On the heterogeneous machine interference with limited server's availability

In this paper three models are developed for the heterogeneous machine interference problem where the occurrence of ancillary duty makes the operator non-available for repair activities. The machines are supposed to be stochastically different, the i-th machine is characterized by exponentially distributed running time with parameter λ −1 i and exponentially distributed required repair time with mean 1/μ i . The ancillary duty which has preemptive priority over the machines arises randomly being governed by exponential law with rate depending on the operator's state, i.e., whether he is busy or idle. The time taken to complete an ancillary duty is assumed to be an exponentially distributed random variable. The machines are repaired according to first-in, first-out (FIFO), priority processor sharing (PPS) and preemptive resume priority (PR) service disciplines. The aim of the present paper is to give the main steady-state characteristics of the system, such as operative utilization, mean length of busy period, average number of machines not in working order, machine productivity and duration of time while the machines are failing. In addition some optimization problems are treated. Finally, numerical examples illustrate the problem in question.