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Abstract. The aim of this paper is to show how to use in practice the strong stability method and also to prove its efficiency. That is why we chose the GI/M/1 model for which there exist analytical results.For this purpose, we first determine the approximation conditions of the characteristics of the GI/M/1 system. Under these conditions, we obtain the stability inequalities of the stationary distribution of the queue size.We finally elaborate upon an algorithm for the approximation of the GI/M/1 system by the M/M/1 system, which calculates the approximation error with an exact computation. In order to give some idea about its application in practice, we give a numerical example.The accuracy of the approach is evaluated by comparison with some known exact results.

Wireless sensor networks are very constrained by a low bandwidth and high latency due to the shared nature of the radio medium. Nevertheless, the real critical issue in these networks is energy. Several routing protocols have been proposed in the literature to maximize the lifetime of wireless sensor networks, however, most of these solutions use a routing through a single path, which can rapidly deplete the energy of some nodes (those are part of the optimal path) more than the other nodes. This usually leads to partitioning in the network and of course to the death of this later. The aim of this paper is to propose a new protocol for multi-path routing in which nodes choose one route among several routes with a probability which will count the residual energy, the energy of the communication and the number of paths including the forwarding node. Our approach allows the sensor nodes of the network wasting their energy in an equitable manner. Thus, our protocol enhances the lifetime of the sensor network. This is proved by simulation on SENSIM. We have implemented our solution and compared it with EAR, results show that our protocol outperforms EAR by enhancing the network lifetime.