ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT
AZOJETE, June, 2019. Vol. 15(2):406-417

Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria.
Print ISSN: 1596-2490, Electronic ISSN: 2545-5818

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406

ORIGINAL RESEARCH ARTICLE

PREDICTION OF BUS TRAVEL TIME ON URBAN ROUTES WITHOUT DESIGNATED BUS
STOPS IN MAKURDI TOWN, BENUE STATE, NIGERIA

P. T. Adeke1*, O. J. Inalegwu2 and K. Jirgba3
(1,2Department of Civil Engineering, College of Engineering, Federal University of Agriculture Makurdi,

Benue State, Nigeria.
3Department of Civil Engineering, Faculty of Engineering and Technology, University of Ilorin, Ilorin,

Kwara State, Nigeria)
*Corresponding author’s e-mail address: adeke.pt@outlook.com

ARTICLE INFORMATION

Submitted 14 September, 2018
Revised 17 February, 2019
Accepted 19 February, 2019

Keywords:
Makurdi town
bus services
Bus travel time
multiple linear regression
model
ANN model

ABSTRACT
The lack of information on bus travel time in Makurdi town to enable
trip makers plan for journeys is seen as a challenge in recent times. This
study developed a multiple linear regression model for predicting bus
travel time along bus routes in Makurdi town. Specifically, the study
assessed bus travel time on routes without designated bus stops,
examined geometric features of bus routes, assessed bus dwell time
and travel speeds in a heterogeneous traffic stream on routes in
Makurdi town. It developed and validated a model for the bus travel
time. Field survey focused on the major bus routes in Makurdi town
which included; High Level roundabout to School of Remedial Studies
junction (HL-SRS), High Level roundabout to Federal Medical Centre
junction (HL–FMC), Wurukum roundabout to Coca Cola Complex (W-
CCC) and Wurukum roundabout to Welfare Quarters junction (W–WQ).
Independent parameters examined on the sites for model development
included; bus route length, bus travel speed, average dwell time at
random stops for pick-up and alighting of passengers, bus headway,
the total number of cross and Tee intersections along the bus route,
volume of motorcycles, private cars and trucks in the traffic stream,
while the dependent variable was bus travel time. Based on the built
model, 15 minutes approximately was established as the average bus
travel time for all bus routes in Makurdi town assuming all other
variables have zero magnitude. Goodness of fit test of the model
yielded significant value for coefficient of determination (R2 = 0.952)
and the use of Artificial Neural Network (ANN) method for validating
the model also confirmed it accuracy at 93% approximately. It was
therefore concluded that, bus travel time on major routes in Makurdi
town could be accurately estimated using the built multiple linear
regression model provided all essential input parameters of the model
are used. The establishment of designated bus stops along bus routes
within Makurdi town to minimise bus dwell frequency and for accurate
estimation of bus travel time, as well as erection of travel information
bill boards along bus routes stating average bus travel time to inform
commuters that have high value of travel time were recommended.

© 2019 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved.

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Arid Zone Journal of Engineering, Technology and Environment, June, 2019; Vol. 15(2):406-417. ISSN 1596-2490;
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407

1.0 Introduction
One of the essential parameters used for measuring the level of liveability of cities is the
effectiveness of their public transport systems which mostly focuses on bus services (Cullinane,
2002; Ceder, 2007; Gurmu, 2010; Ibarra-Rojas et al., 2015; Gudmundsson et al., 2015). Public
transport services in most urban areas of developing countries like Makurdi town of Benue State
employ the use of mini buses. These buses are usually owned and operated by non-
governmental organisations or private individuals who gain profit from the business of providing
public transport services. Bus services for public transport has been in use from time immemorial
especially in developed countries (Cullinane, 2002; Zheng, 2011). The capacity of mini buses
ranges between 10 – 14 persons, unlike standard bus services in modern cities in Europe, USA,
Canada, etc. that use coaches whose capacities range between 20 – 60 persons. In most cities of
developing countries, the minibuses usually shuttle along routes to pick-up and alight
passengers at non-designated stops that are rather convenient to the passengers as they alert
drivers whenever they wish to alight. These buses operate in an interrupted and heterogeneous
traffic stream characterised by mixed traffic flow and pedestrian interferences (crossing at non
designated spots). This disorderly and continues stop-and-move movement of mini-buses along
routes in search of passengers, boarding and alighting has significant impact on the smooth flow
of traffic, hence affects travel time significantly (Izadpanah, 2010; Ibarra-Rojas et al., 2015). Also,
while commuters hope to arrive at their destinations quickly, bus travel time is basically
influenced by time used for walking from/to the bus stops, waiting time at the stop, in-vehicle
travel time, and mode transfer period, etc. These processes are associated with traffic congestion
and affects the certainty of travel time estimation which makes its prediction more complicated
(Ibarra-Rojas et al., 2015). In such a mixed traffic situation with a lot of complications, it is more
meaningful to attempt a short term bus travel time prediction which falls within the range of 0 to
60 minutes so as to minimise the impact of variability among estimated variables (Izadpanah,
2010; Gurmu, 2010). In line with previous researches, it has been observed that all essential
parameters employ for estimation of (bus) travel time exhibit stochastic properties with high
degree of uncertainty (Jeong, 2004; Ramezani and Geroliminis, 2012), which therefore requires
sophisticated method of analysis.
The importance of travel time in assessing road network performance by transport planners and
engineers for efficient operation management and for developing travellers’ information system
for commuters cannot be overemphasised. This is because most travellers’ are keen about trip
planning and wish to optimise or minimise waiting time due to their high value of travel time
(Schiller et al., 2010; Zheng, 2011; Zaki et al., 2013; Mannini et al., 2015; Gudmundsson et al.,
2015). According to Bonsall et al. (2005), the act of modelling behaviour of transport systems
using realistic assumptions is very essential, “it is better to use values that are realistic-but-
unsafe than values that are safe-but-unrealistic”.
Like many other prediction models, researchers have stated that accurate prediction of bus
travel time is very difficult, especially in a system where public transport system is not given
priority (Liu, 2010), only average value could be easily estimated since most factors affecting the
estimation of travel time are stochastic in nature (Ramezani and Geroliminis, 2012; Bharti et al.,
2017). These factors include weather condition, time of the day, driver behaviour, traffic volume,
vehicle characteristics, etc. (Izadpanah, 2010; Liu and Sinha, 2007). Technically, major factors that
can influence bus travel time include; intersection delays due to queues and traffic control
operations, delay caused by turning vehicles, on-street parking of vehicles, crossing pedestrians
and cyclists, etc. (Zheng, 2011; Liu et al., 1999). Others include travel distance, number of stops,

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Adeke, et al: Prediction of Bus Travel Time on Urban Routes Without Designated Bus Stops in Makurdi Town, Benue
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Corresponding author’s e-mail address: adeke.pt@outlook.com 408

dwell times, number of boarding passengers and alighting passengers and weather description
(Gurmu and Fan, 2014). Though a difficult task to achieve, technologies used for data collection
in developed countries for the purpose of travel time prediction have improved accuracy of
estimations. Morden devices used for data collection include; probe vehicles, loop detectors,
digital cameras, Automatic Number Plate Recognition (ANPR) camera, Bluetooth scanners, speed
sensors (Coifman, 2000; Zheng, 2011; Bharti et al., 2017).
There are several bus travel time prediction models developed by previous researchers.
Analytical techniques such as probability theorem (Bharti et al., 2017), regression models (You
and Kim, 2000; Wu et. al., 2004; Bharti et al., 2017), Artificial Intelligence techniques (Gurmu, 2010;
Gurmu and Fan, 2014; Bharti et al., 2017; Zaki et al., 2013; Kumar et al., 2017), etc. have been
used in the past. The degree of accuracy of these models depends on the level of variability of
input parameters and the reliability of the analytical technique used (Izadpanah, 2010; Gurmu,
2010; Kumar et al. 2017). Zaki et al. (2013) combined the Neural Network (NN) and the Kalman
Filter Techniques to form a hybrid methodological algorithm for estimating arrival time at bus
stops using Global Positioning System (GPS) data and historic travel speed data, the study
yielded satisfactory results.
Bharti et al. (2017) considered traffic volume and car percentage composition in traffic stream as
independent variables for travel time estimation modelling. The authors recommended the use
of Artificial Intelligence method such as the Artificial Neural Networks (ANN) and the use of
Stochastic Response Surface Methods (SRSM) since they yielded relatively accurate results
compared to the multiple linear regression model. Though, the multiple linear regression model
dose not predict bus travel time accurately as stated by other researches (Gurmu and Fan, 2014;
Bharti et al., 2017), its approach is capable of measuring the degree of sensitivity of all the input
variables used for predicting the bus travel time (Gurmu and Fan, 2014).

It is not certain if the transferability of calibrated and validated bus travel time prediction models
built by previous researchers for other locations will suite cities like Makurdi town, Benue state of
Nigeria. Major challenges of bus services in cities of developing countries like Makurdi town
include poor services characterised by disorderly and uncertain/non-organised operations on
routes without designated bus stops (Zheng, 2011). It therefore becomes a challenge for
concerned persons or organisation to develop local models that actually suits the unique
properties of developing societies. Some of the peculiar properties that may weaken the
strength of other existing models for use in developed cities include the use of bus rapid
transport (BRT), bus assigned lanes, designated bus stops, bus time table, etc. Efficient public
transport system in cities is important because it improves their liveability and boost economic
and social growth of the cities (Gurmu, 2010). Because there is no previous research work which
attempted to predict bus travel time on routes without designated bus stops in a heterogeneous
traffic stream associated with several uncertainties in estimating model input parameters, in this
part of the world, this study is relevant and justified.
The study aims at developing a multiple linear regression model for predicting bus travel time
on urban roads without designated bus stops based on bus services in Makurdi town and, then
validate the model using ANN technique. Objectives of the study include; to assess bus travel
time on routes without designated bus stops, to examine geometric features of roadways, to
assess bus dwell time and travel speeds in a heterogeneous traffic stream on routes in Makurdi
town, to validate the built model and examine sensitivity of all input variables.

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2. Literature Review
2.1 Multiple Linear Regression Model
The multiple linear regression model is a mathematical function that defines the relationship
between independent (input) and the dependent (output) variables that explain the behaviour of
a system (Rohatgi and Saleh, 2001; Soong, 2004). Development of multiple linear regression
model usually employs statistical tools such as; Statistical Product for Service Solution (SPSS), R
Programming, Microsoft Excel, etc. which are capable of defining the relationship between the
independent and dependent variables in form of a function. The strength of the function is
usually examined using it coefficient of determination (also known as r square – R2) value which
ranges from 0 – 1, with 0 defining a weak relationship and 1 showing a stronger relationship
between variables (Rohatgi and Saleh, 2001). Another relevant model performance indicator is
the measure of sensitivity of input variables using their respective p-values. The p-value tests the
null hypothesis that coefficient of a variable is equal to zero, meaning the variable has no effect
on the model; such that a low p-value (< 0.05) indicates that the null hypothesis should be
rejected, that is, the variable is likely to be meaningful to the model. Multiple linear regression
models are generally expressed as mathematical function in the form shown in Equation 1;

Y = β0 + β1X1 + β2X2 + β3X3 + . . . + βnXn - - - - - (1)
where, Y is the dependent variable, Xi and βi for i = 1, 2, . . n denote the independent variables
or input parameters and their respective coefficients, β0 is the constant value which defines the
average behaviour of the system when the magnitude of all other variables is zero. n represents
the total number of input variables used in the model. The use of multiple linear regression
model for property or performance prediction of engineering systems has been in use over a
long period of time (Ramakrishna et al., 2006; Gurmu and Fan, 2014). The model best suites
systems that exhibits deterministic behaviour rather than those that are stochastic in nature,
since stochastic systems exhibit behaviours that are nonlinear or uncertain and difficult to
predict (Zheng 2011).

2.2 Artificial Neural Network (ANN) Models
The ANN method is an Artificial Intelligence (AI) technique used for analysing systems
(Munakata, 2008; Russell and Norvig, 2010). The application of ANN models in predicting bus
travel time has gained acceptance decades ago (Balaubramanian and Rao, 2015; Amita et al.,
2015). It is an iterative simulation process which has gained wide acceptance in predicting
system behaviour due to its ability to handle system complexities of nonlinearity and challenges
of missing or incomplete dataset, inaccurate data, etc. The network consists of numerous layers
of parallel processing neurons. Hidden layers exist between input and output layers. Neurons in
one or more hidden layers are connected to the neurons of the neighbouring layers by weighted
factor that is adjustable during model training process. ANN model could adopt a sigmoid
performance function which is probabilistic in nature having multilayer processing framework
capable of accepting multiple inputs to produce the desired outputs. Running an ANN model is
an iterative and a trial-and-error process which requires specifying the number of layers which
are usually more than one (Gurmu and Fan, 2014). The training process requires a feed forward-
backward propagation algorithm, specification of the maximum number of training epochs and
number of iterations which describes the number of times a batch of data passes through the
algorithm for forward and backward propagations. From the process, mean square errors and

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Adeke, et al: Prediction of Bus Travel Time on Urban Routes Without Designated Bus Stops in Makurdi Town, Benue
State, Nigeria. AZOJETE, 15(2):406-417. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: adeke.pt@outlook.com 410

biases of estimations are usually computed using the model function specified. Figure 1 is an
architectural presentation of a typical ANN model.

Figure 1: The Architecture of an ANN Model (Amita et al., 2015)

The ANN method is usually implemented using software that are capable of simulating the
probabilistic behaviour of the systems such as the ANN tool found in MATLAB (Zheng, 2011;
MATLAB, 2018). The ANN tool in MATLAB is used to simulate systems based on the ANN model.
It requires input parameters, targeted output values, then validate results to a certain degree of
accuracy. It is therefore relevant to employ such technique in this study for model validation to
check for variations caused by the probabilistic nature of some input variables such as dwell time,
bus headway, traffic composition, etc. as they influence the regression model significantly
(Gurmu and Fan, 2014; Amita et al., 2015).

3. Materials and Methods
3.1 Description of Study Area
This study was carried out in Makurdi town, Benue state of Nigeria. Makurdi town is an urban
area known to be the capital city of Benue State, Nigeria. The city located on Latitude 7° 43’ 56”
and Longitude 8° 32’ 21” (Google Earth, 2018) has an estimated human population of over
367,588 persons with a land mass of approximately 800 km2 (NPC, 2006). Traffic streams in
Makurdi town are described as being heterogeneous since they comprise private cars, mini
buses, Heavy Goods Vehicles (HGV) and Light Goods Vehicles (LGV), motorcycles, tricycles and
pedestrians. Though mini-buses are the major mode for mass transit in Makurdi town, the
design and construction of roadways in the town does not provide special road facilities such as
bus lane for the mini-buses therefore, the buses travel and share lanes with other traffic
components. This is described as a mixed traffic stream since it comprises different modes
including pedestrians. Traffic flow in Makurdi town is generally characterised by interruptions

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from differed sources such as pedestrian crossing, the stop-and-move pattern of mini-buses that
have no designated stopping spots (bus stops) along the routes, operations of intersection, etc.
Town shuttle mini-buses operating within the city travel along the arterials conveying
commuters along the routes. The routes in Makurdi town considered by this study as presented
in Figure 2 included; the High Level roundabout – School of Remedial Studies Junction (HL -
SRS), High level roundabout – Federal medical centre junction (HL – FMC), Wurukum
roundabout – Coca cola complex (W - CCC) and Wurukum roundabout – Welfare quarters (W –
WQ).

Figure 2: Sampled Routes on An extract Map of Makurdi town (Google Earth, 2018)

3.2 Data Collection
Trained traffic enumerators carried out the field survey. The road network in Makurdi town was
divided into routes namely; HL - SRS, HL – FMC, W – CCC and W – WQ. The movement of mini-
buses used for public transport services in Makurdi town within the traffic streams was examined
from 07:00 am to 05:00pm daily. The geometric characteristics of bus routes such as; route
length, average lane width and number of lanes in both directions. Other essential model
parameters and methods of measurements were as following;
Traffic volume in one direction (veh/h) - This was measured using manual traffic count technique.
The composition volume of motorcycles, private cars and trucks in the traffic stream were
estimated. Materials used were basically record sheets, stop watch and writing instruments.
Bus travel speed (km/h) – It was estimated using the plate number matching methods. This
involved identifying the bus plate number from its journey origin, then total travel speed was
estimated using time lapse during the journey period, and the route length measured using a
meter counter wheel.
Average Bus headway (s) – It is the average time lapse between the passage of a sampled lead
bus and the following bus measured from bomber-to-bomber using a defined reference spot
marked on the road pavement as buses pass over along the routes.

W-CC

HL-SRS

HL-FMC

W - WQ

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Adeke, et al: Prediction of Bus Travel Time on Urban Routes Without Designated Bus Stops in Makurdi Town, Benue
State, Nigeria. AZOJETE, 15(2):406-417. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: adeke.pt@outlook.com 412

Average dwell time (s) – This is the time lapse between stops for pick-up of passengers and
start-up movement of buses. It was measure by an enumerator who travelled along with the bus
from its origin to the destination.
Bus Travel time in minutes (min) – This is the time required for a mini-bus to travel from its
origin to the terminal point of the journey or destination of the trip.
Number of intersection (unit) – These were counted by the enumerator who travelled along with
the bus. Types of intersection identified included; roundabouts, cross-intersection and T-
intersections.
Total distance travel (m) – This is the distance between the origin and destination of the journey
measured along the travel route using the meter counter wheel. For a given road segment, it
was measured in meters (m).

3.3 Data Analysis
A multiple linear regression model for estimating short term bus travel time along routes
without designated bus stops was developed using SPSS. The process involved creation of a
spreadsheet in Microsoft Excel for the raw data which comprised the independent and
dependent variables. The Excel file was then imported into SPSS for statistical analysis to build
the regression model. Results of the analysis revealed the data characteristics which was used to
check for accuracy of the built model. The built model was first validated using goodness of fit
test based on the measured (on field) and predicted (using model) bus travel times. It was
further validated using ANN tool simulated in MATLAB. The simulation process involved series of
iterations at several times to arrive at a better fit for the network model testing, validation,
training and estimation of the overall coefficient of determination of variables. The validation
process aimed at comparing outputs of the multiple linear regression model and those of the
ANN model using, coefficient of determination value for best fit.

4.0 Results and Discussion
Table 1 shows the geometric characteristics of bus routes in Makurdi town as considered by this
study.
Table 1: Geometric Characteristics of Minibus Routes in Makurdi Town
Name of
Bus Route

Carriageway
Share
(Dual/Single)

Number of
lanes in one
direction

Avg. Lane
width (m)

Route
Length
(m)

Number of Intersections
Roundabouts Cross Tee

HL – SRS 70%/30% 2 3.60 6420 1 3 2
HL – FMC 80%/20% 2 3.47 4000 1 1 3
W – CCC 100%/0% 2 3.70 5000 0 3 4
W - WQ 0%/100% 1 3.50 4000 0 1 5

Table 1 revealed that, only few bus routes in Makurdi town have dual and single carriageway
along the entire route length. Some routes have alternating type of carriageway for dual and
single. Only major cross and Tee intersections connecting the highways and arterials were
counted. Intersections connecting minor streets supplying less than 50 Veh/h were ignored. Only
traffic flow in the direction of movement of sampled mini-buses with corresponding geometric
features were considered.

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4.1 Model Development
This study employed the multiple linear regression and ANN methods of modelling for the
prediction of bus travel time along routes in Makurdi town.

4.1.1 The Multiple Linear Regression Model
A multiple linear regression model for estimating short term bus travel time on routes within
Makurdi town was developed using SPSS software, the summary of results from the statistical
analysis were as shown in Table 2.

Table 2: Summary of Statistical Results of the Multiple Linear Regression Model
Model Unstandardized

Coefficient
t-statistic p-value 95% Confidence interval for βi

βi Std.
Error

Lower bound Upper bound

Constant 14.962 1.604 9.328 0.000 11.757 18.167
Js -0.024 0.002 -13.292 0.000 -0.027 -0.020
Rl 0.002 0.000 8.281 0.000 0.002 0.003
Tm 0.001 0.002 0.744 0.460 -0.002 0.005
Tpc -0.006 0.003 -1.959 0.055 -0.013 0.000
Tt -0.029 0.019 -1.531 0.131 -0.066 0.009
ADt 0.008 0.006 1.363 0.178 -0.004 0.020
Cj 0.507 0.256 1.978 0.052 -0.005 1.018
Bh -2.374 2.305 -1.030 0.307 -6.980 2.232

R2 = 0.954
Adjusted R2 = 0.949

Table 2 revealed that journey speed, composition of private cars and trucks in a traffic stream
and bus time headway affects bus travel time negatively, in other words, the variables are
inversely proportional to bus travel time. This implies that the higher the magnitude of these
aforementioned variables the lesser the bus travel time. On the other hand, the higher the
magnitude of route length, composition of motorcycle and tricycles in the traffic stream, average
dwell time and number of cross-junctions along the route the higher the bus travel time. These
results agreed with findings of Gurmu and Fan (2014). This model indicates that, the estimated
average bus travel time along routes in Makurdi town without considering the impacts of other
variables is approximate 15 minutes (constant).
Table 2 also shows the statistical strength of the built multiple linear regression model. Though
the coefficient of determination obtained from the analysis (Adj. R2 = 0.949) showed a strong
relationship in estimating output using the input variables considered by the study, only p-
values for the journey speed and route length variables showed a stronger relationship (having
value of 0.00) between the input and output variables in the model. The p-values for traffic
composition of private cars and number of crossed intersections along the route showed a slight
(> 0.05) variation which indicates it significant strength in determining short term bus travel time
using this model. Other independent variables such as the composition of motorcycle and trucks
in the traffic stream, average dwell time and average bus headway showed less importance in

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Adeke, et al: Prediction of Bus Travel Time on Urban Routes Without Designated Bus Stops in Makurdi Town, Benue
State, Nigeria. AZOJETE, 15(2):406-417. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: adeke.pt@outlook.com 414

estimating bus travel time using this model, which agreed with findings of previous researchers
(Gurmu and Fan, 2014). Therefore, the developed mathematical model for predicting short term
bus travel time is as shown in equation 1;

TT = 14.962 − 0.024Js + 0.002Rl + 0.001Tm − 0.006Tpc − 0.029Tt + 0.008ADt + 0.507Cj - 2.374Bh
- - - - - - - (2)

Where: TT is the estimated bus travel time measured in minutes, Js is journey speed of the bus
measured in meter per minute, Rl is the bus route length measured in meters, Tm is the volume
of motorcycles in the traffic stream measured in units per hour, Tpc is the volume of private cars
in the traffic stream measured in vehicles per hour, Tt is the volume of trucks in the traffic stream
measured in vehicles per hour, ADt is the average dwell time measured in seconds. Some
variables such as the number of roundabout along routes,, number of Tee intersections along
routes and the composition of motorcycles in traffic stream as obtained from the field work were
ignored by the statistical tool (SPSS) used for the analysis which indicated their irrelevance to a
great extent in predicting bus travel time using the built model.

4.1.2 Model Validation
Statistical test for goodness of fit using the actual and estimated dataset was carried out using
the plot shown in Figure 3. The coefficient of determination obtained from the plot was 0.95
which indicated that, the model discribes up to 95% of the vaiables considered in the study
which shows a statistically good fit.

Figure 3: Model Validation using Statistical Method

An intelligent approach was also employed to further examined the fitness of the built model
since p-values of some variables considered by the model such as the composition of
motorcycle and trucks in the traffic stream, average bus dwell time and bus headway did not
show statistically satisfactory relationship between the input and output variables of the model
(p–value > 0.05). This involved developing an ANN model using the MATLAB tool to further
check for accuracy of the built multiple linear regression model.

4.2 The ANN Model
A MATLAB tool based on the nntool command was used for this study. The tool used for
simulating the ANN models is capable of estimating weighted mean values, mean square errors

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415

and biases from the input variables. Model validation using the ANN approach implemented in
MATLAB yielded results as shown in Figure 4.

Figure 4: Model Validation using ANN Model
Figure 4 showed fitness of the built model in defining the relationship between the input and
output variables considered by the study. The training, validation and testing of the model using
1000 iterations for a sigmoidal function gave satisfactory output measured at levels 100%, 93%
and 98% respectively. The entire performance of the model is measured at 99% approximately,
which showed a strong relationship between variables. Thus, using this model, all performance
indicators of the model showed satisfactory results.

5.0 Conclusion
This study developed a multiple linear regression model for predicting bus travel time using
SPSS software. Input variables required by the model included; bus route length, bus travel
speed, average dwell time at random stops for pick-up and alighting of passengers, bus
headway, volume of motorcycles in the traffic stream, volume of private cars in the traffic stream,
volume of trucks in the traffic stream and the total number of cross intersections along the route.
Based on the built model, an average bus travel time of 15 minutes approximately was
established as bus travel time for all bus routes in Makurdi town (assuming all other variables
have zero magnitude). Goodness of fit test in statistics and ANN model were used to confirm the
accuracy of the built model for predicting short team bus travel time on bus routes within
Makurdi town, in Benue State. It was therefore concluded that, bus travel time on major routes in
Makurdi town could be accurately estimated using the built multiple linear regression model

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Adeke, et al: Prediction of Bus Travel Time on Urban Routes Without Designated Bus Stops in Makurdi Town, Benue
State, Nigeria. AZOJETE, 15(2):406-417. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng

Corresponding author’s e-mail address: adeke.pt@outlook.com 416

provided all essential input parameters required by the model were available. The following
recommendations were therefore made;
Establishment of designated bus stops along bus routes within Makurdi town was recommended
to minimise bus dwell frequency and for more accurate estimation of travel time in line with the
design and development of modern cities.
Travel information bill boards should be erected at strategic locations along bus routes in
Makurdi town stating their average bus travel time to help enlighten commuters that have high
value of travel time.

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Arid Zone Journal of Engineering, Technology and Environment, June, 2019; Vol. 15(2):406-417. ISSN 1596-2490;
e-ISSN 2545-5818; www.azojete.com.ng

Corresponding author’s e-mail address: adeke.pt@outlook.com

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