VARIABILITY OF PARATRANSIT TRAVEL TIMES: THE CASE OF KUMASI, GHANA

ABSTRACT

While much has been reported about bus travel times and their variability for formal bus services, little is known about travel time variation for paratransit, the dominant means of transportation in most low- and middle-income countries (LMICs). This study quantifies the components of paratransit travel time on a selected route in Kumasi, Ghana. It analyzes the variability of travel times within the day and from day to day. A mobile phone app was employed to conduct a travel time survey onboard paratransit vehicles on the study route. GPS and stop-related data were collected. Various travel time variability measures and heat map was used for within day and day-to-day variability analysis in both directions of the study section. About 16% of travel time in the study section was spent dwelling (boarding and alighting). The variation in travel times across the day was comparatively higher than those of formal bus services and fluctuated across the day with no distinct pattern within any given time period. Both early and late trips contributed to this variation across the day. Fridays had significantly different variability from other weekdays.

KEYWORDS:

• Travel time variability
• trotro
• paratransit
• bus travel time
• public transport

1. Introduction

The carrying capacity that public transport vehicles (buses, trains, etc.) have and the savings in roadway space gained by having many people use a single vehicle against private cars are two of the obvious advantages of public transport. Its potential for congestion reduction in urban cities and reductions in noise and air pollution are some other compelling arguments for the massive use of public transport for mobility in cities. Public transport in most sub-Saharan African cities is largely informal, referred to as paratransit (Behrens, McCormick, and Mfinanga, 2015). Paratransit is a term conventionally used to describe a flexible mode of public passenger transportation that does not follow fixed schedules, typically in small to medium-sized buses. In low- and middle-income countries, paratransit services are usually provided at a far larger scale for the general population, often by weakly regulated or illegal operators within the informal sector (Behrens, McCormick, and Mfinanga, 2015).

Paratransit takes up a substantial share of urban mobility in many African cities (Salazar, 2015), even where some formal bus services like the Bus Rapid Transit (BRT) have been introduced. They are recognized by different nomenclatures in the various cities where they exist. It is called trotro in Ghana (Poku-Boansi & Adarkwa, 2011; Saddier & Johnson, 2018), matatu in Nairobi (Williams et al., 2015), daladalas, danfos, and gbakas in Der es Salaam, Lagos, and Abidjan, respectively Lagos, and Abidjan, respectively (Behrens, McCormick, and Mfinanga, 2015). Booysen et al. (2013) compared paratransit with other forms of public bus service based on certain criteria and concluded that paratransit within the sub-Saharan context is privately owned, weakly regulated, operates largely from a station or rank without a schedule (fill and go), stops based on demand, and operates on partially fixed routes.

Associated with every trip, whether by private car or public bus service, are uncertainties arising from daily variations in traffic volume and other roadway conditions. However, inherent in the setup of paratransit at the institutional and operational levels are practices such as a customer requested stop to deliver a package for instance, that breeds more uncertainty in user trips. The users have reported low service quality and unreliability of paratransit services (Dzisi et al., 2021; Nwachukwu, 2014; Sam et al., 2018). Providing travel information such as travel time has proven to help ease anxiety and improve user experiences for formal bus services (Brakewood & Watkins, 2019; Gooze et al., 2013) and has been recommended for paratransit services (Sam et al., 2018).

To model the travel time of the service, provide reliable information, or implement any intervention that will improve reliability and user experiences, there is a need to first understand the nature and variability of the travel times of trips made by paratransit vehicles. The insight gained from this understanding is important to both users and planning authorities. The travel times of trips can help the users plan their departure times to arrive at appropriate times at the destination. Travelers value variation in travel times more than average travel times (Bates et al., 2001), thus underscoring the importance of understanding the nature of variation in paratransit travel times. The variation in trip times is a reflection of the reliability of the service. It is a key performance evaluation metric for the service and is useful to planning authorities in making interventions. Much effort has been made within the literature to gain insight into bus travel time variation for formal bus services. Two major approaches exist in the literature around investigating or analyzing travel time variability (TTV) for formal bus operations. Some studies use visuals and charts to explore relationships between certain measures of travel time variation. The second approach involves using probability distributions to characterize the variation in travel times.

Mazloumi et al. (2010) used various travel time variability measures based on percentiles to describe the variation in travel times within the day for a bus service in Australia. In characterizing day-to-day variability, probability distributions of travel time data were analyzed for varying departure windows to investigate the effect of departure window on the travel time distribution. Yazici et al. (2014) studied travel time variability patterns for highways and urban roads using data from the same metropolitan area. At the heart of their study was the investigation of how average travel times and variability patterns compare for both facility types. Travel rates, standard deviation, and coefficient of variation were variables used in heat maps to explore day-to-day variation in travel times. Kathuria et al. (2020) used the 10^th, 50th, and 90^th percentile plots in a chart in which travel time was plotted against time of day. Travel time was aggregated into 30-minute departure time windows (DTW). Heat maps were employed to describe the day-to-day variation in travel times using the coefficient of variation for two bus rapid transit routes.

Various single-mode distributions were fitted to bus travel times with mixed results. The lognormal distribution emerged as the recommended distribution to describe bus travel time variability in some situations (Chen et al., 2018; Kieu et al., 2015; Mazloumi et al., 2010; Rahman et al., 2018; Yan et al., 2016). The Generalized Extreme Value (GEV), Logistic, and Burr distributions have also been reported as the best fit for bus travel times within the literature (Durán-Hormazábal & Tirachini, 2016; Harsha et al., 2020; Low et al., 2021; Susilawati et al., 2011). Guo et al. (2010) argued that the assumption of using a single-mode distribution to fit traffic data is not true given the complex nature of traffic situations and thus cannot sufficiently model a wide variety of traffic situations. They went on to fit a two-component normal distribution to travel time data and found it fit better than single-mode distributions. This finding has been corroborated by the findings of Susilawati et al. (2011), Ma et al. (2016), and Chen and Sun (2019).

All the studies reported above were for formal bus services that operate on a markedly different model from paratransit. Little is reported on travel time variability studies in the African context. Most studies around travel time variability have been targeted at the roadway section, covering the entire vehicle composition in the traffic stream. Biliyamin and Bello (2012) observed vehicular movements at three congested locations of a road corridor in Abuja for one hour each on a weekday and weekend using video recording. The aim was to identify factors causing congestion and investigate the variation in travel times along those corridors. A similar study was conducted by Yesufu et al. (2019) in Kano, Nigeria, focusing on investigating the relationship between travel time variability and the capacity of the road section. They used the approach of video recording and license plate matching of morning peak period traffic flow for five weekdays on the given section. The distribution of travel times was then analyzed. They found that the peak traffic flow rate was inversely proportional to the degree of variation in travel time.

Obiri-Yeboah et al. (2020) report the perspective of Ghana on the variation of travel times on selected routes in Kumasi. They sought to investigate the differences in travel times in various time periods during the day for three different road transport modes. Field travel time observations for each of the modes were recorded on three different road segments for a period of 13 days, covering weekdays and weekends. ANOVA was used to compare the means of travel times in each time period for each vehicle type. The travel times were statistically different for most of the scenarios, thus suggesting variable travel times across the day for all the modes. Saddier et al. (2017) assessed the travel time reliability of paratransit trips originating from 12 trotro stations in Accra. They leveraged quantitative data collected onboard paratransit vehicles using a developed mobile application for a two-month period. They collected data for over 1200 trips on 65 routes for all days of the week for a 15-hour period on each day. The standard deviation of travel times was used to understand the variation in travel times. They found that, taken together, the travel time variation indicated by the standard deviation was quite stable but differed significantly when specific route legs were considered.

A critical analysis of travel time variability studies in the review indicates that there is a need for more studies within the African context to focus on public transport modes. Most studies targeted the entire traffic stream and were geared toward congestion investigations. While these are necessary in improving congested situations that may impact all modes in the stream, there is a need for targeted studies to address variation in paratransit trips that can help in understanding trip characteristics at route level and help improve service quality for dissatisfied users. Furthermore, there is a need to further build upon the work of Saddier et al. (2017), where they concluded that while paratransit travel time variability on all the routes they studied is stable when considered at the aggregate level, it varies significantly when specific route legs are considered. Given that only a few trips were collected for a few days on individual routes, there is a need to investigate travel time variability on specific paratransit routes using a larger dataset that can capture the trends in travel times for a longer period of time.

This paper studied the nature and variability of paratransit travel times. It first quantified the share of the various components of paratransit travel time and then explored within-day and day-to-day variation in the travel times. The paper contributes to bridging the gap in literature existing between bus travel time variability studies in formal bus services and those in informal public bus services. It used a rich volume of quantitative datasets to study the nature and variability of paratransit travel time. Insights gained from the analysis and findings can help planning authorities introduce interventions within the roadway environment or give travel advisories that can help users make informed choices that may improve their experiences using paratransit. The contribution of this paper takes on added importance given the fact that paratransit operators generally resist efforts at formalizing or replacing them, such that the understanding it yields can help planning authorities introduce measures that can help improve user experiences without full confrontation with operators of the service. The rest of the paper is organized in the following manner: A brief description of the study area is given in the methodology section, as are the data collection approach, processing, and analysis carried out. This will be followed by the results and discussions of some of the findings. The paper will end with a conclusion section.

2. Methodology

This study investigates the variability of paratransit travel time to gain insight that can help transport planners and relevant authorities proffer solutions to improve paratransit user experiences. The description of the study area, data collection design, and data processing are presented in this section.

2.1. Description of the study area and selected study route

The study was carried out in Kumasi. Kumasi is the second-largest city in Ghana after the capital, Accra. It is the capital of the Ashanti region. It is located at latitude 6°6666′N and longitude 1°6163′W. Kumasi is the heart of the Ashanti people, has a rich heritage of culture and tourism, and is a robust commercial hub. The city is made up of a metropolitan area and six municipal areas comprising Kumasi Metropolis, Oforikrom Municipality, Asokwa Municipality, Asokore Mampong Municipality, Suame Municipality, Kwadaso Municipality, and Tafo Municipality, covering a land area of about 254 km² (Cobbinah et al., 2020; Santuoh, 2022), which makes up about 0.9% of the region’s land area (Ghana Statistical Service, 2010). Kumasi, comprising the metropolitan area and sub-metros with the aforementioned municipal areas, has a total population of about 1,379,335 (Ghana Statistical Service, 2021; Santuoh, 2022).

Public transport in the city is predominantly private sector-supplied, comprising taxis, minibuses (trotro), buses, and three-wheelers in recent times (Poku-Boansi & Adarkwa, 2011). Trotros are second-hand minibuses with a carrying capacity of 10 to 20 passengers (Saddier et al., 2016), including the driver and his assistant, popularly called a ‘mate’. This particular mode is prevalent and was selected as the focus of the study. The trotro route from Adum in the central business district (CBD) to Ejisu was chosen for the study. A section of this route from Asafo Market to Zongo Junction has been isolated for analysis. This section has uniform roadway features throughout and beyond this section in the inbound direction into the CBD; different trajectories are available to access the station. The route is the entry point for travel from Accra and has a significant connection to the city center. It carries a high volume of traffic daily (specifically trotro trips), has a uniform roadway section throughout, and contains various roadway features like roundabouts, signals, and intersections. Figure 1 shows the location of the chosen study route, while Table 1 details the features of the route.

Figure 1. Map of the study route.

Table 1. Summary of roadway features for the section of the study route.

S/N	Road Features	Description of study route
1	Roadway description, carriageway type, and lanes	Urban Arterial, double carriageway, double lane in both directions
2	Number of roundabouts	4
3	Number of signal intersections	5
4	Length of study section	16.25km

The Adum end of the route is operated out of a typical paratransit station, which observes a queue with a fill-and-go system. This is not the case for the Ejisu end of the road, where there is no delineated station where trotros operate. The boarding point is a built-in bus stop close to the major roundabout. While the incentive to make a profit requires that the vehicle be full before the trip, the absence of an organized station means some buses can begin journeys without being full. Unregistered buses (floaters) are a part of the system and thrive by operating out of such locations. This makes the character of trips out of the Ejisu end distinct from the Adum end, hence the need to study both directions of the route.

2.2. Field data collection

Several pilot trips were made on the chosen route to get GPS coordinates of the points of the study section, test the data collection instrument, and gather information about typical trips that helped in the data collection strategy. The data collection approach and design reported here were part of a more extensive survey geared towards the real-time prediction of paratransit travel times using a machine learning model. A reasonably large amount of data will be required. Saddier et al. (2016) reported a methodology in which many trips were made in a short time and budget onboard paratransit buses to collect data using a mobile phone app. The use of mobile applications for data collection onboard paratransit vehicles has been adopted by other investigators (Coetzee et al., 2018; Falchetta et al., 2021; Gaibe & Vanderschuren, 2010; Joseph et al., 2020; Ndibatya & Booysen, 2020; Ndibatya et al., 2016; Saddier & Johnson, 2018). These studies have established that with mobile applications, a decent amount of location- and stop-related data can be collected simultaneously within a short time and budget. Thus, the study used a mobile application called Trands.

The Trands application is a mobile phone application for collecting GPS and stop-related data in a moving vehicle. It allows the user to record vehicle trip information such as type of vehicle, trip start times, trip pause or stop times, number of passengers, vehicle velocity, and periodic location data recorded every six seconds. The app uses the phone’s features to record GPS traces and speed in the background, while the user interface provides a platform for recording stops and other information. The collected data is stored locally on the phone first and can be uploaded later to the server, where the user can view and download it via a web platform. Users can set their preferred type of vehicle via the admin panel. They can assign multiple users to sign on and collect trip data for a single project. Currently, it only works on the Android platform.

Trained enumerators carried out the data collection. Travel time and stop data were collected on weekdays only from morning (06:30) to evening (18:00) by teams working in shifts for eight weeks. Eight enumerators were divided into two groups of four, each working the morning shift (06:30 to 13:30) and afternoon shift (12:30 to 18:00) for eight weeks, beginning late September to mid-November. On any shift, two enumerators begin their task at one end of the route while the others begin at the other. One enumerator is designated as the lead, while the other is the follower. The leader boards the trotro while the follower waits and plans their boarding and departure such that it is within 20 minutes maximum of the departure time of the lead. That way, they travel in a pilot system with a headway of no more than 20 minutes. SMS messaging between the leader and follower was used to track the departure times of the leader and follower in order to ensure that this design was followed. On each trip, whether by leader or follower, the data collection app records a GPS trace every six-second interval, including latitude and longitude, time stamp, and speed. The second category of information collected was stop-related. The app had an interface to record stop details, including the stop type (passenger-related and signal stops), stop location, and the number of passengers boarding and alighting when a stop is made.

At the start of a trip, the enumerator enters the origin and destination of the journey in the app and the passenger count at the start. When a stop is made for boarding or alighting purposes after the trip has begun, a passenger stop is indicated on the app. An interface will open to enter the number of passengers that boarded or alighted at that stop. After pushing this stop indication, the enumerator waits and watches movements in and out of the bus. The resume trip button is pressed when the bus has joined the traffic again, having entered the numbers of passengers that went off or came in at the stop. On the approach to a signal intersection, when the bus joins a queue and comes to a complete stop because of a stop indication, the delay button on the app is pushed. When the signal comes to continue and the bus begins to move as the queue ahead of it starts moving, the resume trip button is pressed by the enumerator, having entered any boardings or alightings that may have occurred at the traffic stop. If the bus does not clear the signal at one green indication, the delay indication is pushed again, and the same procedure is followed until the bus clears the signal intersection. This process of recording passenger-related stops and stops at approaches to signal intersections continues alongside the recording of other events on the trip until the bus arrives at its destination. At this point, the end trip button is pushed, and the trip record ends.

2.3. Data processing, cleaning, and analysis

Recorded trip data was retrieved from the app server as CSV files and processed into route travel times, dwell times, signal delays, and running times in Excel by taking advantage of features like power query, visual basic, etc. that allow for task automation. Using the GPS coordinates at both ends of the study section, the time a trip passed these points was filtered out of the trace data, and travel time was calculated as the time difference at the two ends. Dwell time and signal delays were estimated as the time difference between when the trip stopped and resumed, as provided by the app. These were then aggregated for all such stops on every trip. Running time was obtained by subtracting the sum of dwell time and signal delay from the trip travel time. Trips with incomplete or defective data were removed, and the box plot of travel time was used to clean out outliers. The box plot approach was used to clean out excessively long trips. Paratransit drivers are profit-driven and will adopt strategies, including an extended dwell time to wait for passengers at some strategic locations. These and other behaviors typical of paratransit service make some trips travel times longer. Such trips will be easily eliminated as outliers in other data cleaning approaches.

The fraction of the travel time that each component shares was determined by dividing each time component per trip by the trip travel time and expressed as a percentage. This was done for all trips, and the average was taken as the share of each component. The travel time data was aggregated into various one-hour departure windows to explore the within-day variation of paratransit travel time. These travel times were then plotted against the departure time to show the spread of travel times across the day. Various travel time variability measures that employ marked percentiles were used to investigate the variability in travel times within the day. T90–T10 measure the distribution’s width or spread (Bogers et al., 2008; Mazloumi et al., 2010). The larger the width, the more variability there is in travel times. T90–T10/T50 normalizes the distribution width around the median value. It is the 80% travel time ratio around the median relative to the median. Higher values of this measure indicate a high variation in travel time. T90–T50 and T50–T10 are measures that reflect how late and early trips relate to the median (Mazloumi et al., 2010). These measures were calculated for each hourly departure window and plotted against time to analyze the variation in travel time from hour to hour across the day. Heat maps, based on the coefficient of variation of travel times aggregated into various one-hour windows for each weekday, were employed in analyzing day-to-day variation in the travel times.

3. Results and discussions

The results of the analysis carried out to quantify the components of paratransit travel time and explore the variability of paratransit travel times for both directions of the study route are reported. In all, 1894 trips in both directions were made in the data collection effort. These were cleaned, processed, and used for the analysis described in the previous section.

3.1. Quantifying paratransit travel times

The dwell time, running time, and control delay component of trip travel times in both directions of the study section were aggregated to determine the share of each component. Table 2 summarizes the percentage share of the various parts.

Table 2. The percentage share of paratransit travel time components on the study route.

ROUTE/DIRECTION	DWELL TIME (%)	CONTROL DELAY (%)	RUNNING TIME (%)	NO OF TRIPS
Adum to Ejisu	15	15	70	699
Ejisu to Adum	16	13	71	592

In the outbound direction from the CBD (Adum to Ejisu direction), about 15% of travel time was spent on boarding and alighting. In the reverse direction, 16% of the time is spent for dwelling purposes, a slight increase of 1% from the outbound direction. Comparatively, this is higher than in formal bus services, which yielded 13% and 10.3%, respectively, in studies conducted by Bertini and El-Geneidy (2004) and Tirachini (2013). This is expected for an informal service where stops are made on the route on demand. The more stops, the longer the dwell time. Also, it is common for stops to be made waiting for passengers to arrive and for casual passenger requests for personal reasons. All these contribute to increasing the amount of travel time spent dwelling.

3.2. Within-day travel time variability

Travel time data in both directions of the route was aggregated into a one-hour departure time window. Figure 2 shows the spread of travel time across the day. The 10^th, 50^th, and 90^th percentiles have been marked on the plot. Each point on the plot represents the travel time for a completed trip in the study section. The points on any given departure hour are the travel times of trips that occurred in the hour preceding it. For instance, the points on the 7:00 a.m. departure time represent travel times of trips departing in the hour from 6:00 a.m. to 7:00 a.m. The percentile point on each departure hour indicates the travel time limit of the corresponding percentile.

Figure 2. Travel time observation within the day in different one-hour departure windows with 10^th, 50^th, and 90^th percentiles: (a) Adum to Ejisu (b) Ejisu to Adum.

Three time periods can be made from the result of the spread of travel times in both directions. A morning peak period from 6 a.m. to 10 a.m., an off-peak period from 10 a.m. to 3 p.m., and an evening peak from 3 p.m. to 6 p.m. In the morning peak period, the outbound direction (Adum to Ejisu) shows lower travel time values, increasing as the day progresses. This is due to directional demand. Less traffic is leaving the CBD in the morning. Also, trips made from the station at the CBD during the morning period will likely be shorter as the buses start with a full passenger load, and most passengers will start alighting long into the trips, thus reducing the stoppages at the early trip stages. The reverse is the case in the inbound direction (Ejisu to Adum direction) in the morning into the CBD. A distinct morning peak with higher travel times is observed due to increased traffic and demand for morning trips into the city center. This reduces during the day as the demand continually declines. Notice how the 10th, 50th, and 90th percentile trends are more parallel in the inbound direction than the outbound direction. This indicates a comparatively stable variation in travel times over the day in this direction.

Figure 3 shows the plot of the various travel time variability measures across the day. In the Adum to Ejisu direction (Figure 3a), there is a fluctuating trend in the variation in travel time, as indicated by the width and normalized width of the distribution. There were high points of variability in the morning peak period (10 a.m.), off-peak period (12 p.m. and 2 p.m.), and evening peak period (6 p.m.). Early trips are contributing to the variability in travel time almost throughout the day in this direction. Early trips are those with travel times in the tenth percentile for all trips occurring within the given departure hour, while late trips are those in the ninetieth percentile. The early trips are characterized by a relatively lesser number of stops, longer dwell times, and a higher load factor compared to other trips in the departure hours. This is because many passengers boarding at the station are alighting long into the trip, such that the vehicles travel with a high load factor for much of the trip. In the inbound direction into the CBD (Figure 3b), the width of the distribution reaches its highest point in the morning peak period. Then it becomes relatively stable over a given range for the day.

Figure 3. Differences in travel time percentiles across the day in different one-hour departure windows: (a) Adum to Ejisu (b) Ejisu to Adum.

When the width of the distribution is normalized against the median, the morning peak period is less variable than all other periods in the day, with the highest variability occurring in the evening peak period. Late and early trips are contributing to the high variation in travel time from the morning and afternoon periods in the Ejisu to Adum direction. Late trips were mainly responsible for the variation experienced in the evening period in this direction. The late trips have comparatively more stops, dwell times, and load factors than the other trips in the departure hour. The lack of a dedicated station may be responsible for late trips, contributing to the variation in travel times in this direction. Because many vehicles begin the trips without full capacity, they will adopt slower driving styles and idle at some stops in active search for passengers. This contributes to their longer dwell times, and as many such trips occur, the travel times become more variable.

To contextualize the observed variabilities in paratransit travel times on the study route, they were compared with findings on a formal bus route almost double the length of the study route (Mazloumi et al., 2010). The highest difference in the distribution width for the study section in the Ejisu to Adum direction (into the CBD) was more than twice the highest for that of the formal bus service in the CBD-bound direction. Paratransit travel times varied more throughout the day and showed no distinct pattern. The nature of paratransit operations on the route is thus reflected in their variability across the day. More understanding can be gained from exploring the variability in each one-hour window from day to day.

The operation of a typical paratransit station where the fill-and-go system is in effect or the lack of it has been shown to play a role in the travel time variabilities of trotro trips on the studied route. In the trip direction where the station is operational, a lot of early trips are occurring compared to trips with average travel time for most parts of the day. This has implications for servicing demand for trips along the route, as users who are not very far away from the station and require the service will wait longer for vehicles whose capacity is not full. This presents an opportunity for exploring a staggered fill-and-go system at the station end where some vehicles depart at full load and others at 50% or 75% full so that demand at early trip stages can be met while at the same time improving the gap in travel time variation. A solid business case that shows that driver earnings would not be significantly affected or would be covered where earnings are affected will be needed to implement such a proposal.

3.3. Day-to-day variability analysis

The travel time dataset was filtered into specific weekdays and for each departure time window to understand the day-to-day variation in travel times on the study routes. The coefficient of variation (CV) was used as the variability measure in the heat map to describe the daily variation in both directions of the study route (Figure 4). The entire travel time dataset was clustered into various one hour departure window for each of the weekdays and used to estimate the coefficient of variation for each period. The deeper the intensity in color on the heat map, the higher the variation in travel time for the given departure hour.

Figure 4. Coefficient of variation based day to day variability of trotro travel times in both directions on route 1: (a) Adum to Ejisu (b) Ejisu to Adum.

In the outbound direction (Figure 4a), Fridays perform better than all other days, with Wednesdays being the worst in terms of variabilities in travel times. In the reverse direction, however, Wednesdays have the least number of periods with high variation in travel times (Figure 4b), with Tuesdays having more one-hour periods with the highest variability range. It is observed from the heat maps that the day-to-day variability is comparatively less in the morning from 6:00 a.m. to 12 p.m. than the rest of the day in the inbound direction into the CBD (Figure 4b), while the variation in travel times is comparatively higher in the morning period from 6:00 a.m. to 12 p.m. than in other parts of the day in the outbound direction (Figure 4a). Paratransit trip and traffic demand as well as driver behaviors largely account for comparatively lesser variation in daily travel times in peak periods in both study route directions.

In the outbound direction in the morning, demand for paratransit trips and traffic is lower because most journeys are made into the CBD for work, business, and other purposes. Trips originating from the CBD are always full because of the fill-and-go system at the station. With a high load factor at the beginning of trips and a relatively light traffic situation, many trips are likely to happen faster (early trips). However, the profit-seeking behavior of paratransit will get the better of some trips in the morning periods in this direction, so that in later parts of the trip, when the load factor on the vehicle reduces, a slower speed and idling at stops for passengers are adopted by the drivers, thus widening the difference in travel times with those of early trips. Because of this gap in the drivers’ behavior, travel time variability is greater in periods of low traffic, and demand for paratransit trips is higher. In periods of higher trip demand and traffic, such as in the later part of the day in the outbound direction and the morning in the inbound direction, most paratransit vehicles will operate at a high load factor. This reduces the need for longer dwell times at stops for passengers to arrive. At the same time, the higher traffic situation ensures that a driver’s desire to go faster to complete a trip is curtailed, thus ensuring that driving behaviors are more aligned in these periods. The resultant effect of these is a higher travel time, but with comparatively lesser variation in travel times than in periods of lesser demand and traffic.

The Kolmogorov-Smirnov (KS) test was carried out to determine if the variation in travel times among weekdays was significantly different in both directions of the same study route. Since the distribution of travel times for a given day captures its variability and other characteristics, the null hypothesis, in this case, was that the travel times for each combination of days were from the same distribution. The results for all combinations of weekdays in both directions are shown in Table 3.

Table 3. Kolmogorov Smirnov (KS) test for significant variation in trip times among weekdays in both directions of the study route.

Combination of Days	Adum to Ejisu Direction		Ejisu to Adum Direction
	P - Value	Hypothesis	P - Value	Hypothesis
Monday & Tuesday	0.452	1	0.941	1
Monday & Wednesday	0.041	0	0.816	1
Monday & Thursday	0.501	1	0.198	1
Monday & Friday	0.048	0	0.009	0
Tuesday & Wednesday	0.103	1	0.607	1
Tuesday & Thursday	0.923	1	0.192	1
Tuesday & Friday	0.018	0	0.005	0
Wednesday & Thursday	0.156	1	0.144	1
Wednesday & Friday	0.000	0	0.014	0
Thursday & Friday	0.023	0	0.132	1

The hypothesis column is the decision from the test as a result of the p-values. One indicates that the null hypothesis is accepted, i.e. that there is no significant variation in travel times among the compared days. Zero means the null hypothesis is rejected, and the compared days significantly differ in trip travel times over the entire period of those days. Five combinations of days were significantly different in the Adum-Ejisu direction, four of which involved Fridays. This shows that travel times on Friday in that direction are drawn from a different distribution and experience a distinct variation in trip times from other days. In the reverse direction, three combinations were significantly different, all with Friday involved. The same conclusion can be drawn for the reverse direction: travel time variation on Friday significantly differs from other days. Such a finding is crucial in a paratransit travel time prediction model, for instance. Introducing the day of the week as a variable will require clustering the dataset by the day of the week, thus reducing the number of observations available for building the model. This is a limitation for paratransit vehicles, where no technology like automatic vehicle location and automatic passenger counters is available for continuous data collection to generate massive datasets. By knowing how significantly different variability is from day to day, a decision can be made about a modeling scheme that caters to the limitations of the available data that face paratransit while also ensuring the high performance of the models.

4. Conclusions, policy implications, and Future Research direction

This study sought to understand the nature of paratransit travel times by first quantifying the various components of travel time and exploring the variability in travel times within the day and from day to day. A unique travel time survey that used a designed mobile application onboard a paratransit vehicle on the study route was used to collect a large dataset in both directions on the study route. The result shows that, on average, 15% and 16% of the travel time was spent for boarding and alighting purposes in the inbound and outbound directions of the study route, respectively. The informal nature of the paratransit service was reflected in the variation in travel time, which was comparatively higher than in formal bus services. Interestingly, and contrary to intuitive reasoning, travel times were relatively less variable within the day in periods of higher trip demand and traffic (afternoon to evening in the outbound direction and morning to afternoon in the inbound direction) than in periods of lower demand and lesser traffic. The insights gained from the study are significant for planning purposes and can bring real improvements that will benefit the users. For instance, knowing the fraction of the components of travel time can help formulate interventions geared toward reducing the share of the given component. Output like the heat map of day-to-day variation can be used to provide travel advice about the reliability of routes and for general information purposes.

This study has demonstrated that valuable insights can be gained from travel time variability analysis that can help users and planning authorities. Most paratransit regulatory and transport planning authorities focus on revenue-generating functions like granting permits and licenses to driver unions and enforcing compliance, to the detriment of service users. The users of the service who have expressed dissatisfaction with the quality of service they receive must be considered in policy formulation and practice. While paratransit is informal and privately owned, such that interference in their mode of operation by the government is frowned upon, studies like this can help the government implement strategies that can improve travel times for the users in the road environment where they have authority. Also, the day-to-day variability reported here through heatmaps can be expanded on major paratransit routes and used as travel advisories to keep users informed. Putting the interests of users in the consideration and focus of the authorities would require significant capacity improvements by the relevant authorities for data collection and analysis that can yield outcomes that will help the users. The need for dialogue and engagement with the paratransit drivers and owner unions about the interests of the users should be encouraged and entrenched. That way, it becomes easier for soft interventions from the authorities that do not infringe on the owners’ and drivers’ desire to control how they run their businesses to be introduced without much resistance.

Understanding the variability in travel time of paratransit trips within the day and from day to day is a practical first step towards modeling travel times to provide information to the user. Future research efforts in this direction might want to exclude the day of the week variable from their considerations, as this study showed that most days of the week have similar variabilities. While including this variable may likely yield better prediction accuracies, clustering datasets into day-of-the-week variables reduces data volumes, making such an approach unsuitable for machine learning techniques. Since paratransit vehicles do not have onboard devices for continuous data collection, modeling efforts would have to trade off a slight reduction in accuracy by excluding the day of the week variable with the cost of manually collecting more data onboard the vehicles. This study is limited in that it did not consider weekends. Future studies can include weekends and compare findings with weekday variabilities.

Acknowledgments

The authors acknowledge the Regional Transport Research and Education Centre, Kumasi (TRECK), of the Department of Civil Engineering, Kwame Nkrumah University of Science and Technology, Kumasi (KNUST), Ghana, whose grant funded the research. The authors wish to thank Mrs. Theresa Adjaidoo of the Department of Computer Science, KNUST, who modified the data collection app (Trands) that was used in the data collection. We also acknowledge the efforts of Randolph Wilson of the Department of Transport, Kumasi Metropolitan Assembly (KMA), who provided information about trotro services and provided initial support for getting enumerators for the data collection.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The work was supported by the Kwame Nkrumah University of Science and Technology .