A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route

A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route

Average waiting time is considered as one of the basic performance indicators for a bottleneck zone on a route for commuter traffic. It turns out that the average waiting time in a queue remains paradoxically unchanged regardless of how fast the queue dissolves for a single bottleneck problem. In th...

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Main Authors: Hakan Özaktaş, Nureddin Kırkavak, Ayşe Nilay Alpay
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Modelling and Simulation in Engineering
Online Access:http://dx.doi.org/10.1155/2021/2315987
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spelling doaj-3216b89b52c94ec8a60848e1ce3806262021-06-07T02:14:10ZengHindawi LimitedModelling and Simulation in Engineering1687-56052021-01-01202110.1155/2021/2315987A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ RouteHakan Özaktaş0Nureddin Kırkavak1Ayşe Nilay Alpay2Department of Industrial EngineeringDepartment of Industrial EngineeringOvacık Sınav CollegeAverage waiting time is considered as one of the basic performance indicators for a bottleneck zone on a route for commuter traffic. It turns out that the average waiting time in a queue remains paradoxically unchanged regardless of how fast the queue dissolves for a single bottleneck problem. In this study, the paradox is verified theoretically for the deterministic case with constant arrival and departure rates. Consistent results with the deterministic case have also been obtained by simulation runs for which vehicle interarrival time is a random variable. Results are tabulated for interarrival times which have uniform, triangular, normal, and exponential distributions along with a statistical verification of the average waiting time paradox.http://dx.doi.org/10.1155/2021/2315987
collection DOAJ
language English
format Article
sources DOAJ
author Hakan Özaktaş
Nureddin Kırkavak
Ayşe Nilay Alpay
spellingShingle Hakan Özaktaş
Nureddin Kırkavak
Ayşe Nilay Alpay
A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route
Modelling and Simulation in Engineering
author_facet Hakan Özaktaş
Nureddin Kırkavak
Ayşe Nilay Alpay
author_sort Hakan Özaktaş
title A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route
title_short A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route
title_full A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route
title_fullStr A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route
title_full_unstemmed A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters’ Route
title_sort paradox of the average waiting time for the case of a single bottleneck on the commuters’ route
publisher Hindawi Limited
series Modelling and Simulation in Engineering
issn 1687-5605
publishDate 2021-01-01
description Average waiting time is considered as one of the basic performance indicators for a bottleneck zone on a route for commuter traffic. It turns out that the average waiting time in a queue remains paradoxically unchanged regardless of how fast the queue dissolves for a single bottleneck problem. In this study, the paradox is verified theoretically for the deterministic case with constant arrival and departure rates. Consistent results with the deterministic case have also been obtained by simulation runs for which vehicle interarrival time is a random variable. Results are tabulated for interarrival times which have uniform, triangular, normal, and exponential distributions along with a statistical verification of the average waiting time paradox.
url http://dx.doi.org/10.1155/2021/2315987
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