In this paper, we characterize the optimal strategies focusing on the throughput and the system energy efficiency of wireless-powered communication networks (WPCNs) in the presence of delay-limited sources. Each energy-harvesting user equipment is assumed to be subject to limitations on the buffer overflow probability, specified by the quality of service (QoS) exponent theta. Correspondingly, the time allocation strategies for downlink energy harvesting and uplink information transfer depend on these QoS constraints, potentially overriding the doubly near-far problem of WPCNs. We consider the non-orthogonal transmission and time-division multiple access protocols for the uplink information transfer of WPCN, and for both cases, we formulate energy efficiency and throughput maximizing problems to obtain the globally optimal solution that satisfy the statistical QoS constraints. Since these optimization problems fall into concave or pseudo-concave categories, Karush-Kuhn-Tucker conditions are necessary and sufficient for global optimality, using which we obtain analytical expressions for the optimal operating intervals. In addition, in several cases, due to difficulty in providing closed-form expressions, we develop algorithms to solve the problems numerically. Finally, we provide the simulation results to confirm and further analyze the theoretical characterizations. We mainly observe that QoS constraints primarily affect the optimal time allocation policies as well as achievable rate distribution among the users, enabling us to overcome the doubly near-far problem of energy-harvesting communications networks pointed out as one of the critical issues in the literature.