A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters' Route. (24th May 2021)

• Record Type: Journal Article
• Authors: Özaktaş, Hakan; Kırkavak, Nureddin; Alpay, Ayşe Nilay
• Other Names: Calì Michele Academic Editor.
• Is Part Of: Modelling and simulation in engineering. Volume 2021(2021)
• Publication Date: 2021-05-24
• Subjects: Engineering -- Simulation methods -- Periodicals; Engineering -- Mathematical models -- Periodicals; 620.004
• DOI: 10.1155/2021/2315987
• Languages: English
• ISSNs: 1687-5591

Abstract

Abstract : 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.