Using CVIS to Improve Bus Schedule Adherence: A Predictive Control Strategy and Its Hardware-in-the-Loop Field Tests

Table 1

Notations.

Type	Symbol	Definition
Set	𝑖∈𝐼	The set of intersections
	𝑙∈𝐿	The set of links
	𝑏𝑠∈𝐵𝑆	The set of bus stops
	𝑡𝑝∈𝑇𝑃	The set of key-time node of planned arrival time
	𝑡𝑙∈𝑇𝐿	The set of key-time node of latest planned arrival time
Timing variable	𝐾𝑖	Signal time when bus arrives at intersection 𝑖
	𝐶	Common cycle
	𝑡^𝑎𝑖	Predicted arrival time point in one cycle when bus arrives at intersection 𝑖
	𝑇𝑖^𝑡𝑒	Red time between 𝑡^𝑎𝑖 and the ending time of the red phase at intersection 𝑖
	𝑟^𝑎𝑖	Back-stepping arrival time point in one cycle when bus arrives at intersection 𝑖
	𝑇𝑖^𝑡𝑠	Red time between 𝑡^𝑎𝑖 and the starting time of the red phase at intersection 𝑖
	𝑡^𝑇𝑃𝑏𝑠	The planned arrival time point to 𝑏𝑠 downstream stop
	𝑡^𝑇𝐿𝑏𝑠	The latest planned arrival time point to 𝑏𝑠 downstream stop
	𝑡0	Current time
Data	𝑉𝑐	Current speed of bus
	𝑉𝑙	Empirical bus speed at link 𝑙
	𝐿𝑙	Length of link 𝑙
	𝐿𝑏𝑠	Distance between bus and 𝑏𝑠th downstream stop
	𝑙0	Current link
	𝑙^𝑠𝑏𝑠	Link in which 𝑏𝑠th downstream stop is located
	𝑉𝑙	Empirical bus speed at link 𝑙