# Time-Dependent Performance of a Multi-Hop Software Defined Network
## 1 Introduction  
Software defined networking (SDN) is a dynamic, adaptable, and manageable paradigm that facilitates innovations in computer networks [1], together with the prototyping and deployment of flexible routing mechanisms [2, 3]. Traditional networking is based on manual configurations of distributed proprietary network devices, a cumbersome and error-prone process that can underutilize network resources [4]. SDN offers a programmable architecture where routing decisions are moved to centralized controllers. SDN data plane switches are simple forwarding devices that forward the data traffic depending on the controller's flow forwarding rules. Routing algorithms are implemented and communicated by each SDN controller to the SDN switches, which follow its instructions. Metrics such as hub count, delay, packet loss, bandwidth, jitter, and power consumption can be measured by SDN switches and sent to the controllers, which may use these metrics to determine the best routing paths and then install the flow forwarding rules in the data plane SDN switches. Indeed, the IoT [5] interacting Cloud Services [6] for the decision and control of the cyber-physical world create challenges for networks that achieve a better quality of service (QoS) and security and less energy consumption, and can exploit the opportunities offered by machine learning [7, 8, 9]. These challenges can be met by SDN networks [9, 10], which offer greater flexibility and ease of implementation [2, 11]. These developments suggest that SDN is likely to become the preferred networking approach not only in core networks because of the centralized network intelligence and management that it enables but also for sub-networks of IoT devices and edge devices with specific QoS needs that can benefit from SDN programmability and flexibility. Thus,in [12], conventional routing protocols such as RIP, OSPF, EIGRP, and BGP, are compared with SDN with respect to convergence times after link failures, showing that SDN routing is better than conventional IP networks. Considerable work has also shown that SDN can select routing paths based on criteria such as quality of service (QoS) [13; 14; 15; 16], while energy-aware SDN routing has also been discussed in several papers [17; 18; 19]. The scalability of SDN routers that conduct QoS routing has been studied in [20], where the authors propose an SDN-based scalable QoS routing scheme between autonomous systems. In [21], a survey of the scalability issues that arise when SDN's centralized scheme deals with relatively frequent path updates is conducted. Both hierarchical and concurrent (distributed) approaches are investigated to alleviate SDN controllers' additional workload. In recent work, [22] SDN is discussed as a means to choose the best paths based on a function of time-varying traffic in order to optimize the QoS metrics of interest. Other work [23] examines a broad class of QoS-based algorithms to assign paths to flows in SDN and analyzes the resulting performance. In addition, the work in [24] discusses the implementation of SDN based real-time QoS in industrial settings with mobile robots or palets, where motion and reliability requirements impose changes in paths to constantly meet real-time requirements. In [25], the use of AI-driven dynamic QoS routing in SDN is used to optimize QoS, reduce energy consumption, and improve security based on Autonomic Communications [7] and the Cognitive Packet Network algorithm [26]. However, in addition to scalability issues, QoS-driven SDN routing can create traffic and time-dependent changes in network topology and in the load and paths that are serviced by SDN switches.