23-Ind-A6 Systems Simulation · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2017 — 98-Ind-A6 Systems Simulation. Three-hour, closed-book exam; one of two permitted calculators (Sharp or Casio), two 8.5″×11.0″ aid sheets (both sides). Format: eight questions of equal value (10 marks each); candidates complete SIX of the EIGHT (only the first six as they appear in the answer book are marked). All eight questions are solved below for completeness (the paper's own Q6 is printed with an orphan leading "6." followed by "2. Consider an M/M/1 system…" and is answered as the paper's sixth question). Common Discrete/Continuous Distribution tables, Student-t and Chi-square tables were supplied with the exam; the values below are the same table values obtained by direct computation.
Reference texts: Banks, Carson, Nelson & Nicol, Discrete-Event System Simulation (5th ed., Pearson) — random-number/random-variate generation, input data analysis, output analysis (replications), comparing alternative systems, queueing simulation, and the simulation study life cycle.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Given. Five independent short-answer prompts spanning simulation-output-analysis strategy, random-number generation, and V&V terminology.
Find. A 1–3 line answer to each of (a)–(e).
(a) A terminating-simulation example. A retail bank branch that opens empty at 9:00 a.m. and closes at 5:00 p.m.: simulate exactly one business day, from the well-defined initial state (empty, idle) to the well-defined terminating event $E$ (closing time). It is appropriate as a terminating (finite-horizon) model because a specific event unambiguously ends the run and the initial condition is itself the state management cares about — there is no long-run steady state to reach, only that one day's transient performance.
(b) Replication/Deletion advantage over Batch Means. Because each replication uses an independent random-number stream, the $R$ replication means are a genuine i.i.d. sample, so a standard $t$-based confidence interval is valid immediately — Batch Means instead works within one long run, where adjacent batch means can remain autocorrelated unless batch size is large, risking an artificially narrow (overconfident) interval unless independence is explicitly checked.
(c) LCG random numbers. Using $X_{n+1} = (aX_n + c) \bmod m$ with $X_0=27,\ a=10,\ c=10,\ m=64$:
(d) Verification vs. validation. Verification is "building the model right": confirming the computer program correctly implements the intended conceptual/logical model (debugging, structured walkthroughs, tracing against hand-computed test cases) — a purely internal correctness check. Validation is "building the right model": confirming the model as a whole is an accurate representation of the real system for its intended purpose, checked by comparing model output against real-world data or expert/face judgment — an external fidelity check.
(e) Poor majorizing function in Acceptance-Rejection. If the majorizing function $c\,g(x) \ge f(x)$ is a loose envelope (the constant $c$ is far larger than necessary because $g$ does not hug $f$ closely), the acceptance probability $1/c$ is small, so a large fraction of candidate variates are rejected. This is purely an efficiency penalty — many more uniform draws and candidate evaluations are needed per accepted variate, slowing the simulation — not a bias or correctness problem.
| Sub-part | Result |
|---|---|
| (c) first two LCG draws | $X_1=24 \Rightarrow U_1=0.375$; $X_2=58 \Rightarrow U_2=0.90625$ |
