Recently, handover execution has still been damaging 5G latency requirement due to having three states in virtual evolved packet core (vEPC). Here, the desired end-to-end delay (e2eDelay) should be less than 4 m/sec without any mobility interruption on an enhanced mobile broadband (eMBB) service of vEPC. To handle this requirement, we need to focus on the Markov model of e2eDelay. It can be measured by the concatenation of edge and core delays in the downlink eMBB service from a remote source to a mobile user. Here, edge delay is directly affected by the core network via a decreased packet delivery ratio to edge under huge-traffic intensity background. Therefore, target eNodeB decision by considering only edge network can be misleading. To overcome this, we jointly consider edge and core delays, which are differently affected by each handover states: 1) preparation, 2) execution, and 3) completion. The joint consideration of edge and core can be only handled with a novel cost-effective software-defined ultra-dense network (SDUN) framework by dynamically removing state 2). It triggers handover via network-centric monitoring; and then, it predetermines optimal TeNB with a proposed optimization formula and shortest core path according to traffic intensities of OpenFlow switches. Here, SDUN controller is cost-efficient by the proposed parallel runnable algorithms: parallel edge delay optimization and parallel shortest delay path. In the performance evaluation SDUN is first emulated for a specific eMBB traffic, i.e., QUIC based HTTP/3 video content traffic with 1080p resolution, and second simulated in system-level on MATLAB. It meets 5G requirements as follows: SDUN decreases core delay 7.16 m/sec per a UE under huge-traffic intensity and keeps edge delay under 5G requirement with 20% more delivery ratio than conventional one. Moreover, the cost of SDUN controller is analyzed as O(k(4)log(2)(k)) and the cost efficiency is observed as the 50% increased scalability level with the acceptable 8% extra virtual memory usage.