Modeling of multi-server repair problem with switching failure and reboot delay and related profit analysis

• We model a standby system with switching failure, reboot delay and repair pressure.
• Steady-state probabilities are developed in terms of matrix forms.
• A profit model is given to search the optimal parameters using an efficient approach.
• Some managerial insights are derived from an application example.

This study examines a warm-standby machine repair problem which involves a switching failure probability, reboot delay and a repair pressure coefficient. The machine repair problem has M operating machines with W warm standbys and R repairpersons. When all repairpersons are busy and waiting line is very long (heavy loading), the repairpersons increase their repair rate to reduce the queue length because of the pressure. This phenomenon is very common in many realistic service systems. A matrix-analytic method is adopted to develop a function of the steady-state expected profit per unit time. The probabilistic global search Lausanne (PGSL) method is employed to determine the joint optimal parameter values that maximize the profit and satisfy the availability constraint. Some numerical results of various system performance measures under optimal operating conditions are presented. Finally, several managerial insights are provided by demonstrating an example of the application to assist system analysts for decision making.