First, I don't think that an extra cost of stopping vs non-stop passing the station is any special for HS trains vs "regular" trains. HS trains (max speed over 160 or 200 kmph?) are "special" only in the sense that they use electric propulsion (usually AC) and not diesel.

The acceleration/deceleration cost in the narrow sense is the just the cost of extra electric energy which must be used vs non-stop passing the station. It seems to be just a problem of calculating that cost from "theoretical" technical parameters of the train and verifying it in practice (in "field conditions").

But there may be some more costs imposed by each extra stop. They may mailny result from a longer duration of the entire journey (longer lighting of the interior/heating/cooling by air conditioning, longer work time of train staff etc.). Those costs seem to be directly proportional to the longer duration of the journey but there may also exist some non-proportional "indirect" cost. Eg. the longer duration may make it impossible for passengers to have enough time to change to another train at the destination station and they will not choose the considered train service at all, There may be not enough time to maintenance activities like cleaning the train at the destionation station, no possibility to match to available time slots at busy stations or to keep a specific scheduled tact (eg. one train every hour).

All the possible I presented above don't result from my research (I rather study ticket pricing and its relationship to the national an EU law) and they are just loose considerations. However, if you are inetrested in knowing the costs of stopping a train in a wider sense ( extending beyong the "direct: costs of energy resulting directly from the laws of physics), you must consider the whole context of a specific itrain service (legal regulations, schedules, ticket pricing, timing of maintenance activities and - I guess - some other factors I forgot).

Przemysław Kowalik Thanks a lot for the detailed answer, we are going to analyze the different stooping schemes for the high speed (Engine Type. CRH380A), while considering different variants and parameters, the cost was also a factor there, we already consider many factors, as you mentioned. As per our team understanding, it was quite clear that there is a huge cost involved, when the brakes apply, Such as (Corrosion cost, rail gauge maintenance cost, rail flange cost, the electric energy needed to stop the High-speed train, and energy needed to bring him in a smooth motion). it's quite clear as per my understanding that, when the rail will change its state from zero to motion, the energy level required is different at different stages, and when it's in smooth motion the energy level required is different. till now i didn't find any literature/report/academic article where they analyze this cost, but till now I found nothing.

Thanks once again, for the guidance.

From the aspect of rail maintenance, the braking and acceleration of the vehicle is unfavorable. For example, short pitch corrugations are thought to form from the differential wear caused by a repetitious longitudinal sliding action of the wheel on the rail, whether through acceleration, braking or lateral motion across the rail. Squat rail defect is a rolling contact fatigue phenomenon which occur mainly on straight lines and curves of radius R≥3000 m with high shear stresses, especially zones where accelerations and breaking occurs.

Rail break is the last phase of crack development process and might lead to catastrophic derailment. The consequences can include death, injury, costs and loss of public confi dence. In addition, these events may have devastating and long-lasting effects on the industry. Mostly known traffic accident happened in Hatfield (UK) on October the 17 th 2001. Rail breakages appeared on 35 m of rail length with 300 critical rail breaks. After this disaster, EU began with intense safety inspections. Furthermore, the rail inspection costs are estimated at about € 70 million per year in EU .