Example: Machine Tool with Breakdowns

It is described in different sources [1, 2]. So, this is chapter 13 of [2] and section 6.12 of [1].

Jobs arrive to a machine tool on the average of one per hour. The distribution of 
these interarrival times is exponential. During normal operation, the jobs are 
processed on a first-in, first-out basis. The time to process a job in hours is 
normally distributed with a mean of 0.5 and a standard deviation of 0.1. In addition 
to the processing time, there is a set up time that is uniformly distributed between 
0.2 and 0.5 of an hour. Jobs that have been processed by the machine tool are routed 
to a different section of the shop and are considered to have left the machine tool 
area.

The machine tool experiences breakdowns during which time it can no longer process 
jobs. The time between breakdowns is normally distributed with a mean of 20 hours 
and a standard deviation of 2 hours. When a breakdown occurs, the job being processed 
is removed from the machine tool and is placed at the head of the queue of jobs 
waiting to be processed. Jobs preempted restart from the point at which they were 
interrupted.

When the machine tool breaks down, a repair process is initiated which is 
accomplished in three phases. Each phase is exponentially distributed with a mean of 
3/4 of an hour. Since the repair time is the sum of independent and identically 
distributed exponential random variables, the repair time is Erlang distributed. 
The machine tool is to be analyzed for 500 hours to obtain information on 
the utilization of the machine tool and the time required to process a job. 
Statistics are to be collected for thousand simulation runs.

[1] A. Alan B. Pritsker, Simulation with Visual SLAM and AweSim, 2nd ed.
[2] Труб И.И., Объектно-ориентированное моделирование на C++: Учебный курс. - СПб.: Питер, 2006