Gap-acceptance in road traffic

We find the distribution of delay to minor road vehicles waiting to merge or cross a single stream of major road traffic. The decision to cross is taken on the basis of a gap-acceptance function. The model turns out to be a simple queueing problem in which a customer finding an empty queue has a different service time distribution from queueing customers. The key to this representation is given in Section 3. Some numerical results in Section 6 indicate that in most circumstances a simple model will give adequate results.

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Delays to road traffic at an intersection

Journal of Applied Probability ◽

10.2307/3211861 ◽

1964 ◽

Vol 1 (2) ◽

pp. 297-310 ◽

Cited By ~ 20

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.

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Delays to road traffic at an intersection

Journal of Applied Probability ◽

10.1017/s0021900200108411 ◽

1964 ◽

Vol 1 (02) ◽

pp. 297-310 ◽

Cited By ~ 3

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.

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Hitting time in an M/G/1 queue

Journal of Applied Probability ◽

10.1017/s0021900200017691 ◽

1999 ◽

Vol 36 (03) ◽

pp. 934-940 ◽

Cited By ~ 1

Author(s):

Sheldon M. Ross ◽

Sridhar Seshadri

Keyword(s):

Service Time ◽

Time Distribution ◽

Arrival Rate ◽

Hitting Time ◽

Service Time Distribution ◽

Expected Time ◽

Efficient Simulation ◽

Simulation Procedure ◽

Poisson Arrival ◽

Stationary Delay

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.

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Sight Distance for Stop-Controlled Intersections Based on Gap Acceptance

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/1701-05 ◽

2000 ◽

Vol 1701 (1) ◽

pp. 32-41 ◽

Cited By ~ 6

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.

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Minor Road Traffic Delays at Priority Junctions on Low Speed Roads in Suburban Areas

Jurnal Teknologi ◽

10.11113/jt.v70.3496 ◽

2014 ◽

Vol 70 (4) ◽

Cited By ~ 4

Author(s):

Mohammad Ali Sahraei ◽

Othman Che Puan ◽

M. Al–Muz–zammil Yasin

Keyword(s):

Time Delays ◽

Road Traffic ◽

Video Recording ◽

Operational Performance ◽

Road Vehicles ◽

Recording Technique ◽

Suburban Areas ◽

Minor Road ◽

Traffic Delays ◽

Traffic Delay

Traffic delay is one of the important aspects considered in the assessment of the operational performance of intersections. In the analysis of priority or unsignalised junctions, delays to minor road vehicles are often estimated using the existing mathematical models. However, the applicability of such a model depends on the basis and the source of the data with which the model was calibrated. This study was carried out to evaluate traffic delays to minor road vehicles at priority junctions in suburban areas. The data were collected at two priority junctions using video recording technique. The results showed that the day time delays were longer than of those observed during the twilight time. In both situations, delay to minor road vehicles increases as the volume of major road traffic increases. However, the effect of conflicting volume on the delay to the minor road vehicles is not clear. The comparisons between observed delay and the values predicted using the HCM and Tanner’s models indicated that, in general, the observed delays are much lower than the values predicted by both models particularly during the day time. Such a finding suggests that both HCM and Tanner’s models are not directly applicable to the analysis of delays at priority junctions in Malaysia.

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The general bulk queue as a matrix factorisation problem of the Wiener-Hopf type. Part II.

Advances in Applied Probability ◽

10.2307/1426133 ◽

1975 ◽

Vol 7 (3) ◽

pp. 647-655 ◽

Cited By ~ 4

Author(s):

John Dagsvik

Keyword(s):

Waiting Time ◽

Service Time ◽

Time Distribution ◽

Single Server ◽

Service Time Distribution ◽

Time Process ◽

Waiting Time Process ◽

Bulk Queue ◽

Erlang Distributions ◽

Matrix Factorisation

In a previous paper (Dagsvik (1975)) the waiting time process of the single server bulk queue is considered and a corresponding waiting time equation is established. In this paper the waiting time equation is solved when the inter-arrival or service time distribution is a linear combination of Erlang distributions. The analysis is essentially based on algebraic arguments.

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An extension of Erlang's formulas which distinguishes individual servers

Journal of Applied Probability ◽

10.2307/3212648 ◽

1972 ◽

Vol 9 (1) ◽

pp. 192-197 ◽

Cited By ~ 11

Author(s):

Jan M. Chaiken ◽

Edward Ignall

Keyword(s):

Service Time ◽

Time Distribution ◽

The State ◽

Service Time Distribution ◽

Loss System ◽

Arbitrary Service Time

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.

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