Optimal Design of Public Bus Service with Demand Equilibrium

Solution Approach for Bus Transit Model with a Rectangular Service Area

“…Tirachini and Hensher [11] developed bus transit systems besides headway, vehicle capacity, number of bus routes, and bus stop spacing, they also considered bus fare, and bus operating speed to construct new systems. Lin and Hopscotch [12] examined the first transit model of Imam [13] to show that his model was unreasonable. Owing to Imam [13], who did not provide numerical examples, Lin and Hopscotch [12] adopted numerical data from Kocur and Hendrickson [1] to demonstrate their challenge to Imam [13].…”

“…Lin and Hopscotch [12] examined the first transit model of Imam [13] to show that his model was unreasonable. Owing to Imam [13], who did not provide numerical examples, Lin and Hopscotch [12] adopted numerical data from Kocur and Hendrickson [1] to demonstrate their challenge to Imam [13]. Chen and Julian [14] studied the second transit model of Imam [13] to point out that the solution procedure proposed by Imam [13] contained less accurate results, and then Chen and Julian [14] presented their formulated solutions.…”

“…Owing to Imam [13], who did not provide numerical examples, Lin and Hopscotch [12] adopted numerical data from Kocur and Hendrickson [1] to demonstrate their challenge to Imam [13]. Chen and Julian [14] studied the second transit model of Imam [13] to point out that the solution procedure proposed by Imam [13] contained less accurate results, and then Chen and Julian [14] presented their formulated solutions. Fielbaum et al [15] used directness, encompassing the number of transfers, number of stops, and passenger route lengths to study scale economies and transit lines in public transport.…”

“…Yang et al [30] pointed out that if the length of the rectangular service area extends to infinite, the maximum profit will also increase to infinite. Hence, the first transit model proposed by Imam [13] is less accurate. Luo [31] studied the solution procedure of Yang et al [26], Hung and Julianne [27], and Tung et al [29] to remove their extra conditions and then provided his new convergent sequence.…”

Development of optimization methods for the operation of a fixed route system under emergency conditions

“…However, since the early 1980s, studies included aspects of elastic demand in modeling the TRNDP (Hasselstrom, 1981;Kocur and Hendrickson, 1982 Schonfeld (1991,1993a,b) and Spacovic et al (1994) estimated demand as a direct function of travel times and fares with respect to their elasticities, while Chien and Spacovic (2001), followed the same approach assuming that demand is additionally affected by headways, route spacing and fares. Finally, studies by Leblanc (1988), Imam (1998), Cipriani et al (2004), Lee and Vuchic (2005) and Fan and Machemehl (2006a) based demand estimation on mode choice models for estimating transit demand as a function of total demand for travel.…”