Unit 5.2
Discrete-Event Simulation
Entities, events, queues, and the clock that ties them together.
- Unit 5.1
- Unit 5.2
§ Overview
A discrete-event simulation (DES) models a system in which entities move through a process, competing for resources and waiting in queues. The state of the system changes only at discrete points in time, called events, and the simulation clock advances from one event to the next rather than in fixed steps.
This unit covers the vocabulary of discrete-event systems (entities, events, resources, queues), the mechanism that drives the simulation (event calendars and clock advancement), and the output analysis that distinguishes the initial transient from the steady state.
Lesson 1
Entities, events, resources, and queues
Lesson 2
Event calendars and clock advancement
Lesson 3
Output analysis and warm-up bias
Laboratory 10
Discrete-event simulation
§ Learning outcomes
By the end of Unit 5.2 you will be able to
- Identify the entities, events, resources, and queues in a discrete-event system.
- Design an event calendar and clock-advancement mechanism for a simple system.
- Implement a single-server queueing simulation in a spreadsheet.
- Distinguish transient from steady-state behaviour and identify a warm-up period.
- Apply replication with independent seeds to estimate steady-state performance measures.
- Report simulation results with appropriate output analysis.
§ Lessons
Entities, events, resources, and queues
The vocabulary of discrete-event systems. Every DES is described in terms of these four concepts.
Lesson 2Event calendars and clock advancement
The mechanism that makes a discrete-event simulation a simulation. Without it, there is no DES.
Lesson 3Output analysis and warm-up bias
Separate transient from steady-state behaviour before reporting results.
§ The event-clock mechanism
A discrete-event simulation maintains an event calendar (also called a future-events list or event queue): a list of pending events, each with a timestamp. The simulation loop is:
- Remove the event with the earliest timestamp from the calendar.
- Advance the simulation clock to that timestamp.
- Process the event: update system state, and possibly schedule new events.
- Repeat until the calendar is empty or the clock exceeds the termination time.
The clock advances irregularly, skipping from one event timestamp to the next. There may be long idle periods between events, and the simulation does not spend time on them.
No event calendar, no DES
A simulation that advances the clock in fixed steps and processes state changes at those steps is not a discrete-event simulation. The defining feature of DES is the event calendar: the model decides which event happens next, and the clock advances to that event's time.
§ Output analysis
A discrete-event simulation typically begins in an artificial state (empty system, no customers) and runs until a termination condition. The initial portion of the run is not representative of the steady state the model is usually meant to describe. Analysing output without accounting for this warm-up bias produces misleading results.
Two standard approaches to output analysis:
-
Warm-up removal. Run a single long simulation,
discard the first
Wtime units as warm-up, and compute statistics over the remaining period. Simple, but wastes the discarded portion. -
Replication with warm-up. Run
Rindependent replications, each starting in the same initial state, each discarding the firstWtime units. Compute the performance measure in each replication, then average across replications. More computation, but provides valid standard errors.
Choosing the warm-up period
There is no universal rule for choosing W. A common
approach is to plot the cumulative-average performance measure over
time and identify the point at which the curve stabilises. The
warm-up period is at least that long.
§ Key terms
- Entity
- An object that moves through the system, receives service, and eventually departs. In a queueing model, the entities are usually customers, jobs, or patients.
- Event
- A point in time at which the state of the system changes. Arrival events create entities; departure events remove them.
- Resource
- A facility that serves entities. A resource has a capacity: the number of entities it can serve simultaneously.
- Queue
- A waiting line for a resource. Entities that arrive when the resource is busy join the queue and wait for their turn.
- Event calendar
- The list of pending events, ordered by their scheduled time. The simulation always processes the earliest event next.
- Simulation clock
- A variable holding the current simulated time. It advances to the timestamp of the next event.
- Warm-up period
- The initial portion of a simulation run that is discarded to remove transient bias before computing steady-state statistics.
- Steady state
- The condition in which the system's probability distribution no longer changes with time. The long-run behaviour of the model.
§ Self-check
Check your understanding
Question 1
In a discrete-event simulation, the clock advances:
Show answer
From one event to the next.
Question 2
Entities in a queueing model typically represent:
Show answer
Customers, jobs, or patients.
Question 3
The event calendar is:
Show answer
A list of pending events ordered by scheduled time.
Question 4
Warm-up bias occurs because:
Show answer
The initial state is not representative of steady state. Discarding the warm-up period removes this bias.
Question 5
Replication with warm-up refers to:
Show answer
Running many independent simulations, each with a warm-up period. This provides valid standard errors across replications.