In this paper, we consider two types of power consumption control policies for the long lifetime of wireless sensor node based on the discrete-time Geo/G/1 queue. One is the max(N, D)-policy, which triggers transmission mode of radio server when the N and D policies are met simultaneously, and another is the min (N, D)-policy, which restarts transmission function of radio server when either of the N and D policies is first satisfied. Under two control policies, the steady-state queueing analysis of sensor node is mathematically carried out. The mean queueing measures of sensor node, such as the mean number of data packets, mean transmission time backlog, mean waiting time, mean busy period, mean busy cycle period, and so on, are derived. Two power consumption functions are constructed through the queueing measures obtained. Numerical experiments validate that two policies are feasible and efficient for power consumption control of sensor node. At a minimum power consumption, the superiority of the N-policy, D-policy, and two dyadic (N, D) policies is numerically compared. Some practical insights on the operation of two (N, D) polices in power consumption control of sensor node are obtained.

This paper introduces finite vacations from a reliability theory viewpoint and deals with a one-unit repairable system with a repairman who takes finite vacations. A total probability decomposition method for analyzing the reliability problems of the system is presented with the help of the renewal process theory. With the decomposition method, two key reliability characteristics of the system i.e. the availability and mean failure number of the system are discussed under some assumptions. It is important that the steady-state availability and steady-state failure frequency of the system are obtained. Furthermore, three special cases of the model have showed that the vacation number taken by the repairman affects the performance of the system and the results presented in this paper are more general than the existing results in some literatures.

This paper examines a discrete‐time modified D‐policy Geo/G/1 queue with Bernoulli feedback. Using a decomposition method, the steady‐state system size distribution at epoch n⁺ is obtained. Moreover, the steady‐state system size distributions at epochs n⁻ and n are also derived. Two special cases are given. Finally, a wireless local area network is numerically presented to validate the applicability of steady‐state system size distribution and its important application in system capacity design.