The capacity of an intersection with non-stationary traffic

1976 ◽  
Vol 13 (02) ◽  
pp. 418-422
Author(s):  
Helmut Wegmann
Keyword(s):  
Road Traffic ◽  
Intensity Function ◽  
Major Road ◽  
Homogeneous Case ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Minor Road ◽  
Traffic Stream ◽  
A Minor ◽  
Non Homogeneous Poisson Process

The average number of vehicles being able to enter an intersection per time unit from a minor road with a stop or yield sign — the capacity of the intersection — depends on the density of the traffic stream on the major road. In case the time-process of the major road traffic at the intersection is a non-homogeneous Poisson process with a periodic intensity function the capacity is calculated and compared with the capacity in the homogeneous case.

The capacity of an intersection with non-stationary traffic

1976 ◽  
Vol 13 (2) ◽  
pp. 418-422 ◽  
Author(s):  
Helmut Wegmann
Keyword(s):  
Road Traffic ◽  
Intensity Function ◽  
Major Road ◽  
Homogeneous Case ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Minor Road ◽  
Traffic Stream ◽  
A Minor ◽  
Non Homogeneous Poisson Process

The average number of vehicles being able to enter an intersection per time unit from a minor road with a stop or yield sign — the capacity of the intersection — depends on the density of the traffic stream on the major road. In case the time-process of the major road traffic at the intersection is a non-homogeneous Poisson process with a periodic intensity function the capacity is calculated and compared with the capacity in the homogeneous case.

Weak limit results for the extremes of a class of shot noise processes

1995 ◽  
Vol 32 (03) ◽  
pp. 707-726 ◽  
Author(s):  
Patrick Homble ◽  
William P. McCormick
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Impulse Response Function ◽  
Weak Limit ◽  
Intensity Function ◽  
Important Class ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Non Homogeneous Poisson Process ◽  
Over Time

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

Weak limit results for the extremes of a class of shot noise processes

1995 ◽  
Vol 32 (3) ◽  
pp. 707-726 ◽  
Author(s):  
Patrick Homble ◽  
William P. McCormick
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Impulse Response Function ◽  
Weak Limit ◽  
Intensity Function ◽  
Important Class ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Non Homogeneous Poisson Process ◽  
Over Time

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

Delays to road traffic at an intersection

1964 ◽  
Vol 1 (2) ◽  
pp. 297-310 ◽  
Author(s):  
G. F. Yeo ◽  
B. Weesakul
Keyword(s):  
Road Traffic ◽  
Partial Solution ◽  
Major Road ◽  
Gap Acceptance ◽  
Road Vehicle ◽  
Mean Delay ◽  
Minor Road ◽  
The Mean ◽  
Stationary Waiting Time ◽  
A Minor

A model for road traffic delays at intersections is considered where vehicles arriving, possibly in bunches, in a Poisson process in a one way minor road yield right of way to traffic, which forms alternate bunches and gaps, in a major road. The gap acceptance times are random variables, and depend on whether or not a minor road vehicle is immediately following another minor road vehicle into the intersection or not.The transforms of the stationary waiting time and queue size distributions, and the mean stationary delay, for minor road vehicles are obtained by substitution of determined service time distributions into results for a generalisation of the M/G/1 queueing system. Some numerical results are given to illustrate the increase in the mean delay for variable gap acceptance times for a Borel-Tanner distribution of major road traffic, and a partial solution is given for a two way major road.

Delays to road traffic at an intersection

1964 ◽  
Vol 1 (02) ◽  
pp. 297-310 ◽  
Author(s):  
G. F. Yeo ◽  
B. Weesakul
Keyword(s):  
Road Traffic ◽  
Partial Solution ◽  
Major Road ◽  
Gap Acceptance ◽  
Road Vehicle ◽  
Mean Delay ◽  
Minor Road ◽  
The Mean ◽  
Stationary Waiting Time ◽  
A Minor

A model for road traffic delays at intersections is considered where vehicles arriving, possibly in bunches, in a Poisson process in a one way minor road yield right of way to traffic, which forms alternate bunches and gaps, in a major road. The gap acceptance times are random variables, and depend on whether or not a minor road vehicle is immediately following another minor road vehicle into the intersection or not. The transforms of the stationary waiting time and queue size distributions, and the mean stationary delay, for minor road vehicles are obtained by substitution of determined service time distributions into results for a generalisation of the M/G/1 queueing system. Some numerical results are given to illustrate the increase in the mean delay for variable gap acceptance times for a Borel-Tanner distribution of major road traffic, and a partial solution is given for a two way major road.

Sight Distance for Stop-Controlled Intersections Based on Gap Acceptance

2000 ◽  
Vol 1701 (1) ◽  
pp. 32-41 ◽  
Author(s):  
Douglas W. Harwood ◽  
John M. Mason ◽  
Robert E. Brydia
Keyword(s):  
Travel Time ◽  
Field Studies ◽  
Major Road ◽  
Gap Acceptance ◽  
Road Vehicle ◽  
Sight Distance ◽  
Minor Road ◽  
Distance Model ◽  
Design Speed ◽  
A Minor

The current AASHTO policy for sight distance at Stop-controlled intersections is based on a model of the acceleration performance of a minor-road vehicle turning left or right onto a major road and the deceleration performance of the following major road vehicle. An alternative intersection sight distance model based on gap acceptance is developed and quantified. Field studies that were performed to determine the critical gaps appropriate for use in sight distance design are described. It is recommended that the sight distance along the major road for a passenger car at a Stop-controlled intersection should be based on a distance equal to 7.5 s of travel time at the design speed of the major road. Longer sight distances are recommended for minor-road approaches that have sufficient truck volumes to warrant consideration of a truck as the design vehicle.

An age-dependent counting process generated from a renewal process

1988 ◽  
Vol 20 (4) ◽  
pp. 739-755 ◽  
Author(s):  
Ushio Sumita ◽  
J. George Shanthikumar
Keyword(s):  
Renewal Process ◽  
Counting Process ◽  
Intensity Function ◽  
Sufficient Condition ◽  
Minimal Repair ◽  
Homogeneous Poisson Process ◽  
Stochastic Convexity ◽  
Age Dependent ◽  
Non Homogeneous Poisson Process ◽  
Age Process

Let {N(t)} be a renewal process having the associated age process {X(t)}. Of interest is the counting process {M(t)} characterized by a non-homogeneous Poisson process with age-dependent intensity function λ (X(t)). The trivariate process {Y(t) = [M(t), N(t), X(t)]} is analyzed obtaining its Laplace transform generating function explicitly. Based on this result, asymptotic behavior of {S(t) = cM(t) + dN(t)} as t → ∞ is discussed. Furthermore, a sufficient condition is given under which {M(t), –N(t), X(t)} is stochastically monotone and associated. This condition also assures increasing stochastic convexity of {M(t)}. The usefulness of these results is demonstrated through an application to the age-dependent minimal repair problem.

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