Discrete event simulation Totally Explained

Everything about Discrete Event Simulation totally explained

In discrete-event simulation, the operation of a system is represented as a chronological sequence of events. Each event occurs at an instant in time and marks a change of state in the system . For example, if an elevator is simulated, an event could be "level 6 button pressed", with the resulting system state of "lift moving" and eventually (unless one chooses to simulate the failure of the lift) "lift at level 6". A common exercise in learning how to build discrete-event simulations is to model a queue, such as customers arriving at a bank to be served by a teller. In this example, the system entities are CUSTOMER-QUEUE and TELLERS. The system events are CUSTOMER-ARRIVAL and CUSTOMER-DEPARTURE. (The event of TELLER-BEGINS-SERVICE can be part of the logic of the arrival and departure events.) The system states, which are changed by these events, are NUMBER-OF-CUSTOMERS-IN-THE-QUEUE (an integer from 0 to n) and TELLER-STATUS (busy or idle). The random variables that need to be characterized to model this system stochastically are CUSTOMER-INTERARRIVAL-TIME and TELLER-SERVICE-TIME.
A number of mechanisms have been proposed for carrying out discrete-event simulation, among them are the event-based, activity-based, process-based and three-phase approaches (Pidd, 1998). The three-phase approach is used by a number of commercial simulation software packages, but from the user's point of view, the specifics of the underlying simulation method are generally hidden.

Components of a Discrete-Event Simulation

In addition to the representation of system state variables and the logic of what happens when system events occur, discrete event simulations include the following:

Clock

The simulation must keep track of the current simulation time, in whatever measurement units are suitable for the system being modeled. In discrete-event simulations, as opposed to real time simulations, time ‘hops’ because events are instantaneous – the clock skips to the next event start time as the simulation proceeds.

Events List

The simulation maintains at least one list of simulation events. An event must have a start time, some kind of code that constitutes the performance of the event itself, and possibly an end time. In some approaches, there are separate lists for current and future events. Events in their lists are sorted by event start time. Typically, events are “bootstrapped” – that is, they're scheduled dynamically as the simulation proceeds. For example, in the bank example noted above, the event CUSTOMER-ARRIVAL at time t would, if the CUSTOMER_QUEUE was empty and TELLER was idle, include the creation of the subsequent event CUSTOMER-DEPARTURE to occur at time t+s, where s is a number generated from the SERVICE-TIME distribution.

Random-Number Generators

The simulation needs to generate random variables of various kinds, depending on the system model. This is accomplished by one or more pseudorandom-number generators. The use of pseudorandom numbers as opposed to true random numbers is a benefit should a simulation need a rerun with exactly the same behaviour.

Statistics

The simulation typically keeps track of the system's statistics, which quantify the aspects of interest. In the bank example, it's of interest to track the mean service times.

Ending Condition

Because events are bootstrapped, theoretically a discrete-event simulation could run forever. So the simulation designer must decide when the simulation will end. Typical choices are “at time t” or “after processing n number of events” or, more generally, “when statistical measure X reaches the value x”.

Simulation Engine Logic

The main loop of a discrete-event simulation will be something like this:

Start

Initialize Ending Condition to FALSE.
Initialize system state variables.
Initialize Clock (usually starts at simulation time zero).
Schedule an initial event (for example, put some initial event into the Events List).

“Do loop” or “While loop”

While (Ending Condition is FALSE) then do the following:

Set clock to next event time.

Do next event and remove from the Events List.

Update statistics.

End

Generate statistical report.Further Information

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