An analysis of the fixed-cycle traffic-light problem

1981 ◽  
Vol 18 (03) ◽  
pp. 672-683 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Arrival Process ◽  
Traffic Light ◽  
Traffic Lights ◽  
Poisson Arrival ◽  
Pass Through ◽  
Poisson Arrival Process

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

An analysis of the fixed-cycle traffic-light problem

1981 ◽  
Vol 18 (3) ◽  
pp. 672-683 ◽  
Author(s):  
Richard Cowan
Keyword(s):  
Arrival Process ◽  
Traffic Light ◽  
Traffic Lights ◽  
Poisson Arrival ◽  
Pass Through ◽  
Poisson Arrival Process

A realistic non-Poisson arrival process is used in a model for intersections controlled by fixed-cycle traffic lights. Average delays, queue sizes and percentage of delayed vehicles are derived. The distribution of the number of vehicles which pass through during the green phases is found. Certain model anomalies which are inherent in earlier work are eliminated by the use of this model.

scholarly journals Information system for the management of intelligent traffic lights

2020 ◽  
pp. 21-26
Author(s):  
Alejandro ORTIZ-FIGUEROA ◽  
Ramona Evelia CHÁVEZ-VALDEZ ◽  
Jesús Alberto VERDUZCO-RAMIREZ ◽  
Ismael VILLAVICENCIO-JACOBO
Keyword(s):  
Information System ◽  
Traffic Management ◽  
Population Increase ◽  
Traffic Light ◽  
Traffic Lights ◽  
Vehicle Data ◽  
Software Engineering Process ◽  
Unified Process ◽  
Pass Through

Derived from the population increase and urban growth, vehicle traffic has increased in the cities of Colima and Villa de Álvarez located in Mexico, and with it the problems of road safety and traffic management; the increasing number of roads and traffic lights implies recording the information of each one of these; Therefore, this article presents an information system for the management of intelligent traffic light infrastructure. In the software engineering process, the Agile Unified Process was used to manage the main risks early and guarantee the quality of the product during its life cycle. The system was tested at a prototype level with satisfactory results, as a result a web system contributes to improving road and citizen safety, since based on two vehicle data it connects with web services to other databases, and identifies Immediately form the incidents of vehicles that pass through the roads, including stolen vehicle, speeding and a panic button. The expectations are to scale it to the real environment, and make available to the corresponding authorities the information collected to favor decision-making.

The departure process from a queueing system

1976 ◽  
Vol 80 (2) ◽  
pp. 283-285 ◽  
Author(s):  
F. P. Kelly
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Departure Process ◽  
Common Distribution ◽  
Poisson Arrival ◽  
Queue Discipline ◽  
Common Distribution Function ◽  
Image Position ◽  
Poisson Arrival Process

Consider a single-server queueing system with a Poisson arrival process at rate λ and positive service requirements independently distributed with common distribution function B(z) and finite expectationwhere βλ < 1, i.e. an M/G/1 system. When the queue discipline is first come first served, or last come first served without pre-emption, the stationary departure process is Poisson if and only if G = M (i.e. B(z) = 1 − exp (−z/β)); see (8), (4) and (2). In this paper it is shown that when the queue discipline is last come first served with pre-emption the stationary departure process is Poisson whatever the form of B(z). The method used is adapted from the approach of Takács (10) and Shanbhag and Tambouratzis (9).

A time-varying Poisson arrival process generator

SIMULATION ◽  
1984 ◽  
Vol 43 (4) ◽  
pp. 193-195 ◽  
Author(s):  
Robert W. Klein ◽  
Stephen D. Roberts
Keyword(s):  
Arrival Process ◽  
Time Varying ◽  
Poisson Arrival ◽  
Poisson Arrival Process

A solution to the fixed-cycle traffic light problem for compound Poisson arrivals

1968 ◽  
Vol 5 (3) ◽  
pp. 624-635 ◽  
Author(s):  
Donald R. McNeil
Keyword(s):  
Traffic Flow ◽  
Cycle Time ◽  
Mathematical Theory ◽  
Basic Problem ◽  
Arrival Process ◽  
Traffic Light ◽  
Compound Poisson ◽  
Factors Affecting ◽  
Poisson Arrivals ◽  
Pass Through

A basic problem in the mathematical theory of traffic flow is to obtain the expected delay to a vehicle at a fixed-cycle traffic light controlling an intersection. The factors affecting this expected delay are the cycle time, the fraction of time the traffic light is effectively red, the number of vehicles which can pass through when the signal is green, and the nature of the (random) arrival process for the vehicles. Once a solution is known, it is possible to fix the cycle time and the effective red period in such a way that the expected delay is minimized.

Two sufficient properties for the insensitivity of a class of queueing models

1991 ◽  
Vol 28 (03) ◽  
pp. 664-672
Author(s):  
Moshe Haviv
Keyword(s):  
Arrival Process ◽  
Queueing Models ◽  
Sufficient Condition ◽  
Poisson Arrival ◽  
System 2 ◽  
Poisson Arrival Process

For indivisible strong work-conserving queueing models with a Poisson arrival process, each of the following two properties is a sufficient condition for insensitivity. (1) The completed workload of a job receiving service is independent of the number of jobs in the system. (2) Independently of the completed workloads of the jobs in the system, they all are equally likely to be in service. For models which additionally belong to the class described by two families of parameters each of these properties is also necessary for insensitivity.

The asymptotic behavior o queues with time-varying arrival rates

1984 ◽  
Vol 21 (01) ◽  
pp. 143-156 ◽  
Author(s):  
Daniel P. Heyman ◽  
Ward Whitt
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Stability ◽  
Limit Theorems ◽  
Arrival Process ◽  
Periodic Case ◽  
Time Varying ◽  
Poisson Arrival ◽  
Poisson Arrival Process

This paper discusses the asymptotic behavior of the Mt/G/c queue having a Poisson arrival process with a general deterministic intensity. Since traditional equilibrium does not always exist, other notions of asymptotic stability are introduced and investigated. For the periodic case, limit theorems are proved complementing Harrison and Lemoine (1977) and Lemoine (1981).

Analysis of Tandem Retrial Queue with Common Orbit and Poisson Arrival Process

2021 ◽  
pp. 441-456
Author(s):  
Anatoly Nazarov ◽  
Svetlana Paul ◽  
Tuan Phung-Duc ◽  
Mariya Morozova
Keyword(s):  
Retrial Queue ◽  
Arrival Process ◽  
Poisson Arrival ◽  
Poisson Arrival Process
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