In this paper, we consider a wireless scenario in which multiple-nodes operating under delay constraints transmit finite alphabet input signals for simultaneous wireless information and power transfer (SWIPT). These nodes communicate through time-division multiple access channels, and the receiving node harvests energy from the received signal while decoding information by applying power splitting scheme. In addition, the transmitting nodes are subject to limitations on the buffer overflow probability, specified by the quality of service (QoS) exponent. Due to harvested energy constraint, we have introduced a novel approach that assigns probabilities non-uniformly to different signals in the constellation which improves the overall performance in terms of throughput and energy efficiency (EE). We formulate optimization problems to maximize the effective capacity and effective EE while taking input signal probabilities, operating intervals, and splitting factor into account. Since obtaining closed-form expressions for the optimization parameters is unlikely, we develop an algorithm to determine the solutions numerically. In the numerical results, we observe that QoS constraints primarily affect achievable rate distribution among the users, and override the channel conditions. In addition, having static slope characteristics for non-uniform probability assignment is more energy efficient than having dynamic characteristics.