| The target of this research is to investigate stochastically a class of security, reliability and disaster recovery systems, which are based on a closed single-channel queueing model. These stochastic security systems include a repair facility and three types of “unreliable” machines: the main facility (internal resources) of working and reserve machines, and an auxiliary facility of “super-reserve” machines (also called external resources); working machines break down exponentially and they are immediately replaced by reserve machines available. Defective machines line up for repair, whose duration is arbitrarily distributed. Refurbished machines return to the main facility. If the main facility is restored to its original quantity, the repair facility leaves on routine maintenance and auxiliary machines are being used for back-ups. These kinds of security systems provide terms for retraining internal resources and maintenance of a repair facility by utilizing external resources to improve reliability and availability in security respects. In addition, decision making points ate added to control the usage of super-reserve machines in further embellishments. These unique systems are applicable in real-world applications such as computer networking, human resources, and manufacturing processes.; The techniques in this research include two-variate Markov and semi-regenerative processes, and a duality principle to find the probability distribution of the number of intact machines. Explicit formulas obtained demonstrate a relatively effortless use of functionals of the main stochastic characteristics (such as expenses due to repair, maintenance, waiting, and rewards for higher reliability) and optimization of their objective function. |
