This is a model of the soaking pit furnace. It is described in different sources [1, 2].
[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
Steel ingots arrive at a soaking pit furnace in a steel plant with
an interarrival time that is exponentially distributed with mean
of 2.25 hours. The soaking pit furnace heats an ingot so that it
can be economically rolled in the next stage of the process.
The temperature change of an ingot in the soaking pit furnace is
described by the following differential equation.
d(h_i)/dt = (H - h_i) * C_i,
where h_i is the temperature of the i-th ingot in the soaking pit;
C_i is the heating time coefficient of an ingot and is equal to X + 0.1
where X is normally distributed with mean of 0.05 and standard deviation
of 0.01; and H is the furnace temperature which is heated toward 2600 F
with a heating rate constant if 0.2, that is,
dH/dt = (2600 - H) * 0.2.
The ingots interact with one another in that adding a "cold" ingot
to the furnace reduces the temperature of the furnace and thus changes
the heating time for all ingots in the furnace. The temperature reduction
is equal to the difference between furnace and ingot temperatures, divided
by the number of ingots in the furnace. There are 10 soaking pits in
the furnace. When a new ingot arrives and the furnace is full, it is
stored in an ingot storage bank. It is assumed that the initial temperature
of an arriving ingot is uniformly distributed in the interval from 400 to 500 F.
All ingots put in the ingot storage bank are assumed to have a temperature of
400 F upon insertion into the soaking pit. The operating policy of the company
is to continue heating the ingots in the furnace until one or more ingots
reach 2200 F. At such a time all ingots with a temperature greater than 2000 F
are removed. The initial conditions are that there are six ingots in the furnace
with initial temperatures of 550, 600, 650, 700, 750 and 800 F. Initially,
the temperature of the furnace is 1650 F, and the next ingot is due to arrive
at time 0.
The objective is to simulate the above system for 500 hours to obtain
estimates of the following quantities:
1) heating time of the ingots;
2) final temperature distribution of the ingots;
3) waiting time of the ingots in the ingot storage bank; and
4) utilization of the soaking pit furnace.