In many real systems in which a state variable should be controlled for being in appropriate range, the length of control (review) intervals is taken to be constant. In such systems, when the cost of reviews and out-of-range values of the state variable are considerable, this method may not be optimal. In this paper we let the length of review intervals to be variable during each operating cycle and construct the related mathematical cost model. Then two scheduled review methods, called U2 and U3, are introduced and the relative annual system costs are analyzed. The model is developed for the case of negative exponential variate as the time between successive consumption Points. It is shown that the new methods results a significant reduction in the expected annual cost of the system.

Workspace analysis is one of the most important issues in the robotic parallel manipulator design. However, the unidirectional constraint imposed by cables causes this analysis more challenging in the cable driven redundant parallel manipulators. Controllable workspace is one of the general workspace in the cable driven redundant parallel manipulators due to the dependency on geometry parameters in the cable driven redundant parallel manipulators. In this paper, a novel tool is presented based on interval analysis for determination of the boundaries and proper assessment of the enclosed region of Controllable workspace of cable-driven redundant parallel manipulators. This algorithm utilizes the fundamental wrench interpretation to analyze the Controllable workspace of cable driven redundant parallel manipulators. Fundamental wrench is the newly definitions that opens new horizons for physical interpretation of Controllable workspace of general cable driven redundant parallel manipulators. Finally, the proposed method is implemented on a spatial cable driven redundant manipulator of interest.

This investigation proposes Markov chain analysis of Controllable multi-server queue with balking. We incorporate an additional server which is added and removed at pre-specified threshold levels of queue size to control the balking behaviour of the customers. The steady state equations are constructed by assuming interdependent arrival and service processes which are characterized by bivariate Poisson distribution. Recursive approach is employed to establish the queue size distribution, which is further used to determine various performance indices.