Research records about Transit Control

In this blog I want to record some notes in transit control, which are basically grasped from published paper.

Some common sense

1. Generally, bus lines with more than 5 buses per hour are regarded as high-frequency bus services.
2. Transit riders typically ignore schedules with headways less than 10–12 min R.
3. Due to high demand, most bus services operate at high frequencies, with headways typically within 10 min along major corridors. With such short headway, operators typically provide only rough headway information, e.g. headway: 5–7 min, but not the exact service timetables.
4. Some studies suggest buses n-1 and n are bunched if their headway is less than 1 min R. Some studies prefer 0 min R.

   Some scientific insignts

5. Transport authorities use punctuality-based key performance indicators (KPIs) to evaluate the performance of low-frequency bus services and regularity-based KPIs to evaluate the performance of high-frequency services R. For high-frequency lines, the objective of control is to maintain low headway variability and alleviate bus bunching R.

6. When bus service circulate on a route, service is best when times between successive bus arrivals (headway) are equal R.

7. Non-uniform arrival patterns can lead to more severe bunching effects over time R.

8. The average passenger waiting time E(W) is related to the average headway E[H] and variance of headway ​Var(H): R

   E(W) = E(H)/2 + Var(H)/[2E(H)]

Some classic mathematical optimization solutions (More than 100 references)

1. An analytic solution for real-time bus holding subject to vehicle capacity limits
   • Strategy:
     • Implement real-time holding control on each stop for each arriving bus.
   • Objective:
     • Minimize squared deviation between the expected/realized forward & backward headways and their target values;
     • Minimize the number of stranded passengers for current bus trip and upcoming bus trip.
   • Method:
     • Constrained convex optimization.
2. An Analytic Stochastic Model for the Transit Vehicle Holding Problem
   • Strategy:
     • Implement real-time holding control on each stop for each arriving bus.
   • Objective:
     • Minimize the waiting time as the formula of headway;
     • Minimize the waiting time of onboard passenger (holding penalty).
   • Method:
     • Linear search optimization algorithm.
3. The Holding Problem with Real–Time Information Available
   • Strategy:
     • Each decision is to determine real-time holding control on one predefined stop for predefined m consecutive following trips.
   • Objective:
     • Minimize the waiting time as the formula of headway on m trips at a time.
   • Method:
     • Heuristic optimization.
4. A model for holding strategy in public transit systems with real-time information
   • Strategy:
     • Determine holding control for all buses at each decision step.
   • Objective:
     • Minimize the waiting time as the formula of headway. Each bus consider its impact on N downstream stops (i.e., Rolling Horizon);
     • Highlight the minimization of waiting time for passengers left behind at first arrving bus.
   • Method:
     • Iterative search method (Simulated annealing)
5. Hybrid predictive control for real-time optimization of public transport systems’ operations based on evolutionary multi-objective optimization
   • Strategy:
     • Determine holding control & stop skipping control for each arriving bus in N future horizon.
   • Objective:
     • Minimize the waiting time of prediced number of passengers (by dynamic state-space model) in N future horizon;
     • Minimize the predicted headway (by dynamic state-space model) with predefined headway in N future horizon;
     • Minimize the hold cost on onboard passengers in N future horizon;
     • Minimize the skip cost on passengers skipped by the vehicles in N future horizon.
   • Method:
     • Evolutionary multi-objective optimization

Some classic analytical solutions (More than 100 references)

1. Dynamic bus holding strategies for schedule reliability: Optimal linear control and performance analysis
   • Strategy:
     • Holding based on a “virtual schedule” of predicted arrival times at stops (as opposed to the published schedule which typically shifts times earlier to avoid early departures from stops).
   • Contribution:
     • Integrate forward and backward headway information to improve both headway regularity and schedule adherence
   • Drawback:
     • The strategies may lose effectiveness under system disruption (i.e., When a bus breaks down or under severe congestion, the target headway and virtual schedule may become obsolete or invalid);
2. A headway-based approach to eliminate bus bunching: Systematic analysis and comparisons
   • Strategy:
     • Holding based on target headway
   • Contribution:
     • First gave a mathematical stability analysis of holding problem based on real-time AVL data.
     • Headway-based control can achieve faster speed in comparison to the schedule-based approach;

• Drawback: * It has forward-looking/non-cooperative character. (i.e., Buses are not allowed to slow down in response to events behind.)

Some recent control solutions (2015-)

1. An online learning approach to eliminate Bus Bunching in real-time
   • Strategy:
     • Holding and stop skipping to maintain a user-defined bus bunching alert headway based on predicted information (i.e., bus travel time).
   • Contribution:
     • A probabilistic framework for detecting a bus bunching event at downstream stops is proposed.
     • Prediction output is used to select and employ corrective actions (holding and stop skipping).
   • Drawback:
     • Do not consider cooperative policy.
2. Two-way-looking self-equalizing headway control for bus operations
   • Strategy:
     • Holding for headway regularity at one control point (i.e., terminal station).
   • Contribution:
     • Consider both the backward headway and the forward headway when deciding how long a vehicle should wait at a control point.
   • Drawback:
     • Do not consider long-term effect.
3. A predictive-control framework to address bus bunching
   • Strategy:
     • Holding to reduce the headway deviation from the target headway.
       • Holding decision at each stop is determined based on predicted headway of approaching trips.
   • Contribution:
     • Combine classic analytical control method with headway prediction technique(i.e., linear regression and extrapolation, kernel regression, neural network, autoregressive-moving-average model).
   • Drawback:
     • Predefined parameters setting.
     • Only local-cooperative control (forward-backward headway consideration)

Others

1. An interesting paradox phenomeon in transit community