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This article analyzes a network of servers that cover mobile phone calls in a given convex service area. All servers work with the same reliability, and can cover all call requests within a circle of the same given radius. When working servers cover the whole area, the network system is working. System reliability is the probability that working servers can cover the whole area. Without loss of generality, we assume that each server's location, coverage radius, and reliability are known. Monte Carlo and Voronoi diagram methods are used to check the system state, and a binary search method is proposed to obtain the system reliability. Also, a simulation method is used to evaluate system reliability in special cases. Finally, numerical examples are studied to investigate the effects of the model parameters on system reliability.
Feng et al. (Mon,) studied this question.