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- Title
An Extension of Analysis of Multiple Period Bus Transit System.
- Authors
Yu-Lan Wang; Chiu-Tang Lin; Junling Zhang; Xiaolin Li
- Abstract
This paper extends the paper of feeder bus systems. In their systems, the condition to guarantee the existence of the optimal solution is not discussed. We investigate the Hessian matrix to find criterion to locate the maximum solution and derive the closed form solution for the profit function. Moreover, we derive a formulated estimation for the route spacing in order to provide readers with a detailed look into existing methods, and their characteristics and applicability to analyze the closed form profit function. In our note, we have found: (a) To find the criterion to insure the profit function has critical points and show the condition to guarantee that the small one is uniquely maximum point; (b) To solve the maximum profit in a closed form and find the condition to insure the maximum profit is positive such that operation of the bus system is profitable; (c) To construct a better formulated approximation and compare numerical examples from their paper.
- Subjects
HESSIAN matrices; BUSES; BUS transportation
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 4, p1594
- ISSN
1992-9978
- Publication type
Article