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Application of Queuing Theory to Traffic Congestion Analysis on the

Asaba–Onitsha Bridge, Nigeria

Ilori, A. Kolawole

, Fidelis N Okechi

, Mark Modebei

, James I. Ajie

, Steve, D. Oluwaniyi

, Pius

Ukwa

National Mathematical Centre, Abuja, Nigeria

*Corresponding Author

DOI: https://doi.org/10.51583/IJLTEMAS.2026.150100058

Received: 20 January 2026; Accepted: 27 January 2026; Published: 06 February 2026

ABSTRACT

Traffic congestion on major transportation corridors poses significant economic and social challenges,

particularly in developing urban regions. This study applies queuing theory to analyze traffic congestion on the

Asaba–Onitsha Bridge, a critical transportation link between Delta State and Anambra State, Nigeria. Using

real-life traffic data, the study evaluates the performance of the bridge in terms of traffic intensity, queue length,

and waiting time under varying service capacity conditions. A quantitative and observational research design

was adopted. Primary traffic data were collected through direct field observation during morning and afternoon

periods, with vehicles classified into small and big categories to reflect traffic composition. An M/M/2 queuing

model was employed. Traffic performance was analyzed under three assumed service rates of 600 veh/hr, 800

veh/hr, and 1000 veh/hr to assess the impact of service capacity on congestion levels. The results reveal clear

temporal variations in traffic flow, with the morning period experiencing significantly higher traffic volumes,

largely due to the dominance of small vehicles, while the flow of big vehicles remains relatively stable

throughout the day. At a service rate of 600 veh/hr, the system operates close to capacity during the morning

peak, resulting in higher traffic intensity, noticeable queues, and increased waiting times, indicating a

marginally adequate service level. Increasing the service rate to 800 veh/hr leads to substantial reductions in

queue length and waiting time, producing efficient traffic flow during both peak and off-peak periods. The best

performance is observed at a service rate of 1000 veh/hr, where traffic intensity remains low and near free-flow

conditions are achieved even during peak demand. The study concludes that congestion on the Asaba–Onitsha

Bridge is strongly influenced by service capacity and temporal traffic demand variations. Enhancing service

capacity through improved traffic management or infrastructure expansion can significantly reduce congestion,

minimize delays, and improve overall traffic flow on the bridge. The findings provide quantitative evidence to

support capacity enhancement through improved traffic management, infrastructure development, and the

integration of Intelligent Transportation Systems that provides a modern, cost-effective, and adaptive approach

for optimizing existing infrastructure and minimizing traffic delays.

Keywords: Queuing Theory, M/M/2 Model, Traffic Flow Analysis, Traffic Congestion, Asaba–Onitsha Bridge.

INTRODUCTION

Queuing theory deals with the systematic study of waiting for service at service points of various kinds and

seeks to explain the formation, behavior, and performance of queues in systems where demand for service is

random (Sztrik, 2012). In most service systems, including transportation facilities, it is generally desirable for

users to spend as little time as possible waiting in queues. However, reducing waiting time often requires

additional capacity or infrastructural investment, which may involve substantial capital outlay. Consequently,

decision makers must evaluate whether such investments yield sufficient operational benefits in terms of

reduced congestion and improved service efficiency.

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Queuing models provide a powerful analytical framework for addressing such decisions by quantifying system

performance measures such as waiting time, queue length, and server utilization. These models have been

widely applied in production systems, transportation networks, communication systems, inventory control, and

information processing systems, particularly for system design with respect to layout, capacity, and control

(Sztrik, 2010; Taha, 2002). By isolating critical stochastic elements such as arrival patterns and service times,

queuing models allow analysts to understand how random demand interacts with limited service capacity to

generate congestion.

Historically, queuing theory originated from the pioneering work of Erlang (1909), who first applied

probabilistic methods to analyze congestion problems in telephone traffic. Since then, the theory has evolved

into one of the most widely used analytical tools in operations research, with applications spanning

telecommunications, traffic engineering, computing systems, manufacturing, healthcare delivery, banking, and

public service operations (Srivastava, Shenoy & Sharma, 2008). In transportation systems, queuing theory is

particularly useful for modeling traffic bottlenecks where arrivals are unpredictable and service capacity is

finite, leading to conflicts for resource usage and the formation of queues (Kleinrock, 1975).

In real-world queuing systems, arrivals often follow a Poisson process with exponentially distributed inter-

arrival times, while service times are frequently assumed to be exponentially distributed and independent of

arrival processes (Sztrik, 2012). Service is commonly rendered on a first-come-first-served basis, and system

capacity may consist of one or multiple parallel servers. Under such assumptions, queuing models enable the

derivation of key performance measures, including the expected waiting time in the queue and the system, the

average queue length, server utilization, and the probability of the system being in specific states such as

empty or congested (Makwana, 2012; Nafees, 2007).

Queues are a pervasive feature of everyday life and are encountered in hospitals, banks, schools, offices, fuel

stations, airports, and road traffic systems. In traffic engineering, queues form when vehicle arrival rates

exceed or approach the service capacity of a roadway section, intersection, or bridge, resulting in delays and

congestion. The severity of such queues depends not only on the average arrival rate but also on the variability

of traffic flow and service processes (Kleinrock, 1975). As such, queuing theory provides a suitable framework

for analyzing traffic congestion problems and evaluating alternative capacity and control strategies.

Several empirical studies have demonstrated the applicability of queuing theory to service systems. Adeleke et

al. (2009) applied queuing models to analyze outpatient waiting times in hospitals, while Ogunwale and

Olubiyi (2012) conducted a comparative analysis of customer waiting times in banks. Tsarouhas (2011)

applied queuing theory to production lines in food processing, and Kumar and Jain (2013) investigated queue

control policies for managing arrivals and services. These studies highlight the versatility of queuing models in

evaluating system efficiency and guiding operational improvements.

Within the Nigerian context, transportation infrastructure, particularly critical corridors and bridges,

experiences frequent congestion due to high traffic demand, limited capacity, and heterogeneous vehicle

composition. The Asaba–Onitsha Bridge serves as a major transportation link between the South-East and

South-South regions of Nigeria and is characterized by heavy daily traffic comprising both small and large

vehicles. Persistent congestion on this bridge results in increased travel time, economic losses, and reduced

service quality for road users.

Against this background, this study applies queuing theory to analyze traffic congestion on the Asaba–Onitsha

Bridge using real-life traffic data. By modeling vehicle arrivals and service processes under different

operational assumptions, the study evaluates the bridge’s performance in terms of traffic intensity, queue

length, and waiting time. The analysis further examines the impact of varying service capacities through multi-

server queuing models, with the aim of identifying effective traffic management strategies capable of reducing

congestion and improving overall traffic flow on the bridge.

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LITERATURE REVIEW

This section presents a review of relevant literature on the application of queuing theory to traffic congestion

and service systems. Queuing theory is a mathematical framework developed to analyze situations in which

entities arrive randomly to receive service from limited facilities. Priyanka Rani and Sharma (2024) describe

queuing theory as a practical and adaptive tool that extends beyond abstract mathematics into real-world

problem solving. According to their study, queuing theory has found wide application in sectors such as

transportation, healthcare, telecommunications, retail, and cloud computing, where demand fluctuates

unpredictably and resources are constrained. The authors emphasize that queuing models provide quantitative

measures of system performance, including average waiting time, queue length, service utilization, and overall

efficiency. By applying appropriate queuing models, system managers are able to improve operational

efficiency, reduce congestion, and enhance user satisfaction.

In the transportation sector, queuing theory has been widely applied to analyze traffic congestion, particularly

at urban intersections and major road networks. Urhode and Tsetimi (2022) investigated traffic congestion and

travel time at the Iwo Road intersection in Ibadan, Oyo State, Nigeria, using queuing models. Their study

employed direct observation and manual vehicle counting during peak and off-peak periods to capture daily

variations in traffic flow. The findings revealed that congestion at the intersection was particularly severe on

Mondays, Saturdays, and Sundays, reflecting both weekday commuter pressure and increased weekend travel

demand. The study further established that vehicle arrival rates frequently exceeded the service capacity of the

intersection, leading to prolonged queues and increased travel time. These results demonstrated the

effectiveness of queuing models in diagnosing congestion problems and assessing traffic performance in urban

settings.

Further evidence of the relevance of queuing theory in traffic analysis is provided by Aderinola, Elemure, and

Laoye (2020), who examined congestion at Jattu Junction in Auchi using queuing theory supported by TORA

and SIDRA traffic analysis software. Their study combined theoretical queuing models with simulation tools to

evaluate traffic performance indicators such as queue length, waiting time, and level of service. The integration

of queuing theory with specialized traffic analysis software allows for more realistic modeling of complex

traffic conditions and improves the accuracy of congestion assessment (Bhattarai et al., 2025). The findings

confirmed that queuing-based approaches are suitable for evaluating traffic bottlenecks and testing the

effectiveness of traffic control measures.

Beyond transportation systems, queuing theory has been widely applied to service-oriented environments,

particularly within the banking sector. Adeleke, Adebiyi, and Akinyemi (2005) applied queuing theory to

customer service operations at Omega Bank Plc in Ado Ekiti, Nigeria, assuming that customers arrive

randomly and are served by a limited number of service counters. Their analysis focused on key performance

indicators such as average waiting time, queue length, and server utilization, demonstrating that queuing

models provide valuable insights into service efficiency and help determine whether existing service capacity

is sufficient to meet customer demand. Similar conclusions have been reported in more recent studies, which

confirm the continued relevance of queuing theory for evaluating and optimizing service performance in

banking and other service systems (Ibukun-Falayi, 2021; Paveun & Danyaro, 2025). Although these studies

were conducted in a banking context, the methodological framework is equally applicable to traffic systems,

where vehicles can be conceptualized as customers and road lanes as service channels.Multi-server queuing

models have also been applied in industrial settings where multiple service points operate simultaneously.

Tsetimi and Orighoyeghe (2021) examined the application of an M/M/S queuing model to selected tank farms

in Oghara, Delta State, Nigeria. The study assumed that service requests followed a Poisson arrival process,

while service times were exponentially distributed. Using this framework, the authors estimated system

performance measures such as traffic intensity, average number of customers in the system and in the queue,

average waiting time, and server utilization. The findings indicated that increasing the number of service

channels significantly reduced congestion and waiting time. Although the study focused on an industrial

system, its conclusions are highly relevant to traffic congestion analysis, particularly in situations where

multiple lanes or parallel service facilities are available.

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Queuing theory is a robust and versatile tool for analyzing congestion and service efficiency across diverse

systems. However, most traffic-related studies in Nigeria have concentrated on road intersections and junctions,

with limited emphasis on major bridge corridors that serve as critical traffic bottlenecks. In addition, few

studies have examined the effect of varying service rate assumptions within multi-server queuing models using

real-life traffic data. These gaps highlight the need for a focused study on the Asaba–Onitsha Bridge, which is

a key transportation link with significant economic importance. The present study seeks to address these gaps

by applying an M/M/2 queuing model to analyze traffic congestion on the bridge and to provide evidence-

based recommendations for improving traffic flow and reducing congestion.

METHODOLOGY

This study adopts a quantitative and observational research design to analyze traffic congestion on the Asaba–

Onitsha Bridge using queuing theory. The methodology is based on the collection and analysis of real-life

traffic flow data and the application of stochastic queuing models to evaluate system performance under

varying traffic demand and service capacity assumptions.

Study Area

The study was conducted on the Asaba–Onitsha Bridge also known as second Niger Bridge, a major

transportation corridor linking Delta State and Anambra State in Nigeria. The bridge serves as a critical

economic and social link, accommodating high volumes of vehicular traffic daily. Due to its strategic

importance and limited service capacity, the bridge frequently experiences traffic congestion, especially during

peak periods.

Source and Method of Data Collection

Primary data were collected through direct field observation. Research members were stationed at designated

observation points on the bridge to record vehicle arrivals during the morning and afternoon traffic sessions.

Data collection focused on capturing real-time traffic flow characteristics under natural operating conditions.

Vehicles were classified by type, specifically into small and big vehicles, to reflect differences in traffic

composition. Observations were conducted during selected peak periods to ensure that congestion-prone

conditions were adequately represented. The data collected included the number of vehicles arriving per unit

time, which formed the basis for estimating arrival rates for the queuing model.

Model Assumptions

To model traffic flow on the Asaba–Onitsha Bridge, the following assumptions were made in line with

standard queuing theory:

1. Vehicle arrivals follow a Poisson process, implying that inter-arrival times are exponentially distributed.

2. Service times are assumed to be exponentially distributed, representing random variations in vehicle

service completion.

3. The traffic system operates under a First-Come, First-Served (FCFS) service discipline.

4. The bridge is modeled as a multi-server system (M/M/2), where the two servers represent parallel service

channels or effective traffic lanes.

5. The system has an infinite queue capacity, meaning that all arriving vehicles join the queue and none are

turned away.

6. Arrival and service processes are independent.

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These assumptions allow the traffic system to be represented as an M/M/2 queuing model, which is suitable for

analyzing multi-lane traffic flow under congested conditions.

DATA ANALYSIS

The collected traffic data were analyzed using queuing theory analytical techniques. Vehicle arrival counts

were first converted into arrival rates (λ), expressed as the average number of vehicles arriving per unit time

for both morning and afternoon sessions.

Different service rate (μ) assumptions were considered to reflect variations in traffic handling capacity due to

factors such as driver behavior, traffic control measures, and road conditions. This enabled the evaluation of

congestion levels under alternative operational scenarios.

Queuing Model Formulation

The traffic system was modeled using the M/M/2 queuing model, where:

Symbol

Definition



Average arrival rate of vehicles (vehicles/unit time)



Average service rate per server (vehicles/unit time)

Number of servers = 2



Traffic intensity per server









Probability that there are no vehicles in the system

Expected number of vehicles in the queue

Expected number of vehicles in the system (queue + service)

Expected waiting time in the queue

Expected waiting time in the system

Steady-State Probabilities

For an M/M/2 queue, the probability that there are n vehicles in the system,

, is

 

, 0 2

, 2

2 2

{

P n

 



 







(1)

The normalization constant

   

/ /

, 1

! 2! 1 2

n n

   





 



 

    

 



 

 



(2)

Performance Measures

Average number of vehicles in the queue (

)

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 

2 1

L P

  







(3)

Average number of vehicles in the system (L):

L L





 

(4)

Average waiting time in the queue (

 ):





(5)

Average waiting time in the system (W):

W W



 

(6)

Server Utilization (



)









(7)

ANALYSIS AND DISCUSSION

This section presents the analysis of traffic flow on the Asaba–Onitsha Bridge using queuing theory. The study

adopts an M/M/2 queuing model, reflecting two parallel traffic lanes operating as service channels. Real-life

traffic arrival data collected for morning and afternoon sessions were analyzed under three assumed service

rates (600 veh/hr, 800 veh/hr, and 1000 veh/hr) to assess system performance under varying capacity

conditions

Table 1: Traffic flow on Asaba-Onisha Bridge

Session

Vehicle Type

Arrival Rate (veh/hr)

Morning

Small vehicles

700 veh/hr

Big vehicles

76 veh/hr

Afternoon

Small vehicles

428 veh/hr

Big vehicles

77 veh/hr

Table 1 shows that traffic flow on the Asaba–Onitsha Bridge varies between the morning and afternoon periods.

During the morning session, the bridge experiences a high volume of small vehicles, with an average arrival

rate of 700 vehicles per hour, while the flow of big vehicles is much lower at 76 vehicles per hour. In the

afternoon, the traffic of small vehicles decreases to 428 vehicles per hour, whereas the arrival rate of big

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vehicles remains relatively stable at 77 vehicles per hour. The bridge experiences its heaviest traffic in the

morning, primarily due to the large number of small vehicles, while the flow of big vehicles remains fairly

constant throughout the day.

Arrival Rate for each Session

Morning Session:

700 76 776 /

morning

veh hr



  

Afternoon Session:

428 77 505 /

afternoon

veh hr



  

Analysis Using M/M/2 Model

Case I: Service Rate of 600 Vehicles per Hour

Morning Session:

776

0.647

2(600)



 

Afternoon Session:

505

0.421

1200



 

Case 2: Service Rate of 800 Vehicles per Hour

Morning Session:

776

0.485

1600



 

Afternoon Session:

505

0.316

1600



 

Case 3: Service Rate of 1000 Vehicles per Hour

Morning Session:

776

0.388

2000



 

Afternoon Session:

505

0.253

2000



 

Table 2: Summarized performance of Queuing system under difference assumed service rate

μ (veh/hr)

Session

Lq (veh)

Wq (hr)

W (hr)

600

Morning

0.647

0.63

0.049

0.051

600

Afternoon

0.421

0.16

0.019

0.12

800

Morning

0.485

0.24

0.018

0.093

800

Afternoon

0.316

0.07

0.008

0.083

1000

Morning

0.388

0.11

0.009

0.069

1000

Afternoon

0.253

0.03

0.004

0.064

The summarized results in Table 2 describe how the traffic queuing system on the Asaba–Onitsha Bridge

performs under different assumed service rates during morning and afternoon periods. Overall, the results

show that traffic conditions improve steadily as the service rate increases, and that congestion is more

pronounced during the morning session than in the afternoon.

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At a service rate of 600 veh/hr, the system experiences relatively high utilization, especially during the

morning period. The traffic intensity in the morning is approximately 0.65, indicating that a significant

proportion of the available service capacity is being utilized. This level of utilization results in noticeable

queuing, with an average of approximately 0.63 of the vehicles waiting, and a small but measurable waiting

time before vehicles are served. Although the system remains stable, it is close to a congested state during peak

morning traffic. In the afternoon, demand is lower, resulting in a reduced traffic intensity of about 0.42, shorter

queues, and smaller waiting times. This suggests that a service rate of 600 veh/hr is barely sufficient for off-

peak periods and is less suitable for peak morning traffic.

When the service rate is increased to 800 veh/hr, the performance of the queuing system improves significantly.

In the morning session, traffic intensity drops below 0.50, indicating a better balance between arrival and

service rates. As a result, the average queue length and waiting time are substantially reduced. The afternoon

session shows even better conditions, with low utilization, very short queues, and minimal waiting times. At

this service level, the bridge operates efficiently for both peak and off-peak traffic periods.

At a service rate of 1000 veh/hr, the system demonstrates the best overall performance. Traffic intensity is low

in both sessions, particularly in the afternoon, where the system operates far below capacity. Queue lengths

become almost negligible, and waiting times are extremely short, even during the morning peak. These

conditions reflect near free-flow traffic and indicate that the system has sufficient capacity to absorb

fluctuations in demand without congestion.

CONCLUSION

This study applied queuing theory to analyze traffic flow on the Asaba–Onitsha Bridge using an M/M/2

queuing model, representing two parallel traffic lanes operating as service channels. Real-life traffic arrival

data for morning and afternoon periods were used to evaluate system performance under different assumed

service rates. The analysis provided quantitative insight into the congestion patterns on the bridge and the

influence of service capacity on traffic performance.

The findings reveal clear temporal variations in traffic flow on the Asaba–Onitsha Bridge. Morning traffic is

significantly heavier than afternoon traffic, largely due to the high volume of small vehicles, while the flow of

big vehicles remains relatively constant throughout the day. This imbalance places greater pressure on the

bridge during the morning period, making it more susceptible to congestion and queuing.

The queuing analysis shows that system performance is highly sensitive to the assumed service rate. At a

service rate of 600 veh/hr, the bridge operates close to its capacity during the morning peak, resulting in higher

traffic intensity, noticeable queues, and increased waiting times. Although the system remains stable, this

service level is only marginally adequate and poses a risk of congestion under peak demand conditions. In

contrast, the same service rate performs more satisfactorily during the afternoon, when traffic demand is lower.

Increasing the service rate to 800 veh/hr leads to a substantial improvement in system performance. Traffic

intensity decreases, queue lengths are significantly reduced, and waiting times become minimal in both

morning and afternoon sessions. This service level provides a more balanced and efficient operation of the

bridge, accommodating both peak and off-peak traffic with minimal congestion.

The best performance is observed at a service rate of 1000 veh/hr. Under this condition, traffic intensity

remains low across both periods, queue lengths are almost negligible, and waiting times are very short, even

during the morning peak. These results indicate near-free-flow traffic conditions and demonstrate that higher

service capacity enables the bridge to absorb fluctuations in traffic demand without experiencing congestion.

Beyond physical capacity enhancement, the integration of modern traffic management technologies,

particularly Intelligent Transportation Systems (ITS), can provide a contemporary and sustainable approach to

congestion mitigation on the Asaba–Onitsha Bridge. ITS applications such as real-time traffic monitoring

using cameras and sensors, adaptive traffic control systems, incident detection and management tools, and

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traveler information systems can significantly improve operational efficiency. By enabling real-time

assessment of traffic conditions, ITS can dynamically adjust traffic control strategies, optimize lane usage, and

provide timely information to road users, thereby reducing arrival rates during peak periods and effectively

increasing the operational service rate of the bridge.

Furthermore, the use of ITS can complement the queuing model framework by transforming it from a purely

analytical tool into a real-time decision support system. Continuous data collection would allow for more

accurate estimation of arrival and service rates, better forecasting of congestion patterns, and quicker response

to unexpected incidents such as accidents or vehicle breakdowns that temporarily reduce service capacity. In

this way, technology-driven traffic management can enhance the practical applicability of queuing theory

results and support proactive congestion control.

In conclusion, congestion on the Asaba–Onitsha Bridge is strongly influenced by service capacity and temporal

variations in traffic demand, with morning traffic imposing the greatest strain on the system. While a service

rate of 600 veh/hr is only marginally sufficient, increasing the service rate to 800 veh/hr or above significantly

enhances traffic performance, and a service rate of 1000 veh/hr provides optimal operating conditions.

However, sustainable congestion management should not rely solely on increasing physical capacity. The

integration of Intelligent Transportation Systems offers a modern, cost-effective, and adaptive approach that

can optimize existing infrastructure, minimize queues and delays, and ensure smooth and reliable traffic flow

throughout the day.

ACKNOWLEDGEMENT

This work is funded by the National Mathematical Centre, Sheda, Kwali, Abuja, Nigeria, in 2024, under the

leadership of Professor Promise Mebine.

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