Managing traditional networks comes with number of challenges due to their limitations, in particular, because there is no central control. Software-Defined Networking (SDN) is a relatively new idea in networking, which enables networks to be centrally controlled or programmed using software applications. Novel traffic shaping (TS) algorithms are proposed for the implementation of a Quality of Service (QoS) bandwidth management technique to optimise performance and solve network congestion problems. Specifically, two algorithms, namely "Packet tagging, Queueing and Forwarding to Queues" and "Allocating Bandwidth", are proposed for implementing a Weighted Fair Queuing (WFQ) technique, as a new methodology in an SDN-sliced testbed to reduce congestion and facilitate a smooth traffic flow. This methodology aimed at improving QoS that does two things simultaneously, first, making traffic conform to an individual rate using WFQ to make the appropriate queue for each packet. Second, the methodology is combined with buffer management, which decides whether to put the packet into the queue according to the proposed algorithm defined for this purpose. In this way, the latency and congestion remain in check, thus meeting the requirements of real-time services. The Differentiated Service (DiffServ) protocol is used to define classes in order to make network traffic patterns more sensitive to the video, audio and data traffic classes, by specifying precedence for each traffic type. SDN networks are controlled by floodlight controller(s) and FlowVisor, the slicing controller, which characterise the behaviour of such networks. Then, the network topology is modelled and simulated via the Mininet Testbed emulator platform. To achieve the highest level of accuracy, The SPSS statistical package Analysis of Variance (ANOVA) is used to analyse particular traffic measures, namely throughput, delay and jitter as separate performance indices, all of which contribute to QoS. The results show that the TS algorithms do, indeed, permit more advanced allocation of bandwidth, and that they reduce critical delays compared to the standard FIFO queueing in SDN.