MATH 4810Computational Modelling

Module 05 · Capstone Project

A Discrete-Event Queueing Simulation

Build a working discrete-event simulation of a queueing system, complete with an event calendar, clock advancement, warm-up analysis, replication, and reported confidence intervals.

Weight Counts toward the module component of the course grade Duration ≈ 14 hours Prerequisite Units 5.1 and 5.2

Module 5 capstone

A Discrete-Event Queueing Simulation

Specify, implement, verify, and report a discrete-event simulation of a queueing system.

§ Project brief

The Module 5 capstone is a complete discrete-event simulation of a queueing system. You will specify the system using the four-concept vocabulary (entities, events, resources, queues), implement an event calendar and clock-advancement mechanism, run the simulation with replication, apply warm-up removal, and report performance measures with confidence intervals.

Optionally, you may also build a Markov-chain model of the same system or a related one, and compare the two approaches. This is encouraged but not required.

Output analysis is not optional

A discrete-event simulation without warm-up removal and replication produces a number of uncertain provenance. The output analysis is the deliverable.

§ Learning outcomes addressed

This capstone assesses

  • Specify a discrete-event system in the four-concept vocabulary.
  • Implement an event calendar and clock-advancement mechanism.
  • Verify against an analytical result where available.
  • Identify the warm-up period and discard it.
  • Run independent replications and construct confidence intervals.
  • Report performance measures with appropriate output analysis.

§ Suggested systems

System A

M/M/1 queue

Single server, Poisson arrivals, exponential service. Analytical results available for verification.

System B

M/M/c queue

Multi-server system. Analytical results available for utilisation and mean wait.

System C

Priority queue

Two or three priority classes. No closed-form solution; verification uses conservation and comparison to a simple case.

System D

Two-stage service

Entities pass through two sequential stages. Queue length at stage 2 depends on the output of stage 1.

§ Deliverables

Deliverables and weights
Deliverable Weight What it should contain
System specification 15% Entities, events, resources, queues, arrival process, service process, routing, termination.
Event calendar implementation 20% Working event calendar and clock advancement. Hand trace of the first few events.
Verification 15% Conservation check (arrivals = departures at termination). Comparison against analytical M/M/1 or M/M/c where applicable.
Warm-up analysis 15% Running-mean plot. Identification of warm-up period. Sensitivity to the chosen period.
Replication and confidence intervals 20% 20+ replications. Mean, SE, and 95% CI for the primary performance measure.
Technical report 15% Three to five pages including specification, implementation, verification, output analysis, and limitations.

§ Milestones

  1. Specify the system Four-concept vocabulary, full specification. Two hours.
  2. Implement the event calendar Priority queue, clock advancement, event handlers. Four hours.
  3. Hand-trace the first few events Compare to a spreadsheet run. Two hours.
  4. Verify conservation and analytical agreement Arrival/departure count; comparison to M/M/1 if applicable. Two hours.
  5. Run the warm-up study Plot the running mean; choose W. One hour.
  6. Run replications 20+ replications with independent seeds; compute mean, SE, CI. Two hours.
  7. Write the report Three to five pages. One hour.

§ Rubric

Assessment criteria
Criterion Excellent Satisfactory Needs work
Specification Every element stated; disciplines and routing justified. Every element stated, but justifications thin. Elements missing or vague.
Implementation Event calendar correct; hand trace matches spreadsheet. Event calendar correct; hand trace approximate. Hand trace missing or does not match.
Verification Conservation check passes; analytical agreement within CI. Conservation check passes; analytical agreement approximate. Verification not performed.
Warm-up Warm-up identified from running-mean plot; sensitivity shown. Warm-up identified but not verified. No warm-up removal.
Replication 20+ replications; CI reported and interpreted. 10–20 replications; CI reported. Fewer than 10 replications or no CI.

§ Common pitfalls

Watch for these

  • Scheduling events in the past. If a scheduled time precedes the current clock, the simulation is broken.
  • Not removing warm-up. The initial transient biases congestion-related measures downward.
  • Using the same seed for all replications. Replications must be independent.
  • Reporting the point estimate without the CI. The CI is part of the result.
  • Confusing simulation precision with model validity. A narrow CI does not imply a correct model.

§ Submission

What to submit

  • A single ZIP archive named M5-capstone-yourid.zip.
  • The archive contains the specification, the simulation code or spreadsheet, the hand trace, the verification evidence, the warm-up study, the replication results, and the technical report.
  • Submit through the course LMS before the deadline listed on the course schedule.
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