Stochastic Modelling of a Computer System with Hardware Redundancy

Abstract

this paper, an effort for the stochastic analysis of a computer system has been made considering the idea of hardware redundancy in cold standby. The hardware and software failures occur independently in the computer system with some probability. A single server is employed immediately to conduct hardware repair and software up- gradation on need basis. The repair and up-gradation activities performed by the server are perfect. The time to hardware and software failures follows negative exponential distribution, whereas the distributions of hardware repair and software up- gradation times are taken as arbitrary with different probability density functions. The expressions for various reliability measures are derived in steady state using semi- Markov process and regenerative point technique. The graphs are drawn for arbitrary values of the parameters to depict the behaviour of some important performance measures of the system model. up-gradation when needed. The repair and up-gradation activities performed by the server are perfect. The time to hardware and software failures follows negative exponential distribution while the distributions of hardware repair and software up-gradation times are taken as arbitrary with different probability density functions. The expressions for various reliability measures such as transition probabilities and mean sojourn times, mean time to system failure (MTSF), availability, busy period of the server due to hardware repair and software up-gradation, expected number of hardware repairs and software up-gradations and profit function are derived in steady state using semi-Markov process and regenerative point technique. The cost-benefit analysis has been made using these measures. The graphs are drawn for arbitrary values of the parameters to depict the behaviour of MTSF, availability and profit function of the system model.