We solve the maximum lifetime problem for a one-dimensional, regular ad-hoc wireless network with one data collector L N for any data transmission cost energy matrix which elements E i,j are superadditive functions, i.e., satisfy the inequality ∀ i≤j≤k E i,j +E j,k ≤ E i,k . We analyze stability of the solution under modification of two sets of parameters, the amount of data Q i , i ∈ [1, N ] generated by each node and location of the nodes x i in the network. We assume, that the data transmission cost energy matrix E i,j is a function of a distance between network nodes and thus the change of the node location causes change of E i,j . We say, that a solution q(t 0 ) of the maximum network lifetime problem is stable under modification of a given parameter t 0 in the stability region U (t 0 ), if the data flow matrix q(t) is a solution of the problem for any t ∈ U (t 0 ). In the paper we estimate the size of the stability region U (Q 0 , d 0 ) for the solution of the maximum network lifetime problem for the L N network in the neighborhoods of the pointsdescribes the shift of the nodes from their initial locationpartition', the second metric discussed in [3]. In this paper we utilize the fifth metric defined in [3], and we will minimize the maximum node costFor a one-dimensional, ad-hoc networks the metrics 'time to network partition' and 'the maximum node cost' are equivalent because the cutset, a set of nodes the removal of which will cause the network to partition, [4], consists of all nodes of the network. This means that obtained results in this paper are valid for network lifetime problems discussed in [1] and [2]. General formulation of the problem of extending the network lifetime depends on a number of initial parameters which characterize the nodes activity, available resources, the network environment or topology. It is known, that solutions of the problem are very sensitive under change of these parameters, [2]. In general even, if we know an exact solution of a given optimization problem there is a need to investigate its stability under change of these initial parameters to understand the structure of the solution and limitations of its applications, [5], [6]. In wireless ad-hoc networks which characterize limited power of energy, for example in sensor networks, the nodes most of their energy utilize for data transmission and extension of the network lifetime is achieved by designing energy efficient transmission protocols. Knowledge about stability of the exact solution of the maximum network lifetime problem allows to understand limitations of implemented transmission protocols in such networks.In the paper we are considering stability of a solution of the maximum network lifetime problem for a one-dimensional, regular ad-hoc wireless network with one data collector L N . The nodes of the regular network L N are located at the points x i = i, i ∈ [0, N ] of a half-line, where at the point x 0 = 0 there is located a data collector. We investigate stability of the solution under changes of two sets of...

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In the paper we analyze the maximum lifetime problem in sensor networks with limited channel capacity for multipoint-to-multipoint and broadcast data transmission services. We show, that in order to achieve an optimal data transmission regarding the maximum lifetime problem we cannot allow for any interference of signals. We propose a new Signal to Interference plus Noise Ratio function and used is to modify the Shannon-Hartley channel capacity formula. For the modified channel capacity formula we solve the maximum lifetime problem in one dimensional regular sensor network L N for discussed data transmission services.