In recent years, there have been significant efforts to standardize a routing protocol for Low-power and Lossy Networks (LLNs). This effort has culminated in standard IPv6 routing protocol for LLNs (RPL). The main interest of RPL is to improve routing in an LLN minimizing the usage of network resources. For this, RPL builds acyclic graphs and applies an Objective Function (OF) which is responsible of choosing the preferred parent and the best links during the construction of the Destination Oriented Directed Acyclic Graph (DODAG). This paper introduces a new OF, based on a Non-Linear Length (NL-OF) which takes into account any number of metrics and constraints for QoS routing. NL-OF ensures that each path in the DODAG respects the input constraints. The NL-OF can be used to meet the requirements of sensible applications, such as real-time applications. A significant part of this work aims at studying the theoretical aspect of the NL-OF. Finally, using Cooja simulator, we evaluate the performance of NL-OF. We show that our new Objective Function gives a good result and outperforms the three existing OFs when considering three QoS parameters which are end-to-end Delay, Packet Loss and Jitter.

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Multimedia applications such as videoconferencing and collaborative applications require the satisfaction of several Quality of Service constraints (QoS). The routing with respect to QoS constraints was proposed in order to satisfy the user requirement and guarantee a certain level of performance to a data flow. As the communication architecture of these applications is often multicasting, the problem of finding a multicast route satisfying the QoS constraints proves to be challenging. In this paper we propose an Integer Linear Program (ILP) for finding the multicast route respecting a set of QoS constraints with minimum cost. Since the problem is NP-hard, we propose an efficient pretreatment algorithm (ArcReduce) to accelerate the resolution time. The pretreatment process can even answer in polynomial time, whether the problem has a solution or not, before starting the resolution process. The computation of the exact solution also allows for comparison of the heuristic solutions to the exact solution. We conduct an analysis of the ILP and the ArcReduce with various sizes of input data regarding the execution time, the success rate and the quality of the generated multicast route.