Stochastic Model of a Cold-Stand by System with Waiting for Arrival & Treatment of Server

The service facility or server is the key constituent to keep a system operational for desired period of time. As any eventuality with the system necessitates immediate presence of it (server) so the time point of arrival and treatment of server significantly affects the system performance. This paper works out the steady state behavior of a cold standby system equipped with two similar units and a server with elapsed arrival and treatment times following general probability distributions. It practices the theory of semi-Markov processes, regenerative point technique and Laplace transforms to derive the expressions for state transition probabilities, mean sojourn times, mean time to system failure, system availability, server busy period and expected frequencies of repairs and treatments. The profit function is also developed taking different costs and revenue in to account. For tracing wider applicability of the model for different reliability and cost-effective systems, a particular case study is also presented as an illustration.