Delay
A delay is a period of time during which an element of a system must wait for something to happen. Delays are an important part of systems design partly because they define the timing of the interactions, and partly because they allow designers to construct more realistic systems models.
When I Use My Credit Card
Pay checks are automatically deposited into a bank account. Because pay checks are only issued every two weeks, there is a delay on the input of these funds. In addition it takes two days for the pay check to move through the bank's automatic depository systems. 
The credit card company sends a statement on the 25th day of every month. The statement takes up to seven days to arrive in my mailbox at home.
I log on to the bank's website and authorize my account to pay a certain amount to the account of the credit card company. There is a one day delay while the payment is sent and the biller's automated system accepts payment.
(Note: The @ sign on a delay means that the event happens periodically on a regular basis. The ~ sign means that the time shown is approximate.)
Delays increase the uncertainty of a system. This happens because while you know that a pay check that has been sent will arrive sometime within the next two days, you cannot specify exactly when it will arrive. This is annoying, but it is real.
When there are multiple delays in a system, it can be impossible to exactly predict the system's behavior.
Factory Production
This diagram describes a factory production unit. Controls monitor the ordering and production processes, and delays are involved in shipping. While this is a more complicated diagram than any presented so far, it is still simple compared to real world industrial systems designs.
A factory requires supplies of two materials in order to fabricate its product. Finished products are stored in a warehouse from which the company's sales division ships orders out to customers.
The factory keeps track of the amount of each material that it has on hand. If the supply falls below a certain amount, the factory issues an order to the supplier and more material is shipped.
The warehouse can only hold so many units of the product. If the warehouse becomes too full, it issues an order to the factory to stop production. If the warehouse becomes too empty, it issues an order to increase production.
Supplier A promises that orders will arrive within one week. Supplier B promises delivery within two weeks. Since both supplies are needed by the factory, either B will have to be ordered on an earlier schedule, or larger supplies of B will need to be stockpiled at the factory. (Or a new supplier will need to be found. Delivery time is a key component in the sales operation of many companies.)
Because it takes more than a week to restart the factory, the company will want to pay close attention to the relationship between sales and production. The size of the warehouse is also important. A larger warehouse would cost more to maintain, but it would reduce the number of factory restarts.
Most of the earlier systems examples had behaviors that were easy to graph. This one does not. Production will be steady as long as the supplies of A and B are steady, but a late delivery will reduce production. The warehouse serves to level out the flow of items from the factory to the customers, but decreases in sales can also interrupt production. We could graph the number of items shipped over time, but this would not really tell us much about the system. A careful study would require attention to A and B shipping, the reorder process, the factory production time, the warehouse capacity, factory shut-down and start-up time, and sales. Any of these might be improved to increase the profitability of the operation.
Remember This
Control loops and delays are essential to describing most real world systems.
Home - Diagramming Topics - Next: Prediction