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This paper introduces a type of circular causation called Congestive Mode-Switching (CMS) that may arise when an increase in congestion penalizes transit relative to driving. In turn, rising congestion persuades some transit riders to drive, which exacerbates congestion further, and so on. This circular causation can beget multiple equilibria with different levels of congestion and transit ridership. The paper explores this logic with a static model of a bus route. When the bus fleet size is fixed, CMS applies because congestion raises the bus cycle time and thus lowers bus frequency, resulting in higher wait times. When the fleet size depends on bus ridership, CMS is joined by economies of scale as a second source of circular causation. We derive the system’s equilibria using a static model in the vein of Walters (1961), which permits us to graphically characterize equilibria in useful ways. The comparative statics of a road improvement show how feedback alters first-order effects. A Downs-Thomson paradox is not possible, because a road improvement aids buses even more than cars. Continuous-time stability analysis shows that multiple equilibria may be stable.
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The Waiting-Time Paradox
Suppose that you are going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer—possibly much longer—than what you might guess from looking at a bus schedule. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. In this article, we explore the waiting-time paradox, explain why it occurs, and discuss some of its implications (beyond the possibility of being late for school).
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- Award ID(s):
- 1922952
- PAR ID:
- 10251491
- Date Published:
- Journal Name:
- Frontiers for Young Minds
- Volume:
- 8
- ISSN:
- 2296-6846
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/frym.2020.582433
