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In this paper we consider task scheduling when sensing and controlling over a network with packet dropping links. We find optimum ways of allocating limited computing resources for estimation and control of a number of linear dynamical systems with different characteristics over communication links with different qualities. We find theoretical expressions relating the optimum sampling rates to the characteristics of the communication links and dynamics of the plants.When considering resource allocation for estimation of the plants, we derive optimum ways of task scheduling for two performance metrics: decay rate and the asymptotic value of the estimation error variance. When scheduling the control tasks, we consider rate of convergence of the state and the overall control cost as performance measures. The work lays the theoretical foundations for considering the impact of both limited computing and communication resources on estimation and control.