Combining deterministic and non-deterministic processes
1. Combining deterministic and non-deterministic processes
Let's bring it all together by building an event-based model for a dynamic system that contains both deterministic and non-deterministic processes.2. Deterministic and non-deterministic processes
There are many examples of dynamic systems that involve a sequence of deterministic and non-deterministic processes. Imagine the management of passenger flow in airports. The arrival time of a particular passenger to the airport cannot be predicted deterministically, but the transport of luggage inside the airport is more predictable once the luggage has been checked in. Other examples include assembly lines in factories, lifts, and others. Let's explore the example of an assembly line in a factory.3. Example: Assembly line in a factory
Factory assembly lines consist of a sequence of automated and less automated steps. On the left, there's a list of processes that are often deterministic because their duration is more predictable. For example, the time a welding machine takes to join two metal pieces may depend only on the length of the welding line. On the right are examples of non-deterministic processes. For example, the time it takes between ordering and receiving raw materials may vary. The manual assembly of complex parts in a factory may also vary. The chart shows the duration of a manual assembly task on different occurrences. It took an average of 100 hours to complete, but it varied by about 15 hours. Let's work through an example. We will start with the deterministic processes and use the example of the assembly line with welding steps.4. Deterministic processes
Let's consider that this assembly line involves two deterministic processes, welding_1 and welding_2. welding_1 is named "Welding component A" and always takes five hours to complete. welding_2 is named "Welding component B" and the processing time depends on the length of the welding line, represented by the variable "length". Notice on the right how we can create a dictionary for each process to cleanly store all the information we need to build the model. Next, let's look at non-deterministic processes.5. Non-deterministic processes
Let's consider that the assembly line also includes two non-deterministic processes, manual_assembly_1 and manual_assembly_2. manual_assembly_1 takes an average of 80 hours to complete with a standard deviation of five hours. manual_assembly_2 takes an average of 20 hours to complete with a standard deviation of two hours. Notice also on the right how we can create a dictionary for each process to cleanly store all the information we need to build the model. Let's now put all processes together.6. Build an event-based simulation
The diagram summarizes the various processes that will be included in the model, which we introduced in the previous slides. First, we need to initialize a time-tracking variable; we named it "time". Second, we need to chronologically add all processes of the assembly line. Notice how using dictionaries allows us to cleanly write the core of our model. We can adjust the properties of our dynamic system by changing the information in the dictionaries.7. Time units and exploring model
Before we start exploring the model, it's important to make sure the time units are consistent for all processes. Now, let's explore the model. Note that because we have non-deterministic processes in our model, every time we run a simulation, we'll have slightly different results. So, as the chart shows, there are various possible outcomes for our dynamic system. Notice that process welding_1, which is deterministic, always takes ten hours to complete. However, the subsequent manual_assembly_1 and manual_assembly_2 are non-deterministic, and so the processing time of the assembly line will start to vary.8. Let's practice!
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