Queueing modelling of machining system with balking, reneging, additional repairmen and two modes of failure

Abstract EN

To improve the system reliability, the provision of spare part support is recommended in machining system.

In this paper, we study M/M/R machine repair problem (MRP) with balking, reneging and additional repairmen.

The units are assumed to fail in two modes with equal probability for each mode.

There is provision of S standby units in the system to improve the system reliability/ availability.

When a unit breaks down, it is replaced by a spare unit if available.

The failed unit is repaired by a repair facility consisting of R permanent and r additional repairmen.

If the number of failed units is more than the number of repairmen then the failed unit will not get repair immediately.

In such circumchance, it may balk or renege.

The machine repair problem is formulated as birth- death process and the steady state queue size distribution is obtained in product form.

Some performance measures such as expected number of failed units, expected number of spare units and machine availability etc.

are obtained.

The expected total cost per unit time has also been facilitated.