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