A model of a factory
The factory produces produces objects of type 1 and type 2 from pieces of raw material which are readily available without limit. For the projection of an object of type 1, a piece of raw material is first processed by a machine of type A, then by a machine of type B, and finally by a machine of type C. For this purpose, a piece of raw material is first placed on a robotized moving platform which transports the piece from one machine to the other and finally deposits the finished product in a storage area. The factory owns 15 moving platforms. The production of objects of type 1 is done as fast as possible, since there appears to be an unlimited demand for such objects. Here is some information about the machines and how they are accessed by the moving platforms:
* There are 3 machines of type A and the platforms with raw material wait in a single queue until one of the machines becomes available.
* There are also 3 machines of type B, but they have separate queues (one per machine), since the machines are located far away from one another within the factory. When an object has been processed by a machine of type A, one of the machines of type B will be selected randomly for the subsequent processing.
* There is a signle machines of type C, with a single waiting queue. The storage area is large and several moving platforms may access it at the same time.
The production of objects of type 2 is done on demand. The production of these objects has priority over the production of objects of type 1, since the factory makes more profit from the production of an object of type 2. The production of objects of type 2 proceeds similar as for objects of type 1, except that the object does not need to be processed by a machine of type B; the platform takes the object directly from the machine of type A to the machine of type C. The arrivals of requests for the production of an object of type 2 arrive randomly with an inter-arrival time uniformly distributed over 5
