EE8405 Queueing Theory with Telecommunications Applications
The Complete Exam Bible · EE8405 Overview
- City University of Hong Kong
- Semester A, 2026/27
- Postgraduate electrical engineering
- Mainly closed book
What this course asks you to do
EE8405 turns uncertainty about demand and service into engineering decisions about delay, loss and capacity. The current Canvas shell uses the EE8405 code while inherited teaching documents retain EE6610, the former code for the same named subject.
- Assessment Test 15%, Group Learning 35%, examination 50%.
- Pass thresholds Reach 30% in continuous assessment and 30% in examination.
- Core method Define the boundary, match the model, calculate, reconcile and interpret.
- Current format Use the live Canvas instructions for examination duration and question count.
How EE8405 is assessed
| Component | Weight | Format |
|---|---|---|
| One Test | 15% | Current deck dates the test 22 October 2026 |
| Group Learning | 35% | Continuous contributions through Canvas discussions |
| Examination | 50% | Mainly closed book with one handwritten double-sided page |
The three published weights total 100%. To pass, students must achieve at least 30% across continuous assessment, comprising the test and Group Learning, and at least 30% in the examination. These are assessment thresholds, not attendance percentages. Falling below either threshold prevents a pass. Confirm the current assessment settings and examination logistics on Canvas.
What EE8405 covers
Ten chapters move from probability inputs through delay and loss models to networks, simulation and model checking.
Probability and Conditional Reasoning
events, Bayes' rule, independence and base-rate reasoningConditional reasoning supplies the language used to describe uncertain arrivals, errors and observations.
- Sample spaces and events
- Conditional probability
- Bayes' rule
- Total probability
- Independence tests
- Base-rate effects
Random Variables, Distributions and Moments
mass, density, cumulative probability, expectation and varianceThis chapter turns outcomes into numerical variables and studies how probability is distributed across their values.
- Probability mass
- Density functions
- Cumulative probability
- Expectation
- Variance and standard deviation
- Second moments
Poisson Processes and Exponential Times
counting intervals, waiting times, superposition and competing clocksA Poisson process describes an event stream through counts in intervals and exponential times between events.
- Poisson counts
- Exponential waits
- Memorylessness
- Superposition
- Thinning
- Competing clocks
Queueing Measures and Little's Formula
system boundaries, utilization, delay, loss and trafficQueue measures become meaningful only after the system boundary and customer population are fixed.
- System boundaries
- Little's formula
- Waiting-room measures
- Utilization
- Offered and carried traffic
- Loss and delay systems
Deterministic Queues and M/M/1
timelines, birth-death states, stability and delayDeterministic queues are traced through known arrival and service events, while M/M/1 is analysed as a birth-death chain with random transitions. Comparing them isolates the effect of variability at equal mean rates.
- Deterministic timelines
- Kendall notation
- Birth-death chains
- M/M/1 stability
- Mean queue size
- Delay growth near saturation
Erlang Loss and Delay Systems
blocking, waiting, recursion and minimal capacityMulti-server systems divide into loss and delay models according to what happens when all servers are busy. Erlang B applies when the arrival is cleared; Erlang C applies when it waits.
- M/M/k/k loss
- M/M/k delay
- Erlang B recursion
- Erlang C probability
- Traffic accounting
- Capacity dimensioning
Finite Buffers and State Dependence
capacity states, blocking, admitted traffic and variable ratesFinite buffers close the state space and make the full state a blocking boundary.
- Finite state spaces
- Boundary transitions
- Stationary normalisation
- PASTA
- Admitted throughput
- State-dependent rates
Service Variability and General Queues
second moments, Pollaczek-Khinchine and service disciplinesGeneral-service queues expose information hidden by the mean. Pollaczek-Khinchine uses the service-time second moment, so variance raises FIFO waiting even when utilization is unchanged.
- M/G/1 assumptions
- Service second moments
- Pollaczek-Khinchine
- M/D/1 comparison
- Processor sharing
- Priority disciplines
Queueing Networks and Mobile Systems
routing equations, feedback, handover and fixed pointsNetworks create internal traffic as customers move and return between queues. This chapter solves flow-balance equations before applying node formulas, checks stability using effective rather than external rates and accumulates delay over repeated visits.
- Traffic equations
- Routing probabilities
- Feedback
- Jackson networks
- Channel holding time
- Erlang fixed points
Simulation, Correlation and Model Checking
event calendars, confidence intervals, dependence and validationDiscrete-event simulation advances from one arrival or departure to the next and records both time-weighted states and customer delays.
- Event calendars
- State updates
- Warm-up bias
- Independent replications
- Confidence intervals
- Correlation and validation
The mathematical work begins with conditional probability, distributions and Poisson processes, then develops system boundaries, Little's formula, deterministic and Markovian queues, Erlang loss and delay systems, finite buffers, service variability, routed networks and simulation.
How the chapters fit together
The early chapters establish inputs and units.
The middle chapters show how capacity and variability shape performance. The final chapters handle feedback, handover and empirical validation.
Every worked solution defines notation, calculates with explicit units, checks the answer through an independent identity and closes with an operational interpretation.
Assessment focus
The 2026 introductory deck publishes a fifteen per cent test, thirty-five per cent Group Learning and a fifty per cent examination.
To pass, students must achieve at least 30% across continuous assessment, comprising the test and Group Learning, and at least 30% in the examination. These are assessment thresholds, not attendance percentages. Falling below either threshold prevents a pass, so confirm the current settings on Canvas. Test and examination are mainly closed book with one handwritten double-sided page.
The live Canvas instructions control the examination logistics.
Where marks are won
The group-learning instructions make the marking priorities unusually clear: accuracy, reproducibility, interpretation, initiative, continuous participation and presentation. Those same habits strengthen examination answers.
Define variables and data, show steps, explain implications, and distinguish a model's calculation from the decision criterion supplied by the engineer or service owner.
Worked example · free
Size a queue only after choosing its service target
- 2Define the queue and calculate offered load.
- 3Check stability and compute the requested delay or blocking metrics.
- 3Compare results against an explicitly stated service target and cost.
Key terms
- Offered Traffic
- Demand presented to a service system before blocking, measured in erlangs.
- Carried Traffic
- The portion of offered traffic that receives service.
- Little's Formula
- The long-run identity relating mean number, throughput and matching mean time.
- Utilization
- The long-run fraction of service capacity that is busy.
- Poisson Process
- A counting process with stationary independent increments and exponential inter-arrival times.
- Blocking Probability
- The probability an offered arrival is rejected because capacity is full.
- Erlang B
- The loss-system formula for blocking with Poisson arrivals and no waiting room.
- Erlang C
- The delay-system formula for the probability an arrival must wait.
- State Probability
- The long-run probability that a queue contains a specified number of customers.
- Second Moment
- The expectation of a squared random variable, combining variance and squared mean.
- Traffic Equation
- A flow-balance equation combining external and routed arrivals at a network node.
- Warm-up Period
- The initial simulation interval excluded to reduce empty-start bias.
EE8405 FAQ
How is the course assessed?
The current introductory deck assigns 15% to one test, 35% to Group Learning and 50% to the examination. These numeric rows total 100%. The live Canvas course should be checked for any operational update before an assessment.
What are the passing conditions?
Yes. To pass, students must achieve at least 30% across continuous assessment, comprising the test and Group Learning, and at least 30% in the examination. These are assessment thresholds, not attendance percentages. Falling below either threshold prevents a pass, so confirm the current assessment settings on Canvas rather than assuming the weighted total can compensate.
What materials are permitted in the examination?
The current deck describes the test and examination as mainly closed book and permits one handwritten double-sided page. It also mentions a later computer-access period when students cannot write in the answer book. Follow live instructions for details.
Which formula should I put on my sheet first?
Prioritise formulas together with their assumptions: Bayes and total probability, moments, Poisson counts and waiting times, Little's formula, M/M/1, Erlang B recursion, Erlang C definitions, finite-buffer balance and Pollaczek-Khinchine.
How should I use the older papers?
Use them to practise question types such as model identification, full numerical derivations, dimensioning, queue-state tables and spreadsheet calculations. Do not import their timing, devices, sections or mark allocation into the current offering.
What earns marks in Group Learning?
The instructions identify self-learning, novelty, initiative, innovation, accuracy, academic ethics, continuous participation and presentation. Numerical contributions should define their inputs, be reproducible by classmates and explain the implications of the result.
When do I use Erlang B rather than Erlang C?
Use Erlang B when an arrival finding every server busy is blocked and cleared. Use Erlang C when that arrival remains in a waiting queue. The customer fate is the quickest reliable model-selection test.
Why does service variance matter?
In an M/G/1 queue, mean waiting depends on the second moment of service time. Two systems can therefore share the same arrival rate, mean service and utilization yet have different delay because their service variability differs.
Questions students ask in each EE8405 chapter
- Why can a sensitive alarm have a low posterior?
- A rare target can generate fewer true alarms than the common non-target population generates false alarms. Bayes' rule retains both routes in the evidence denominator, so the prior remains decisive. Chapter 01 · Probability and Conditional Reasoning
- Why is density not a point probability?
- A continuous variable assigns zero probability to an exact point. Probability is area under the density over an interval, so a density value can exceed one without violating probability rules. Chapter 02 · Random Variables, Distributions and Moments
- When is a Poisson model plausible?
- It is most defensible for independent events from many sources at a roughly constant rate. Trends, coordinated retransmissions, batches and long-range dependence can violate its assumptions. Chapter 03 · Poisson Processes and Exponential Times
- Does Little's formula require exponential times?
- No. It is a broad long-run flow identity and does not depend on exponential distributions, although the means and population must correspond to the same stable boundary. Chapter 04 · Queueing Measures and Little's Formula
- Why can delay explode below full utilization?
- Random arrival clusters create backlogs that require spare capacity to clear. As arrival rate approaches service rate, the clearing margin shrinks and mean delay grows nonlinearly. Chapter 05 · Deterministic Queues and M/M/1
- What is the quickest B versus C test?
- Ask what happens when every server is busy. Immediate rejection selects Erlang B; retention in a queue selects Erlang C. The customer fate decides the model. Chapter 06 · Erlang Loss and Delay Systems
- Can a finite queue have a stationary distribution above unit offered load?
- Yes. Its state space is finite and excess arrivals can be blocked, although high offered load may produce severe loss and near-continuous server use. Report that loss explicitly. Chapter 07 · Finite Buffers and State Dependence
- Why does variance increase waiting?
- Long services create residual work encountered by later arrivals. Squaring service duration makes those rare long jobs contribute disproportionately to the second moment. Mean service alone therefore misses the delay effect. Chapter 08 · Service Variability and General Queues
- Why not use external rates at each node?
- Departures can be routed or fed back, so a node's effective load includes internal arrivals. Ignoring them can hide the true bottleneck and even miss instability. Chapter 09 · Queueing Networks and Mobile Systems
- Why discard a warm-up period?
- A queue started empty does not initially represent steady state. Warm-up removal reduces the bias that this artificial initial condition creates in long-run estimates. Justify the cutoff from diagnostics. Chapter 10 · Simulation, Correlation and Model Checking
How to study for the exam
Rebuild one solved problem from each model family without looking at the answer. On every page write the physical queue, assumptions, units, stability condition, calculation and one independent check. Next, practise selecting between loss, delay, finite-capacity and general-service models from a verbal description.
Use older papers only for question types and computational discipline, while taking current format and assessment rules from the live Canvas materials. Finish each revision session by explaining one result in operational language: what changes for delay, blocking, utilization or required capacity, and which assumption would most threaten the conclusion.
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