DASE

Defence Science Journal 75(1):27–34, 2025 · Hands-on demo

Simulation logic for cyber operations on physical space using C2 effectiveness measurement

How can a constructive training simulation show commanders what an integrity attack on a C2 system costs in the physical fight? The paper chains an information error σa² through Schutzer's C2-effectiveness method into a measure of effectiveness (MÔE), then into a battle-damage assessment. Explore each step, check the published tables, and see where the model needs more work. Paper DOI

Inputs

Scenario constants of Eq. (1), close-combat-attack case

The chain, step by step

  1. Eq. (1) probability of detection and correct association within the C2 time:
    p = 1 / (1 + C1·ρ·vp·tcs²·σa²)
  2. Eq. (2) probability multiplier relative to an error-free system:
    α = (1 − σa²) / (p(1 − σa²) + (1 − p)(1 − σ²)), σ² = 0
  3. Eqs. (3)–(5) Lanchester square law with <N′²> − <M′²> fixed at 1:
    K = α(<M′²> + 1) − <M′²>, and MÔE = K × MOE with MOE = 1
  4. §3.5 the damage-assessment parameter is scaled by MÔE (0.1650 × MÔE) and fed to an agent-based simulator (tab ④).

With the paper's constants, C1·ρ·vp·tcs² = 2.00, so p = 1/(1 + 2σa²) and α = (1 − σa²)(1 + 2σa²)/(1 + σa²). The scenario's speed, density and C2 time enter only through this one number, and C1 was chosen to make p = 0.5 at σa² = 0.5.

Probability value p and multiplier α (cf. Fig. 6)

Effectiveness multiplier K (cf. Fig. 7)

MÔE over information error and enemy asset value (cf. Fig. 8 / Table 2)

Rows: <M′²> = 0…4; columns: σa² = 0…1. Green = effectiveness kept, red = K ≤ 0 (the paper's “red square”: the objective can no longer be reached by combat). The white dot is the current input.

Every number below is recomputed in your browser from Eqs. (1)–(5) with the paper's constants and compared with the printed tables. Cells differing by more than 0.0005 are marked.

Table 1 · Probability value, probability multiplier and effectiveness multiplier

Table 2 · MÔE decline (%) by information error and enemy asset value

“Decline” is (1 − MÔE) × 100. Values above 100% mean MÔE < 0, which the method allows but which has no physical meaning as a share of effectiveness.

The paper samples σa² with Latin hypercube sampling (LHS) instead of plain Monte Carlo (MCS) because LHS spreads samples more evenly (Fig. 3). Here you can see that, and also propagate the samples through the model. The paper reports only a fixed grid σa² = 0, 0.1, …, 1, never the distribution that sampling would give.

MCS: independent uniform draws

LHS: one draw per row and per column

How precisely does each method estimate mean MÔE?

Distribution of MÔE if σa² ~ Uniform(0, 1) (2,000 LHS draws)

The paper feeds the MÔE-scaled parameter into an AnyLogic agent-based model of 297 target units (a mechanised battalion) with 25 minutes available, and reports two numbers per MÔE (Table 3, Fig. 9). The AnyLogic logic is not published. A simple exponential attrition process, removal rate λ = c·MÔE/25 per minute with c ≈ 4.35 fitted to the counts, reproduces both columns, provided “operation complete” means about 4 units remain (297·e−c) rather than zero.

Units destroyed over time. Red = expected value; grey = individual stochastic runs; dashed lines = 25 min available and the model's completion time.

Table 3 vs the attrition model

Model columns: expected value; spread = 5th–95th percentile over 200 stochastic runs. The paper gives a single number per row.

Paper Fig. 9 · BDA results from the AnyLogic simulator

Paper Fig. 9

Review points from today's perspective

  1. The physical scenario barely matters. Density, speed and C2 time enter Eq. (1) only through the product C1·ρ·vp·tcs², and C1 = 28.8259 was set so that p = 0.5 at σa² = 0.5. The result is p = 1/(1 + 2σa²) whatever the scenario. Try it in tab ①: change vp and tcs, then re-solve C1 for the same anchor, and nothing changes.
  2. σa² is undefined. In Schutzer's method σ² is a positional-error variance with units. Here it becomes a dimensionless “degree of information error” in [0, 1] with no definition: fraction of corrupted records? bias? The paper also gives no mapping from attack type, scope or duration to σa². Without that mapping the simulator's cyber input is an arbitrary dial.
  3. α is defined as an improvement (α > 1) but used as a degradation. §3.3 states p = α·pc with α > 1. The case study then uses p ≤ pc and α ≤ 1. This works numerically, but the text should say so.
  4. K becomes negative. With <N′²> − <M′²> fixed at 1, K = α(M + 1) − M falls below zero, giving “declines” of up to 300%. The K = 0 boundary is a useful signal (the objective cannot be reached by combat). Negative MÔE, however, needs a stated interpretation, or the model should clip at 0 as the damage-assessment step implicitly does.
  5. The sampling is not used. LHS is motivated (Fig. 3) but all results come from a fixed 11-point grid. Propagating LHS samples (tab ③) would give the distribution of MÔE and damage that trainees face under uncertainty. In one dimension LHS is simply stratified sampling, so its advantage over MCS is easy to show but should be quantified.
  6. The damage-assessment model is not reproducible. The AnyLogic logic, the meaning of the 0.1650 parameter, the completion criterion and the number of runs are not given. A two-line exponential-attrition model reproduces Table 3 (tab ④), which suggests the simulator adds little beyond time ≈ 25/MÔE. It also implies that “complete” means about 99% destroyed. Stochastic runs show ±5–10 units of spread that a single run hides.
  7. Defender response is missing. For training command and response procedures, σa² should change over time as the blue side detects, isolates and restores (for example σa²(t) falling after a detection delay). The model has one static error value per engagement, so no response decision can change the outcome.
  8. No validation. There is no comparison with exercise data, expert judgement (e.g. a Delphi study) or alternative cyber-mission-impact methods such as MITRE's Cyber Mission Impact Assessment (the paper cites it as ref. 15 but does not compare), and no sensitivity analysis on the M = <M′²> assumption.
  9. Minor: Fig. 7 labels two thresholds as 37.017 and 42.155 instead of 0.37017 and 0.42155. The demo recomputes all four (0.6404, 0.5, 0.4215, 0.3702). Eq. (1) is hard to read in print. Table 1 rounds p inconsistently (0.4546 vs the exact 0.4545).

Classroom exercises

  1. Derive the closed form α = (1 − s)(1 + 2s)/(1 + s) for κ = 2, and find the σa² at which K = 0 for <M′²> = 2 by hand.
  2. Propose a definition of σa² for one concrete integrity attack (e.g. corrupted target coordinates) and say how you would measure it in an exercise.
  3. Add a defender response: let σa² drop linearly to 0 after a detection delay d. How does MÔE averaged over the 25-minute window change with d?
  4. Using tab ④, estimate how many stochastic runs are needed before the mean count at MÔE = 0.29 is known to ±2 units.

What would make the method stronger

  • An explicit attack-to-σa² mapping (attack type, scope, dwell time), ideally calibrated on exercise logs.
  • Uncertainty propagation with the LHS samples the method already proposes, reporting distributions rather than single values.
  • A published damage-assessment model (or the AnyLogic file) with the completion rule and replication count.
  • Time-varying σa² driven by blue-side detection and recovery, so that trainee decisions change the result.
  • Validation against SME judgement and comparison with other mission-impact methods.

Fig. 1 · Cyber operations procedure

Fig. 1

Fig. 2 · Procedure of cyber operation in conjunction with physical warfare

Fig. 2

Fig. 3 · Sampling with MCS and LHS

Fig. 3aFig. 3b

Fig. 4 · Measuring time to mission from the changed MOE

Fig. 4

Fig. 5 · Engagement scenario (close combat attack)

Fig. 5

Fig. 6 · Changing probability values

Fig. 6

Fig. 7 · Changes in effectiveness multiplier

Fig. 7

Fig. 8 · MOE effect reduction

Fig. 8

Source: Lee, S.; Kang, D. Designing Simulation Logic of Cyber Operations on Physical Space Using C2 Effectiveness Measurement. Defence Science Journal 75(1):27–34, 2025. Figures reproduced from the paper.

Research and teaching demo · All calculations run in your browser from the paper's published equations; the damage-assessment model is a reconstruction, since the original simulator is not published.