This study looks at how travelers move between MADINA and JEDDA, using the UPPAAL Stratego tool to tackle the complexities of urban mobility. As cities grow, effective transportation planning becomes more challenging. Travelers have three options: car, bus, and train. The choices for car and bus travel are impacted by traffic conditions, which can vary between heavy and light, affecting both travel time and cost. We propose a detailed mathematical model that captures all possible scenarios related to these travel options, incorporating the uncertainties of real life. This allows us to simulate different traffic situations. By using UPPAAL Stratego, we evaluate three strategies: the Safe Strategy, which minimizes risk; the Fast Strategy, which aims to reduce travel time; and the Fast and Safe Strategy, which seeks a balance between speed and safety. This paper starts with an introduction to the Stochastic Priced Timed Games approach, highlighting its relevance in modeling dynamic travel environments. We then provide an overview of UPPAAL Stratego, showcasing its abilities in generating, optimizing, and comparing strategies. Next, we outline our mathematical model, explaining the assumptions, parameters, and data sources we used. Our simulation results illustrate how each strategy performs under different conditions, shedding light on traveler preferences and behaviors. The findings underscore the significance of accounting for traffic variability in travel planning and offer important insights for urban transportation policies aimed at improving the traveler experience and optimizing resource use. Additionally, we emphasize the theoretical contributions of our model by demonstrating its applicability to real-world scenarios and its potential to inform future research in urban mobility optimization. Ultimately, this research adds to the growing knowledge of smart transportation systems, demonstrating how formal mathematical modeling can address complex real-world challenges and inform future urban mobility strategies.
