Bus bunching: a comprehensive review from demand, supply, and decision-making perspectives

Figures & data

Table 1. Summary of the reviewed control strategies in bunching related articles.

Reference	Control	Input Data	Method	Benchmark	Evaluation		Assumptions and limitation
					Simulation Class	Network Complexity
(Osuna & Newell, 1972)	Dispatch or hold	Synthesised data	Dynamic programming		Simplistic setting	Simple scenario 2 vehicles	Single control point: one & two buses scenarios
(Turnquist & Bowman, 1980)		Real-world operation data: frequency, link travel time, demand	Simulation		Real operation-based setting	Bus route, 4–9 kms	No control strategies are tested
(Hickman, 2001)	Holding: optimal holding time	Synthesised buses and assumed headways	Stochastic programming		Simplistic setting	Bus route, 10 stops	Single bus route
(Fu & Yang, 2002)	Real-time holding: holding location and number	Bus position data from real-world operation	Optimisation model		Real operation-based setting	Bus route, 28 stops	Single bus route, same speed variation for all links and intersections
(Daganzo, 2009)	Adaptive Headway-based holding	Headway information	Analytical: dynamic equation	Schedule-based holding approach	Numerical simulation		Single bus route, forward-headway only
(Xuan et al., 2011)	Dynamic holding	headway & arrival time information	Analytical: complex motion equation	Schedule-based & headway-based holding methods	Numerical simulation		Single bus route
(Daganzo & Pilachowski, 2011)	Speed control	Cruising speed, two-way headway	Analytical: stochastic modelling	Discrete stops line	Simplistic setting	Bus route, 20 stops	Simple scenario, no non-linear effect & human factors in speed variation
(Delgado et al., 2012)	Holding & boarding limit	Various operation and demand related variables	Mathematical programming	No control, threshold control, holding & boarding limit	Simplistic setting	Bus route, 30 stops	Single frequency service, fixed passenger arrival
(Bartholdi & Eisenstein, 2012)	Self-coordinating buses	Bus GPS & passenger count data from single route	Analytical	Schedule-based & headway-based holding methods	Real operation-based setting	Bus route, 5.3 km	Single bus route, simplified operation setting
(Ceder et al., 2013)	Transfer synchronisation	Various operational variables: stop, user, and route attributes	Simulation and linear optimisation model		Real operation-based setting	Multiple bus routes: 3 routes	Bus on-time arrival, non-sensitive demand with arrival time fluctuations, similar bus setting in all routes
(Phillips et al., 2015)	Real-time holding by (Delgado et al., 2012)	Driver non-compliance, failure of communication system with buses	Simulation		Simplistic setting	Bus route, 30 stops, 10 km	Single bus route
(Hernández et al., 2015)	Holding strategy	Effect of multiple bus line	Simulation optimisation	No control scenario	Simplistic setting	Multiple bus routes: 2 routes	Lack of real data
(Argote-Cabanero et al., 2015)	Dynamic holding and driver guidance	Single lines & multiple lines effects	Analytically and simulation	Uncontrol & static holding control methods	Real operation-based setting	Multiple bus routes: 2 routes	Lack of real data
(Delgado et al., 2015)	Integrated holding, boarding limit and transit signal priority controls	GPS & APC data	Deterministic mathematical programming	No control situation	Simplistic setting	Bus route, 30 stops	Single bus route, dedicated bus lane and lack of mixed traffic effect, unchanged stop attributes vs time
(Schmöcker et al., 2016)	Overtaking	Common lines and overtaking effects	Analytical		Numerical simulation	Multiple bus route: 2 routes, 10 stops	Same frequency for both lines, constant arrival at stops, fixed arrival to loading ratios for all stops
(He et al., 2019)	Cruising speed control in dedicated bus lanes	Bus operational variables such as dwell time, passenger’s boarding at various time points	Optimisation model		Numerical simulation	Bus route, 17.95 km, 30 stops	Single bus route, fixed speed through all dedicated lanes
(Seman et al., 2020)	Integrated holding and priority control	Various operational attributes under bidirectional lanes priority control	Non-linear Programming (NLP)	Fixed traffic signal timing	Real operation-based setting	Multiple bus routes: 2 routes	Fixed signal timing effect
(Deng et al., 2020)	Speed control	Intersection delay and heterogenous roadway conditions	Optimisation model		Real operation-based setting	Bus route, 25 km, 40 stops	Single bus route, uniform passenger arrival, endogenous factors exclusion
(Tian et al., 2022)	Short-turning strategy	Various operational attributes: headway, arrival time, traffic condition	Non-linear optimisation model	No control and holding method	Real operation-based setting	Bus route, 33.8 km, 49 stops	Single bus route, operator related factors exclusion included cost
(Drabicki et al., 2022)	Real-time information provision	Real-time bus arrival, onboard crowd, SP survey data	Choice model and BusMezzo simulation model		Real operation-based setting	Bus route, 30 stops	Real-time information provision only, flexible fare/incentives could be included
(Khan et al., 2023)	Autonomous Modular Buses	Departure headway to downstream bus	Bus-Splitting & stop-skipping	Traditional stop-skipping	Numerical simulation	Bus route, 20 stops	Single bus route with quasi-homogenous demand

Figure 1. Bus bunching studies limitations in the literature.

Figure 2. Classification of bunching causes.

Figure 3. Qualitative assessment framework for bunching control strategies in public transport.

Table 2. Qualitative assessment of bunching control methods based on type of intervention and Pax/Opr attributes.

Group affected		Passenger (Pax)				Operator (Opr)				Control method orientation	Source
Objective		Decrease waiting time at stop	Decrease in-vehicle or onboard travel time	Improve trip experience & comfort	User choice (board/wait)	Improve headway regularity	Enhance schedule adherence/recovery	Maximise resource utilisation efficiency	Reduce running time & associated costs
Control method
Headway-based holding	Supply Control	+ + +	– –	–/+	NA	+ + +	+	NR	–	OOM	Section 5.2.1.1
Schedule-based holding		+ +	–	–/+	NA	+	+ + +	NR	–	OOM	Section 5.2.1.2
Signal priority		+ +	+ +	+	NA	+ +	+	NR	+ +	IM	Section 5.2.1.3
Speed control		+	+ +	+	NA	+ +	+ +	NR	+ + +	OOM	Section 5.2.1.3
Short turning		+ +	+ +	NR	NA	+	+ +	+ +	+	OOM	Section 5.2.1.4
Overtaking		+	+ +	–/+	_	+	­NR	+ +	+ +	OOM	Section 5.2.1.5
Stop skipping & boarding limit	Mixed Control	+	+ + +	NR	– –	+ +	NR	+ +	+ + +	OOM	Section 5.2.2.1
Real-time demand control	Demand Control	+	+ +	+ + +	+ + +	+ +	+	+ + +	NR	POM	Section 5.2.3.1
Hybrid method (DDC & MBM)		+?	+ + +?	+ + +?	+ + +?	+ +?	+?	+ + +?	?	POM?	Section 5.2.3.1

Table 3. Evaluation based on decision-making perspectives.

Control method	Control type Group	Control method orientation	Decision-making elements			Decision-making type				Future development potential
			Input variables	Objective	Action	Behavioural-based		Technology-based
						Choice	Enforce	Historical	Real-time
Headway-based holding	Supply Control	OOM	Service headway, arrival time	Improve regularity, reduce waiting time	Hold buses at stop(s)			X	X	High
Schedule-based holding		OOM	Schedule deviation, arrival time	Minimise schedule deviation & waiting time	Hold buses at timepoint(s)			X	X	High
Signal priority		IM	Bus/tram arrival at intersection	Minimise bus delay at intersection	Extend green/ truncate red			X	X	High
Speed control		OOM	Front & rear headways, bus travel time,	Improve regularity and speed	Adjusting cruising speed			X	X	High
Overtaking		OOM	Passenger boarding, service departure, travel time and demand	Minimise total costs, maintain regularity	Overtake		X	X	X	High
Short turning		OOM	Passenger arrival, spatio-temporal running time, service frequency	Minimise waiting time & schedule deviation	Convert selected trips into short-turning trips			X	X	High
Stop skipping & boarding limit	Mixed Control	OOM	Link travel time, number of passengers, schedule deviation	Reduce waiting time, maintain regularity	Skip certain stops, limit boarding		X	X	X	Moderate
Real-time demand control	Demand Control	POM	Real-time bus arrival & onboard crowd, fixed incentives	Distribute onboard load uniformly	Induce boarding & waiting behaviour	X			X	Very high
Hybrid method (DDC & MBM)		POM?	Real-time bus arrival, onboard crowd, dynamic fare incentives	Distribute onboard load, enhance comfort	Induce boarding & waiting behaviour	XX			X	Extremely high

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