Implementing transport over a graph

I have a task at hand in which I have to lay down a rail time table, Now the rail track is straight and I have implemented a Doubly Linked List for the representation of a train terminal, a terminal behind this and a terminal ahead this are represented by the links in the list.

Now I want to implement a train over the tracks laid so far, I am not intrested in implementing a database and all my raw data is in the form of JSON. An example of one terminal in JSON looks like:

{
    "stations_array": [{
            "vertexId": 0,
            "name": "Terminal0",
            "lat": "84.2207",
            "lng": "74.3884",
            "isEndTerminal": true,
            "isFunctional": true,
            "vertNext": 1,
            "vertPrev": null
        },
        {
            "vertexId": 1,
            "name": "Terminal1",
            "lat": "104.2580",
            "lng": "94.4512",
            "isEndTerminal": false,
            "isFunctional": true,
            "vertNext": 2,
            "vertPrev": 1
        },
        {
            "vertexId": 2,
            "name": "Terminal2",
            "lat": "14.1659",
            "lng": "04.5632",
            "isEndTerminal": false,
            "isFunctional": true,
            "vertNext": 3,
            "vertPrev": 1
        }
    ]
}

And I represent a train in JSON as well, which is as below:

{
    "trains_array": [{
        "id": 16,
        "source": "Terminal0",
        "destination": "Terminal2",
        "start_time": "06:00",
        "days": "daily",
        "terminals": [{
                "id": 0,
                "name": "Terminal0",
                "time": "06:00"
            },
            {
                "id": 1,
                "name": "terminal1",
                "time": "06:12"
            },
            {
                "id": 2,
                "name": "Terminal2",
                "time": "06:25"
            }
        ]
    }]
}

Now the terminals array in the above JSON tells me where the train stops (id being the representation of a foreign key inside the terminal array for each object) and I calculate through code to know which train arrives at what time at which station, which station it stops or omits at. however this whole approach seems a bit hardcoded. I want to know if there is a better way I can represent things here.