Discrete Event Simulation

What's Next

The field of simulation is broadly divided into two main kinds of simulation models:

Continuous Simulation or Process Simulation
Discrete Event Simulation

So far, we've been doing Process Simulation. We will now be moving on to Discrete Event Simulation, though there is a great deal of overlap between the two. They both

Have state variables (like holding tanks) that capture the state of the system.
Build quantitative (mathematical) models of how state variables change over time and as a function of the current state variables
Use random number generators model variability and uncertainty. In particular, both kinds of simulation use both discrete distributions (such as the binomial) and continuous distributions (such as the Gaussian).

Discrete Event Simulation

So how is Discrete Event Simulation (DES) different from Process Simulation (PS)? There are two main differences:

The kind of things that the model is about:
- In PS, the state variables measure "amounts" of stuff, such as pollution levels or money or even kangaroos. (Remember, we didn't even bother to round off the number of kangaroos to an integer; we thought of them as continuous quantities.)
- In DES, the model is about entities that enter the system (or are created), move through it, and eventually exit. Some examples are customers coming into a store or bank, parts moving through a manufacturing system, data packets moving through a computer network and so forth).
The way that time moves forward:
- In PS, time moves forward in uniform-size steps. The person building the model chooses the step size so that it is short enough to capture the appropriate dynamics but not so short that it wastes time. In simple process simulation, you don't get to dynamically change the step size during a run.
- In DES, time moves forward in variable-size steps, depending on when the next event occurs. For example, if there are no customers in the store and no one enters the store for a while, nothing is changing so there's no reason to simulate anything.
- The movement of time can be contrasted graphically:

So, in a discrete event simulation, entities have "events" in their "lives" and the simulation is about the aggregate result of those events. The simulation moves from event to event.

Table of Differences

I think the following table is helpful. It's drawn from the Extend v6 manual:

Differences between CP and DES models
Factor	Continuous Modeling	Discrete Event Modeling
What is modeled	Flows of "stuff"	Discrete items or "things"
Characteristics	random number "simulates" characteristics of flows and must be repeated for each query or junction	Using attributes, unique characteristics are assigned to items whch can then be tracked throughout the model
Time Steps	Interval between time steps is constant. Model recalculations are sequential and time dependent.	Interval between events is dependent on when events occur. Model only recalculates when events occur
Ordering	Flows are in FIFO order	Items can flow in FIFO, LIFO, Priority or customized order
Routing	Flows need to be explicitly routed by being turned off at one branch and turned on at the other (flows can go to multiple places at the same time).	Items are automatically routed to the first available branch (items can only be in one place at a time).
Statistical detail	Only general statistics about the system: amount, efficiency, transit time	In addition to general statistics, each item can be tracked: count, utilization, cycle time.
Common Uses	science (biology, chemistry, physics), engineering (electronics, control systems), economics, system dynamics	manufacturing, service industries, business processes, computer networks, digital electronics

Mixing Blocks

Discrete event simulations work in a fundamentally different way. The use of a block from one of the discrete event libraries (either Discrete Event or Manufacturing) makes a model into a Discrete Event Simulation (DES) model. (Paradoxically, DE is often used to stand for Differential Equation, which is the basis for CP models. Don't let this confuse you!)

However, DES models certainly make use of blocks such as constants, random number generators, equations and other math blocks.

There are different connectors in the DES models. The connectors that are for the flow if items have concentric squares, while connectors for ordinary numerical values are just a single square.

The M/M/1 Queue

The classic example of a discrete event simulation is the so-called M/M/1 queue. This model encompasses any situation where:

There is a source of entities, such as customers coming into a shop. They arrive as a Poisson process, meaning that the inter-arrival times are exponentially distributed. The customers are homogenous, in that they all want the same kind of service, say haircuts or tax returns.
The service times are exponentially distributed. That is, most will have short service times, but some will need longer times. This is the less plausible assumption, but it's common.
There is one server.

We'll discuss what this means, in preparation for building such a model in Extend.

Attributes

Attributes are important, for distinguishing one kind of item from another and for recording information about those items. Here's an example of a bathroom simulation, using a "gender" attribute to distinguish men from women. This model doesn't have the different kinds of items come back together after, so the attribute is actuallly unnecessary once they are divided, but that need not be the case.

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