With the progress of urban intelligent construction, urban rail transit trains have become one of the most important ways for urban traffic. Optimization operation is a key to further improve the performance of urban rail transit. In this work, an energy saving velocity planning algorithm for rail transit train with running and computation delays is proposed. First, an optimization model with considering both running and computation delays is established for velocity planning. Then, the velocity planning algorithm frame is proposed based on Gauss pseudospectral distribution, where the running delay and computation delay are tackled separately. Meanwhile, the gradient information of transform nonlinear programming (NLP) problem is derived in detail so that NLP solver can be employed to obtain accuracy results. Furthermore, the implementation steps of the proposed algorithm are given. Finally, simulation tests are carried out on a two-station running rail transit train model with three different delay situations and two different slopes railway. Numerical results and comparison show the effectiveness and correctness of the proposed method for rail transit train velocity planning with delays.

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