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The quality of service, according to a networking context, is the degree of users’ satisfaction of services that a communication system provides. It aims at improving communication behaviour under a correct data transmission and an optimal use of resources. According to this concept, quality of service is typically the performance criteria that evaluate the service provided. Wireless multi-hop networks, including ad hoc networks, with their complex nature impose many constraints than in wired networks. Besides, the quality of service concerns the behaviour of the network, and is dealt with from different points of view. It typically addresses a set of metrics relevant to delay, bandwidth, jitter, packet loss rate, energy consumption, stability, security, and so on. It is worth noting, accordingly, that some criteria are very difficult to discern and can be still considered challenging. In this regard, security is not sufficiently addressed in a QoS context in ad hoc networking studies. Inside the ad hoc networking field, the quality of service issues concern different layers on the network architecture. We distinguish between too main optics of quality of service studies: QoS models and QoS routing. A QoS model defines all mechanisms that the network should respect in order to guarantee the quality of service on the network. The model is based on and characterizes the architecture of the network. It includes all protocols that organize communication and connectivity between the different layers or components. In this respect, QoS routing presents a critical component in the model and a rich field for algorithm development. QoS routing consists of finding the best path to relay a source to a destination and guarantee the quality of service in parallel. In a general case, QoS routing consists to define metrics (usually one) that control the decision making to choose a path. The metrics nature affects the mathematical model and then the algorithm approach used to solve the problem of finding the best path. Mathematical modelling of quality of service in ad hoc networking aims at improving the decision making on networks in an operational meaningful way. It addresses many concerns of the QoS and allows to benefit from various modalities and techniques of optimization theory. This work reviews and discusses several mathematical models developed for or oriented to quality of service in ad hoc networks, and highlights the different forms that a model may take. Because we believe that several metrics of quality of service in ad hoc networks are in contradiction and thus the multicriteria optimization gives more opportunities in decision 5

Mathematic Models for Quality of Service Purposes in Ad Hoc Networks