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

Hakan Özaktaş | Zendy; Nureddin Kırkavak | Zendy; Ayşe Nilay Alpay | Zendy

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

Author(s) -

Hakan Özaktaş,

Nureddin Kırkavak,

Ayşe Nilay Alpay

Publication year - 2021

Publication title -

modelling and simulation in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 20

eISSN - 1687-5591

pISSN - 1687-5605

DOI - 10.1155/2021/2315987

Subject(s) - bottleneck , queue , queueing theory , constant (computer programming) , exponential distribution , random variable , travel time , exponential function , computer science , mathematics , statistics , mathematical optimization , engineering , computer network , transport engineering , mathematical analysis , programming language , embedded system

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.

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