Diffusion Process For G/G/R Machining System With Spares, Balking and Reneging

This paper deals with the g/g/r machining system consisting of m operating machines as well as s cold standbys. the concepts of balking and reneging are incorporated which make our model more versatile to deal with real time systems. the broken-down machines are sent to repair facilities consisting of r permanent repairmen. the failure times and repair times are generally identical and independent distributed random variables. the failed machines are repaired according to fifo rules. by using a diffusion process, the steady-state probability density function for the queue size is obtained in terms of the first two moments of inter-arrival times and repair times of machines. some expressions in explicit form that characterize the system performance are also mentioned.