STATS320: pass the exams, not just read the notes
Your complete guide to University of Auckland's applied stochastic modelling course. See where the marks are, work real practice questions, and study with an AI tutor that knows STATS320.
Sia generates STATS320 practice questions, walks through stochastic models and review of probability foundations step by step, and quizzes you on the material the exam weights most heavily.
Worked example
Customers arrive at a single-server queue as a Poisson process at 12 per hour, and service takes an average of 4 minutes. What is the long-run utilisation, and is the queue stable?
Put both rates in the same units. Arrivals are 12 per hour. Service takes 4 minutes on average, so the server completes 60 divided by 4, that is 15 customers per hour.
Apply the stability condition. A single-server queue is stable when utilisation is strictly below 1, because work arrives more slowly than it can be cleared. Here 0.8 is below 1, so the queue is stable and reaches a steady state.
Note how close stable sits to unusable. At utilisation 0.8 the queue is stable, but expected queue length grows sharply as utilisation approaches 1 — it is proportional to utilisation divided by one minus utilisation. That non-linearity is the practical lesson of queueing theory, and it is why systems running at 95% utilisation feel broken while remaining technically stable.
The trap: Inverting the ratio, which gives option B's 1.25 and reverses the conclusion. Keeping rates rather than times in both numerator and denominator prevents it. Option C confuses stability with congestion — a stable queue still has waiting. classic slip!
One exam decides 65% of your grade. At least 40% required in this component to pass. This whole page is built around that.
Overview
What STATS320 is, and where it sits
STATS 320 is where the probability machinery built in STATS 125 and the inference theory from STATS 210 are turned on real systems. the description states it concentrates on stochastic methods used in operations research, biology and related fields, covering the construction, analysis and simulation of stochastic models together with some optimisation questions connected with them.
The published topic list is specific: the Poisson process, birth and death processes, queueing theory, simulation, random number generation, variance reduction, and optimisation. That sequence moves from describing random arrivals, through modelling populations and service systems, to simulating them when the mathematics becomes intractable.
The department states the course is valuable for students in Business, Economics, Statistics, Mathematics, Computer Science and the Biological Sciences — unusually broad, and it reflects that queues, populations and simulated systems appear in all of them.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is STATS320 hard, and how much time does it take?
STATS320 is manageable if you keep a weekly rhythm and treat the back half as the main event. The pattern is consistent: it starts gently and steepens, and the heaviest assessment is the part that separates grades.
The difficulty curve and the assessment weighting point the same way: the back half is harder and worth more. Front-loading effort there is the highest-return decision in the course.
Is this course for you
Who tends to do well, and who tends to struggle
You will likely do well if
- Your STATS 125 and 210 material is solid; this course assumes both without revisiting them.
- You can move between a described system and its mathematical model in both directions.
- You practise simulation by writing and running it, not by reading about it.
- You prepare thoroughly for the final, which carries at least 65% under either option.
You may struggle if
- You expect the term test to protect you; the alternative weighting simply removes it and raises the examination.
- You treat queueing formulas as recall items rather than consequences of the balance equations.
- You skip random number generation as a technicality, when it underpins the entire simulation half.
- You confuse stability with good performance — a queue at 0.95 utilisation is stable and unusable.
- For every process, state its assumptions and what breaks when they fail. Memorylessness is the one most often assumed silently.
- Derive the single-server results from balance equations once rather than memorising them; everything else in queueing follows the same pattern.
- Implement one simulation end to end, including the variance reduction step, so the theory has something concrete underneath it.
- Work past examinations under time; with 65% or more of the grade there, examination technique is the highest-return preparation.
Syllabus
The 11 topics, topic by topic
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Stochastic models and their construction
Course descriptionWhat makes a model stochastic, and how one is built from a described system.
T2 · Review of probability foundations
Prerequisite chain from STATS 125The distributional tools the course assumes from the outset.
T3 · The Poisson process
Course descriptionRandom arrivals in continuous time, and the properties that make the Poisson process tractable.
T4 · Interarrival and waiting times
Standard stochastic processes canonThe exponential distribution and the memoryless property behind it.
T5 · Birth and death processes
Course descriptionContinuous-time chains where the state moves up or down by one.
T6 · Queueing theory: single-server systems
Course descriptionThe single-server queue and its long-run behaviour.
T7 · Queueing theory: multi-server and networks
Course descriptionExtending to several servers and connected systems.
T8 · Random number generation
Course descriptionGenerating variates from a required distribution, the foundation of simulation.
T9 · Simulation of stochastic models
Course descriptionBuilding a simulation when the analysis is intractable, and reading its output correctly.
T10 · Variance reduction
Course descriptionGetting a more precise answer from the same simulation effort.
T11 · Optimisation of stochastic systems
Course descriptionThe optimisation questions connected with these models.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Final examination | 65% | Final examination covering the whole course. Examination period. At least 40% required in this component to pass. |
| Assignments | 25% | Assignments across the semester. Across the semester. Continual assessment. |
| Term test | 10% | Term test. Mid-semester. Summative. |
- The department computes your grade as the better of two published options: assignments 25%, term test 10% and final examination 65%; or assignments 25% and examination 75%. The table above shows the first option. Under either, you must obtain at least 40% in the final examination to pass.
- Note what the alternative option does: if the term test goes badly it is dropped and the examination rises to 75%, so a weak test cannot sink you but it also cannot be compensated for — the examination simply matters more. Either way at least 40% in the final is required.
This is an exam-cram course. With the exams at 75% of the grade and the final examination alone at 65%, your result is overwhelmingly decided by how well you perform under time pressure. At least 40% required in this component to pass.
Final exam timing: During the examination period. Confirm the exact date and venue on your exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The course rewards consistency over cramming, and practice over re-reading. Here is the loop that works, then what to have nailed before each exam.
The weekly loop
Before the mid-semester checklist
- Construct a stochastic model from a described system.
- Work with the Poisson process, interarrival times and the memoryless property.
- Analyse birth and death processes.
- Derive and interpret single-server queueing results.
Before the final heaviest topics
- Analyse multi-server queues and simple networks.
- Generate random variates from a required distribution.
- Build and interpret a simulation of a stochastic model.
- Apply variance reduction and address optimisation questions for stochastic systems.
The mistakes that cost marks
Inverting the utilisation ratio. Utilisation is arrival rate over service rate. Mixing a rate with a mean time reverses the answer and the conclusion.
Assuming memorylessness. The exponential distribution's memoryless property makes analysis tractable and is often untrue of the real system. State the assumption.
Stability read as good performance. A queue is stable below utilisation 1, but expected length grows without bound as utilisation approaches it.
Simulation without variance reduction. A simulation answer without a precision estimate is an anecdote. The course assesses the precision, not only the estimate.
Formula & concept sheet
The vocabulary and formulas you must own
- Stochastic process
- A collection of random variables indexed by time, describing how a system evolves randomly.
- Poisson process
- A counting process for events occurring independently at a constant average rate in continuous time.
- Memoryless property
- The property of the exponential distribution that remaining waiting time does not depend on time already waited.
- Birth and death process
- A continuous-time Markov chain in which transitions move the state up or down by one.
- Utilisation
- The long-run proportion of time a server is busy; the ratio of arrival rate to service rate.
- Single-server queue
- A queue with one server, Poisson arrivals and exponential service times.
- Steady state
- The long-run distribution a stable system settles into, independent of where it started.
- Little's law
- The relationship between average number in a system, arrival rate and average time spent in it.
- Random number generation
- Producing variates from a required distribution, the basis of simulation.
- Variance reduction
- Techniques lowering the variance of a simulation estimate without increasing the run length.
- Monte Carlo simulation
- Estimating a quantity by repeated random sampling from a model.
- Stochastic optimisation
- Choosing decisions that optimise an objective when the system evolves randomly.
Common acronyms: CTMC · MC · PDF · RNG.
Where it fits
Prerequisites, related courses & why it matters
Prerequisites published by the department: 15 points from STATS 125 and STATS 210, and 15 points from STATS 201, 207, 208, 220 or BIOSCI 209. The course is worth 15 points. The department lists Kleijnen and van Groenendaal's Simulation: A Statistical Perspective as recommended rather than required reading.
Your STATS320 study toolkit
Study the course with Sia, not just read about it
Each tool already knows STATS320: your syllabus, your texts, and where the marks are. Grouped by how you study, from first contact to exam week.
FAQ
Frequently asked questions
Is STATS 320 hard?
It rates hard. It builds directly on two prior probability and theory courses, the material is mathematically demanding, and the final examination carries 65% or 75% of the grade depending on which published option gives you the better result.
What is the assessment breakdown?
The better of two options: assignments 25%, term test 10%, final examination 65%; or assignments 25% and examination 75%. You must obtain at least 40% in the final examination to pass.
Why are there two weighting options?
So a poor term test does not penalise you twice. If dropping the test improves your mark, the examination absorbs its weight. It also means the test is low-risk but the examination is unavoidable.
What do I need before taking it?
15 points from STATS 125 and STATS 210, plus 15 points from STATS 201, 207, 208, 220 or BIOSCI 209.
What is the textbook?
The department lists Kleijnen and van Groenendaal, Simulation: A Statistical Perspective (Wiley 1992) as recommended reading rather than a required text.
What is the hardest part?
Usually the move from analysing a model to simulating one, and specifically variance reduction — it requires understanding why a simulation is imprecise before you can make it less so.
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Work through stochastic models, review of probability foundations, the poisson process and the rest of the course with a tutor that knows it and quizzes you on the topics the assessments weight most heavily.
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