30 WSN Coverage Worked Examples
WSN coverage examples, WSN coverage worked examples, coverage evidence, coverage gap repair, WSN duty cycle review, WSN range tradeoff
30.1 Start With the Field Story
Worked examples are useful when they keep the decision visible. For each coverage case, identify the monitoring goal, the assumed range, the active set, the failure case, and the record that would convince a reviewer.
30.2 In 60 Seconds
WSN coverage examples are useful only when they show how a decision is reviewed. A worked example should start with a claim, name the coverage type and redundancy level, inspect the active operating state, compare the claim with field evidence, record the finding, choose a repair or acceptance decision, and define the retest trigger.
This chapter uses examples to practice that review habit. It avoids treating a formula, coverage drawing, or unit-cost comparison as final proof. The learner should leave with a repeatable way to work through coverage decisions without overstating what the evidence proves.
30.3 Learning Objectives
By the end of this chapter, you will be able to:
- Work through WSN coverage examples using claim, evidence, finding, and decision records.
- Identify when a redundant area claim needs repair rather than approval.
- Review duty-cycle choices without letting energy savings break coverage.
- Compare sensing-range options using deployment evidence, not unit price alone.
- State limits and retest triggers for every example decision.
30.4 Quick Check: WSN Coverage Examples
30.5 How to Use Worked Examples
Worked examples should make reasoning visible. They should not imply that one example number, one drawing, or one rule proves every future deployment.
Start with the claim Write what must be sensed, where, when, and at what redundancy level.
Name the evidence Use installed positions, field readings, target lists, crossing tests, route tests, active schedules, and connectivity checks.
Separate the finding Say whether the evidence supports the claim, narrows it, contradicts it, or leaves it unproven.
Record the decision Accept, narrow, repair, or retest. Do not hide limits inside optimistic wording.
30.6 Example Review Route
Use Figure 30.1 as the route for each example. The same route works for area, point, barrier, path, and hybrid coverage examples.
The route keeps examples from drifting into calculation theater. A calculation can support a decision, but the final approval still depends on the deployed state and evidence.
30.7 Example 1: Redundant Area Monitoring
A water treatment room has an area coverage claim: important process conditions should be detected anywhere inside the monitored room during normal operation. The risk is high enough that the design asks for backup sensing at weak points.
Claim: The monitored process room has redundant area coverage during the normal operating schedule.
Evidence: Installed sensor positions, room boundary, active schedule, field readings near corners and equipment, and gateway reachability checks.
Finding: The central area has strong overlap, but corner and edge locations have weaker evidence. Some sensors shown in the planning drawing are not active during the reviewed schedule.
Decision: Do not accept the broad redundant-area claim yet. Narrow the accepted claim to validated zones or add repair evidence for weak edges and the sleep schedule.
Retest trigger: Reopen the review after sensor movement, schedule change, equipment layout change, failed reading, or gateway relocation.
The learning point is not a fixed sensor count. The learning point is that redundant coverage must be true at the weak locations and in the active operating state.
Good repair evidence New readings from weak locations, an updated active-set check, a connectivity pass, and a short note saying which previous gap was closed.
Weak repair evidence A new drawing with more circles but no field readings, no sleep-schedule check, and no reporting-path verification.
30.8 Example 2: Duty-Cycle Evidence
A remote wildlife monitoring deployment needs long battery life. The team proposes a low-duty-cycle schedule so sensors wake briefly, sample, communicate, and then sleep again.
Claim: The corridor remains acceptably monitored while the sleep schedule saves energy.
Evidence: Wake interval, sampling window, event speed, expected detection latency, active sensor set, packet delivery checks, and battery trend evidence.
Finding: The schedule may be acceptable for slow-moving observations, but it is not evidence for immediate alarm detection unless the latency requirement also passes.
Decision: Accept the schedule only for the stated wildlife-monitoring purpose. Do not reuse it for safety, intrusion, or fast event alarms without a new latency review.
Retest trigger: Reopen review after changing sample period, radio settings, event class, animal route, gateway location, firmware, or battery type.
Duty cycling is a coverage decision, not only an energy decision. A sleeping sensor does not count as active coverage unless the accepted rule explains when it wakes and what latency remains.
30.9 Example 3: Sensing Range Tradeoff
A building automation team compares short-range and longer-range occupancy sensors. The longer-range device costs more per unit, but it may reduce installation count and maintenance work.
What to compare Installed locations, room boundaries, sensing behavior, false positives, power plan, communication path, maintenance access, and replacement workflow.
What not to compare alone Unit price. A cheaper sensor can still be the expensive choice if it needs more locations, more batteries, more calibration, or more repair visits.
Evidence limit A longer sensing range can cover more space, but it can also sense through openings, across adjacent zones, or from poor mounting angles. Field validation decides whether the extra range is useful.
Decision pattern: Choose the option that gives reviewable coverage with fewer hidden operations risks, not merely the option with the lowest line-item hardware price.
Retest trigger: Reopen after partition changes, tenant layout changes, sensor replacement, changed mounting height, repeated false occupancy, or repeated missed occupancy.
30.10 Barrier Coverage for Crossings
A facility wants to detect crossings at a perimeter line. The requirement is crossing detection, not full interior tracking.
Likely claim Barrier coverage along the stated boundary, with explicit tests at gates, corners, likely bypasses, and weak line-of-sight points.
Common drift Calling the deployment “site coverage” after a successful crossing test. The test supports the barrier claim, not full interior monitoring.
Repair evidence Additional crossing tests after vegetation growth, fence changes, sensor relocation, or repeated false alarms.
Retest trigger New gate route, changed perimeter, moved sensor, seasonal obstruction, failed crossing test, or response-process change.
Barrier examples should be explicit about weak versus strong claims. Detecting a crossing is not the same as tracking the object continuously after it crosses.
30.11 Example Evidence Record
Use Figure 30.2 to keep the result compact. This record is the output of a worked example.
The record should be short enough to update after maintenance. If it becomes long, split the example into separate claims by area, target list, route, or boundary.
30.12 Common Worked-Example Mistakes
Approving the calculation A calculation can be correct while the deployed claim is still unproven.
Ignoring weak locations Edges, corners, obstructions, gates, route bends, and sleeping sensors often decide whether the claim is honest.
Mixing energy and coverage Battery savings are useful only if the accepted active state still supports the coverage claim.
Using unit cost as the decision Hardware price does not include placement count, installation time, battery visits, false alarms, missed detections, or support ownership.
Overusing one example A wildlife monitoring schedule should not be reused for safety alarms without a fresh latency and consequence review.
No retest trigger Worked examples drift after layout changes, firmware changes, sensor replacement, route changes, and failed validation tests.
30.13 Review Checklist
Before accepting a worked example, check:
- Is the monitoring claim specific enough to approve or reject?
- Does the coverage type match the scenario?
- Is the redundancy level stated separately from the type?
- Which sensors count in the active operating state?
- Does the evidence include weak locations and reporting paths?
- Does the decision say accept, narrow, repair, or retest?
- Are limits visible to future readers?
- Is there an owner for repair or evidence updates?
- What exact change reopens the review?
30.14 Knowledge Check: Redundant Area Example
30.15 Knowledge Check: Duty-Cycle Example
30.16 Matching: Example Evidence
30.17 Ordering: Worked Example Review
30.18 Every Number Needs a Sizing Boundary
The body examples teach how to move from claim to evidence to decision. The deeper layer is the arithmetic boundary behind those decisions. A worked example may include a density formula, a node count, a duty-cycle estimate, or a k-coverage target, but none of those numbers is meaningful until the review names the scope and state that the number describes. The same calculation can be honest for a fenced corridor, misleading for a whole room, and useless after a gateway move.
Use Figure 30.3 to keep example arithmetic tied to the claim, gateway evidence, power evidence, pilot finding, decision, and retest trigger.
That is why a count should be written as a review statement rather than as a bare answer. For example: “For a 100 m by 100 m area, with 10 m sensing radius, random placement, disk-sensing assumption, and 95% expected one-coverage, the planning count is about 96 nodes before gateway, power, and field-margin checks.” This statement is longer than “96 nodes,” but it says what must be true for the answer to be reusable. If the deployment changes to 99%, k=2, triangular planned placement, or a corridor/barrier claim, the earlier number is not simply adjusted by intuition; it is recalculated under the new boundary.
The review also separates arithmetic precision from field certainty. A formula can be evaluated exactly while still relying on a rough sensing radius, a simplified boundary, or a random-placement model that does not match installation practice. The point of the depth layer is not to make the worked example mathematical for its own sake. It is to show where a number came from, what it excludes, and which evidence would make it safe enough to accept.
Scope Name the area, target list, path, or boundary the count is allowed to describe.
Model State sensing radius, placement model, active state, and any excluded obstruction or edge condition.
Decision Say accept, narrow, repair, or retest, then record what change reopens the sizing decision.
30.19 Work the Random-Deployment Count
For nodes scattered randomly under a Poisson model, with density lambda nodes per square metre and sensing radius Rs, the expected fraction of points covered by at least one sensor is p = 1 - e^(-lambda*pi*Rs^2). Rearranging gives lambda = -ln(1-p) / (pi*Rs^2). The planning count is then N = lambda*A for area A. This is a model-based estimate, not a field guarantee.
Use a concrete worked example. Suppose the area is 100 m by 100 m, so A = 10,000 m^2, and the accepted sensing radius is 10 m, so pi*Rs^2 = 314.16 m^2. For 95% expected one-coverage, -ln(0.05) = 2.996, so lambda = 2.996 / 314.16 = 0.00954 nodes per square metre. Multiplying by 10,000 gives 95.4 nodes, so the planning count rounds up to 96 nodes before margin and deployment constraints.
| Target | Mean coverage term | Density for 10 m radius | Count for 10,000 m2 |
|---|---|---|---|
| 90% | 2.303 | 0.00733 / m2 | 74 nodes |
| 95% | 2.996 | 0.00954 / m2 | 96 nodes |
| 99% | 4.605 | 0.01466 / m2 | 147 nodes |
The table shows the diminishing return that a bare diagram hides. Raising the target from 95% to 99% does not mean four percent more nodes. It changes the mean coverage term from about 3.0 to about 4.6, which raises the planning count from 96 to 147 nodes in this example. The reviewer should then ask whether the higher target is justified by the missed-event consequence, and whether field constraints make random placement a fair model.
Round up counts, then add only evidence-backed margin. Do not hide uncertainty by inflating a number without saying whether the extra nodes cover edge effects, failed nodes, gateway reachability, or installation limits.
30.20 k-Coverage Placement Meaning
Two refinements change what the worked number means. First, k-coverage is not a small label added after the count. If the requirement says each point must be sensed by at least two independent sensors, the review is now about the probability of fewer than two sensors at a point, not merely the probability of zero sensors. Under the same Poisson model, the number of sensors covering a point has mean mu = lambda*pi*Rs^2. To make under-coverage unlikely, the mean usually needs to sit above the required k value. The example must say whether redundancy is a resilience requirement, a localization requirement, or just a comfort phrase.
Second, placement model changes the count. Random scattering creates accidental overlaps and gaps, so the formula estimates expected coverage rather than a deterministic guarantee. A planned grid or triangular placement can use the field more efficiently, but only if the team can actually install nodes at those positions and maintain their range assumptions. A warehouse with fixed mounting points, a forest with dropped sensors, and a fenced perimeter with line-of-sight constraints are different worked examples even if their area is similar.
The safe review habit is to keep the count driver visible. Area coverage counts scale with region size and sensing footprint. Point coverage counts scale with target list and redundancy. Barrier coverage counts scale with boundary segments and crossing tests. Path coverage counts scale with route segments and timing windows. A worked example that mixes those drivers should be split before the arithmetic is accepted.
Random estimate Useful when nodes are scattered, but acceptance still needs weak-location and reporting-path evidence.
Planned placement Can reduce waste, but only if installation, calibration, and maintenance preserve the assumed positions.
k-coverage Requires evidence about independent sensing layers, active sets, gateway paths, and failure or sleep rules.
30.21 Knowledge Check: Coverage Count Meaning
30.22 Summary
WSN coverage worked examples should teach review discipline. The strongest examples start with a precise claim, name the coverage type and redundancy level, check the active operating state, compare the claim with field evidence, and record a decision with limits and retest triggers.
Do not let an example drift into unsupported certainty. A useful example shows how to reason from evidence, how to handle weak locations, how to keep energy schedules tied to coverage, and how to prevent one scenario from being reused outside its proof.
30.23 Key Takeaway
Worked coverage examples should connect the claim, weak-location evidence, active state, decision, limit, owner, and retest trigger before any number or drawing is treated as accepted coverage.
30.24 Concept Relationships
- WSN Coverage: Problem Types gives the detailed area, point, barrier, path, and hybrid formulations.
- WSN Coverage Algorithms explains how verification, active-set, rotation, and repair algorithms support example decisions.
- WSN Coverage Implementations turns accepted example decisions into implementation records.
- WSN Deployment Sizing expands sizing arithmetic, pilot evidence, and count-driver review.
30.25 What’s Next
- WSN Coverage Implementations for turning worked-example decisions into deployment records.
- WSN Coverage: K-Coverage and Rotation for redundant coverage and active-set scheduling.
- WSN Energy Duty Cycling for schedule evidence when sleep states affect coverage.