Future Research

Although a real-time control system with adaptive TSP models was prototyped and encouraging results were obtained in this research, there are still many interesting aspects can be further explored:

 Another important future research is the robustness of the R-TSP models or, in the other words, the susceptibility of the R-TSP models to the stochastic nature of the traffic system. In this study, the stochasticity of traffic conditions had been tested in the form of random seed numbers and long simulation periods.

However, buses need to stop at bus stops for passenger loading and unloading, which time is subject to larger randomness. It is hypothesized that performance of the R-TSP models will degrade if more randomness is introduced. The rate of degradation in model performance can serve as a good indicator for the model robustness. If the robustness of the R-TSP model is low, a stochastic R-TSP

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model may need to be developed to explicitly account for the dwell time randomness.

 Alternatively, another way of handling stochastic traffic condition is to extend the stochastic formulation to multiple intersections. This may be the nature next step because 1) that optimizing corridor-level schedule-related performance requires corridor-level priority models, and 2) that it is feasible and necessary to explicitly account for variable bus dwell time using stochastic formulation. However, the large-scale nature of any stochastic programming approach may cause difficulty in finding optimal solutions. A branch-and-cut algorithm based on disjunctive decomposition technique [86] may be needed to provide optimal solutions.

 One important aspect of the R-TSP model requires further investigation is relationship of the effective range of the multipliers for the terms in the objective function and the number of intersections. In this research, the sensitivity analysis established the range of the multipliers for term x and d in which the model operator may make changes to influence the model outcome. This is good to allow some forms of inputs by the system manager to give more or less a priori priorities to certain bus lines. But the authors noticed that the effective range seems to tie to the number of intersections and the number of conflicting phases. Analytical models may be developed to give better guidance in determining the effective range.

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 Another possible extension is to integrate the model with an adaptive signal control system where additional information about the development of vehicle queues at an approach can be estimated in real-time. The additional information relaxes the assumption about constant vehicle arrival and further improves the ability of the SMINP to predict the arrival time distribution of the bus to the stop bar.

 A better queue prediction model could help give a better starting point for drawing the queue diagram in the queue delay algorithm. This change may be incremental, but it may result in more consistent performance by the R-TSP model. In some cases, the author observed that the some buses couldn’t pass through the intersection as planned in the model because the initial queue was much longer than expected. Connected vehicle technology can serve as a better detection mechanism to estimate the initial queue [87].

 A more sophisticated prediction models for predicting bus arrival time at each intersection can be employed to replace the naïve path project approach developed in this research. The multi-class cell-transmission model (M-CTM) developed by [88] appears to be a good candidate due to its efficiency of making predictions for traffic with different speeds, such as bus and passenger car. Also the M-CTM could account for platoon dispersion, which is typical on a long stretch of signal arterial.

 The RTSP model is designed to optimize any bus routes. However, this research only tested routes that are on a linear coordinated signal arterial. In a real-life

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setting, different bus routes may get on only different portion of the arterial. In theory, there is no obvious reason why RTSP model cannot work under those circumstances. But a rigorous simulation study can provide better understanding if any adjustments to the RTSP model can better work in those cases.

185 REFERENCES

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