Abstract-Because of the rising energy prices and environmental concerns, the calculation of energy-optimal reference trajectories for trains is significant for energy saving. On the other hand, with the development automatic train operation (ATO), the optimal trajectory planning is significant to the performance of train operation. In this paper, we present an integrated survey of this field. First, a nonlinear continuoustime train model and a continuous-space model of train operations are described, after which the optimal trajectory planning problem is formulated based on these two models. The various approaches in the literature to calculate the reference trajectory are reviewed and categorized into two groups: analytical solutions and numerical optimization. Finally, a short discussion of some open topics in the field of optimal trajectory planning for train operations are given.

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The tradeoff between the energy efficiency (EE) and delay problem in cooperative relaying system is studied by using Non-orthogonal multiple access (NOMA) in this paper. To obtain an efficiency tradeoff between EE and delay, a stochasticbased EE optimization problem is formulated by considering the system queue stability. Then, the fractional programming and control parameter-based Lyapunov optimization method is proposed to solve the formulated problem. Furthermore, we derive the analytical bounds of EE and delay based on the control parameter. Finally, simulation results verify that the proposed cooperative NOMA system performs better than the traditional orthogonal multiple access (OMA) cooperative system. Index Terms-NOMA, cooperative relaying system, EE, delay I. Introduction NOMA technique has recently been included into the 3GPP long term evolution advanced (LTE-A) standard, owing to its enormous potential in improving system spectrum efficiency [1]. Different from the traditional OMA, the users are allowed to share the same time/frequency resource in NOMA. Meanwhile, the success interference cancellation (SIC) is applied at the receivers to reduce the co-channel interference and extract desired components from the received signals. Recently, cooperative NOMA is further proposed to improve the transmission reliability of the system, by exploiting the spatial diversity gain [2]-[6]. The power allocation strategy is optimized based on the closed form expressions for the base station's outage probability and sum rate in [2]. [3] derives the sum rate region in the cooperative NOMA system with compress-and-forward relaying by using the noisy network coding. In [4], the achievable rate is calculated approximatively through the Gauss-Chebyshev Integration method in a Rician fading channel. [5] proposes a two-stage selection strategy under different quality of services (QoSs) for the users, and then the closed-form expression of the outage probability is obtained. However, recent studies mainly focus on the rate and outage probability for the cooperative NOMA system.

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