Event-Based Rolling Optimization Scheme

In this research, the event-based rolling-horizon optimization scheme is employed, and two events will trigger a new optimization session: 1) detection of a new bus and 2) an existing bus passes through an intersection.

The event-based scheme is more flexible than the fixed-interval rolling scheme. And it can limit the negative effect of dwell time variability by constantly monitoring the conditions and set off an event should any unexpected conditions take place. However, there are two main issues that have to be addressed in implementation:

Normal Cycle 1 2 3 4 5 6 (a) Fixed-Interval Optimization 1 2 3 4 5 6 Event 1 (b) Event-based Rolling Horizon Optimization 1 2 2 3 3 4 5 6 PoO PoO PoO PoO PoO PoO PoO * PoO – Point of Optimization

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 What formulation change needs to be made to allow optimizations to be

conducted at any point over the time horizon instead of just at the beginning of a cycle?

 How to handle multiple bus arrivals either simultaneously or separately before the end of a planning horizon?

5.5.1.1. Formulation Addition

It turns out that it is quite simple to allow optimization to be conducted at any moment. The trick is by adding the following constraints to define the feasible region of the green times of each phase within the planning horizon:

curr ijk ijk g G , , i cur i k jJ   (5-1) past ijk ijk g G

 i,

k j,

J

G and G_ijkpast denote the elapsed green time of current and past phases respectively within the current cycle. These two input parameters can be obtained by directly recording the actual timings from the beginning of the cycle to the point when the optimization occurs. These additional constraints are applicable to the RTSP

formulation. But the same constraints can be written for the SMINP model by simply dropping the intersection index i.

111 5.5.1.2. Handling Multiple Buses

Any good real-time TSP control systems need to handle the arrival of multiple buses. But this is usually difficult when buses do not arrive at the same moments. This is because it is possible that the optimal timing is being implemented for the first bus may not be optimal at all for the second bus. To avoid the optimal timing for the first bus being overwritten by the arrival of the second bus, an active TSP strategy normally enforces a recovery period, during which no new TSP requests will be processed. This First-Come-First-Serve (FCFS) strategy renders very inefficient use the signal timing adjustment, which is the biggest disadvantage of the active TSP strategies.

In this research, since the mathematical formulation developed above allows the arrival inputs from multiple buses, there are two situations in handling multiple buses:

 Situation 1: When buses are detected simultaneously, one optimization session that uses all bus arrival times is needed.

 Situation 2: When buses are detected separately during the planning horizon, the optimizations are done multiple times. Each time, the optimization will include the new buses and update the trajectories of the existing buses.

One question is, however, how to define the background optimal timing if the second situation, the more likely situation, is encountered. The concept of deviation as we introduced earlier uses the background optimal timing as the reference point, and any deviation from that point is considered as impacts to other traffic. In situation 2, the

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second bus arrives within the period when the optimal timing for the first bus is being implemented. There are two ways to define the background optimal timing:

 Definition 1: the timing that yields minimal delay to the prevailing passenger traffic conditions.

 Definition 2: the timing that yields minimal delay to buses arrived earlier but sub-minimal delay to the passenger vehicles.

Using definition 1, the background timing remains strictly tied to the passenger vehicles only and it is the same regardless how many TSP optimization sessions have been conducted. Using definition 2, the background timing adapts to the fact the currently running timing considers both the prevailing traffic conditions and the priority needs of the existing buses.

From a glance, definition 2 seems to fit in better with the adaptive theme of the overall control philosophy. And for single intersection case, there is not much of difference between definition 1 and 2, since all the changes are made locally and do not have a wide-ranging effect. However, a revisit on the concept of deviation suggests otherwise. The concept of deviation uses the optimal background timing to approximate the optimal performance that can be achieved under the prevailing traffic conditions without bus. That implies, if the prevailing traffic condition is not changed, the timing to achieve the optimal performance for all the traffic is not changed. So, regardless how many times the timing is adjusted to fit priority needs of different buses, the optimal background timing

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remains unchanged as long as the prevailing traffic condition is not changed. In fact, the evaluation studies in section 7.2.5 will reveal that definition 1 is a better choice.

But the problem for using definition 1 as the background optimal timing is that it excludes the considerations of the buses which arrived previously but have not left yet. The connected vehicle technology counters this problem. Each bus OBU is constantly communicating with the RSU. So when the second bus is detected, the arrival

information the first bus can be recaptured. The TSP models use the arrival information of both buses as if they are detected at the same time.