She has over 10 years’ experience as a GIS educator and spatial analyst and modeller. She has also worked as a transport geographer and transit planner with a range of research experience in relation to public transport development, driving, spatial navigation and wayfinding and human mobility.

Felix Chan

is an associate professor at the School of Accounting, Economics and Finance. He joined the School of Economics and Finance in 2006 as a Senior Lecturer. He was previously appointed as a Statistical Analyst for the WA Police Service in 2004 and Australian Post-Doctoral Fellow Industry (APDI) in 2005. Felix was also co-founder and partner of Insight Horizon Consulting.

Appendix

See Figs. 7 and 8.

Fig. 7.

Response locations of drivers in Perth. (Color figure online)

Fig. 8.

Survey locations in Kolkata

Authors’ contributions

The authors confirm contribution to the paper as follows: Conceptualization: JC; data curation: JC, DP, CJX; methodology: JC, FC; investigation: JC; formal analysis: JC; writing—original-draft: JC; resources: DP, CJX; funding-acquisition: DP, CJX; writing—review and editing: DP, CJX, FC; supervision: DP, CJX, FC. All authors reviewed the results and approved the final version of the manuscript.

Declarations

Conflict of interest

There is no potential financial and personal conflict-of-interest for this research that can significantly influence the outcome of this research.