This document summarizes a journal review on minimizing traffic congestion using queuing theory. It analyzed traffic data from the Bhagwanpur Golambar intersection in India using M/M/1 and M/D/1 queuing models. The analysis found unbalanced congestion at the four approaches during different periods. Adjusting the green time based on traffic intensity significantly reduced the average delay for two approaches by reducing queue lines. Recommendations included installing a dynamic traffic light system, providing alternative routes to reduce demand, using variable message signs, and optimizing the uneven delays between approaches.

1. AASTU
College of Architecture & Civil Engineering
Department of Construction Technology and Management
System Analysis and Management Techniques (CENG 6105)
A Journal Review On Minimizing Traffic Congestion Using Queuing
Theory
Presented By; Ababyu Shawul
Alemayehu Regasa
Dejene Mengesha
Kidus Zerabruk
Solmon Yirga
March 2021
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2. Outline
 Objective
 Introduction
 Traffic congestion
 Methodology
 Data analysis
 Conclusions
 Recommendations
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3. Objectives
 To evaluate the traffic flow at Bhagwanpur
Golambar intersection by using M/M/1 and
M/D/1 queuing model.
 To suggest the possible minimization method
of traffic congestion.
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4. Introduction
 A queue is said to occur when the rate at which
the demand arises exceeds the rate at which
service is being provided.
 Queuing theory is a study of waiting line in
mathematics
 It has many real life applications
 Traffic system can be major application area of
queuing theory.
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5. Traffic congestion
Definition; is a condition in transport that is characterized
by slower speeds, longer trip times, and increased
vehicular queuing.
It has the following negative impact
 Delay
 Fuel Consumption and Pollution
 Customer dissatisfaction
 Increases travel cost
 Accident, etc…
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6. Methodology
Data source
This review used a secondary data which is obtained from Journal of Mathematics
Volume 12, Issue 1 Ver. II (Jan. - Feb. 2016).
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Bhagwanpur Intersection Video

7. Methodology
M/M/1: a single server the
arrival follow Poisson process
and service times are
exponentially distributed
 Ls =
ρ
1−ρ
 Lq =
ρ2
1−ρ
 Ws=
1
µ−λ
 Wq =
λ
µ(µ−λ)
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M/D/1: a single server where the
arrivals are determined by
Poisson process and service
times are fixed
 Ls =
ρ(2−ρ)
2(1−ρ)
 Lq =
ρ2
2(1−ρ)
d =
r2
2𝐶(1−ρ)
 Ws=
2−ρ
2µ(1−λ)
 Wq =
λ
2µ(µ−λ)
Model used

8. Methodology
M/M/1
 The arriving time follows a Poisson
Process with parameter λ.
 The time taken to complete a single
service is independent and
exponentially distributed with
parameter μ.
 Single server system
 The queuing discipline is general
(FCFS)
 The number of customers in the system
is very large.
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M/D/1
 The assumptions taken
with respect to arriving
time, server system and
queuing discipline are
the same as M/M/1
model. But the service
time is deterministic.
Assumptions

9. Methodology
 In addition to the previous assumptions for M/D/1
cycle time C=90sec (60-90, ideal cycle time for
urban areas)
 The green time was taken in two cases,
Case 1; green time(g) is fixed allover the session.
Case 2; green time(g) is vary with session intensity.
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Additional assumptions

10. Data Analysis
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11. Traffic Intensity (Tabular Form)
Direction Location Timing
Arrival Service Arrival
Rate(λ)
Service Rate(µ)
Traffic
Intensity(ρ)
Vehicle Min Vehicle Min
East
Bairiya to
Bhagwanpur
Golambar
Morning 25 1.19 32 1.01 21.008 31.683 0.663
Afternoon 22 2.55 17 1.07 8.627 15.888 0.543
Evening 31 1.16 29 1.03 26.724 28.155 0.949
South
Gobarsahi to
Bhagwanpur
Golambar
Morning 26 2.32 17 1.44 11.207 11.806 0.949
Afternoon 21 1.33 24 1.01 15.789 23.762 0.664
Evening 19 1.31 21 1 14.504 21 0.691
West
Maripur to
Bhagwanpur
Golambar
Morning 17 2.02 15 1.04 8.416 14.423 0.583
Afternoon 29 1.59 28 1.06 18.239 26.415 0.690
Evening 51 8.09 42 1.45 6.304 28.966 0.218
North
Rewa Road to
Bhagwanpur
Golambar
Morning 28 1.25 35 1.02 22.4 34.314 0.653
Afternoon 29 2.3 49 1.19 12.609 41.176 0.306
Evening 55 4.55 65 2.25 12.088 28.889 0.418
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12. Traffic Intensity (Graphical Form) 12

13. Performance Measure (Tabular Form) 13

14. Performance Measure (Graphical Form) 14
Performance
indicator

15. Average Delay (Tabular Form) 15

16. Average Delay (Graphical Form) 16
Average
delay(sec)

17. Conclusion
 By analyzing the secondary data obtained from
the journal, it was identified that a relative un-
balanced traffic congestion at four approaches
in different session.
 Intensity based allocation green time
significantly decreases average delay of
Maripur and Bairiya approach which able to
them to reduce the queue line.
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18. Recommendation
 It’s better to provide a dynamic traffic light
system(Installing queue length sensitive traffic lights)
 Reducing the demand by providing alternative routes
on the other location.
 Variable message signs can be installed along the
roadway to advice road users.
 Maximizing the road capacity by increasing the width
of the road.
 Finally, we recommended that further studies to
optimize the unevenly distributed delay among the
approaches.
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Thanks a lot for your
attention!