Wireless energy transferring technology offers a constant and instantaneous power for low-power applications such as Internet of Things (IoT) to become an affordable reality. This paper considers simultaneous wireless information and power transfer (SWIPT) over a dual-hop decode-and-forward (DF) relay network with the power-splitting (PS) energy harvesting protocol at the relay. The relay is equipped with a finite capacity battery. The system performance, which is characterized by the average success probability of source to destination transmission, is a function of the resource allocation policy that selects the PS ratio and the transmit energy of the relay. We develop a mathematical framework to find an upper bound for the maximum the average success probability. The upper bound is formulated by a discrete state space Markov decision problem (MDP) and make use of a policy iteration algorithm to calculate it.