Optimising a CSI Rapid DNA Process: Queueing Theory, Simulation, and ROI Analysis

UK police forensics face a fundamental constraint: DNA evidence is only useful for catching suspects if it is processed before the trail goes cold. This project models the end-to-end forensics pipeline — from crime scene collection through to database matching — using queueing theory and discrete-event simulation, then evaluates five progressive operational redesigns against the current process on cost-effectiveness measured in arrests per £1 million spent.

The project was completed jointly with Ahsan Tariq, Arsalan Khan, and Hamza Waseem as part of the coursework. All simulations used Simul8 v31.0 with 500 trials and random seed 4517. ROI analysis used Palisade @Risk with 10,000 Monte Carlo iterations.

Part 1 — Digital fingerprinting: M/M/c queueing analysis

Before modelling the DNA pipeline, the project characterised the upstream crime arrival process using M/M/c queueing theory. Petty crimes arrive exponentially with a mean inter-arrival time of 16 minutes (λ = 0.0625 crimes/min). Each CSI visit takes exponentially distributed time with a mean of 75 minutes (μ = 0.01333 crimes/min per server). CSIs are available 24/7.

For queue stability the condition λ ≤ cμ must hold, which requires at least 4.69 CSIs — rounded up to a minimum of 5. With 5 CSIs the server utilisation is 93.75%, placing the system under near-saturation load. At this utilisation, over 84% of incoming crime scenes must queue before a CSI becomes available.

All four analytical values fall within the 95% CI bounds of the simulation, with deviations below 1% in every case. This confirms the M/M/c model is correctly parameterised and the Simul8 model is a valid representation of the same system.

To determine the minimum number of trials required, all four metrics were monitored simultaneously using the Simul8 convergence analyser. The most demanding KPI — average queue size — required 251 trials; average queue wait required 239. Running 500 trials provides approximately 2× the required number. Convergence is slow because 93.75% utilisation produces heavy-tailed queue distributions where rare large spikes require many trials to average out.

Part 2 — Current DNA process and its bottlenecks

The baseline DNA forensics pipeline spans eight sequential stages: crime occurrence, CSI visit, station data entry, lab transport, sample preparation, DNA sequencing, validation, and database matching. Key structural constraints in the current process are:

• Batch sequencer schedule: the legacy sequencer runs only on Wednesdays at 09:00 and Fridays at 15:00, with a capacity of 100 samples. Each run takes 2,880 minutes (2 days). Samples arriving outside these windows wait until the next scheduled run.
• Fixed transport window: CSIs return samples to the lab at the end of their shift at 16:00, creating a daily batch transport queue rather than continuous flow.
• Monday–Friday working hours: all lab and CSI operations are restricted to standard business hours, producing predictable queue build-up over weekends and shift boundaries.

Simulation of the current process over 500 trials (52 weeks each) shows a mean time in system of 10,970 minutes (7.6 days). Queue analysis identifies four major bottlenecks: the CSI visit queue (driven by end-of-shift batching), sample preparation queue (driven by shift patterns), DNA extraction (taking 2,880 minutes per run), and validation (shift-constrained). All four show regular oscillation in queue depth consistent with weekly shift patterns, and the CSI visit queue shows an additional seasonal peak in early summer.

Part 3 — Five improvement scenarios

Each scenario modifies specific stages of the baseline process. Scenarios build cumulatively: Scenario 5 combines all modifications from Scenarios 2, 3, and 4.

Scenario 1 — Rapid DNA sequencer. Replaces the legacy batch sequencer (2 days, 100 samples) with a Rapid DNA machine (2 hours, 8 samples). The sequencer schedule shifts from twice-weekly batches to continuous availability Monday–Friday 09:00–17:00. Mean time in system falls from 7.6 days to 5.1 days. The main remaining constraint is the end-of-shift transport window.

Scenario 2 — Addition of courier. Introduces a courier who collects samples from crime scenes continuously (Uniform[60,120] minutes, Mon–Fri 08:00–16:00) rather than waiting for CSIs to return at shift end. This removes the bimodal transport queue distribution caused by the fixed 16:00 collection window. Mean time in system falls to 3.5 days. The CSI bottleneck persists upstream.

Scenario 3 — 24-hour CSI operations. Extends CSI coverage to 24/7. This eliminates the primary bottleneck: the CSI visit queue distribution transforms from heavily right-skewed with outliers exceeding 7,000 minutes to one concentrated below 500 minutes — the single most impactful individual change across all scenarios. Mean time falls to 2.9 days, placing many samples near the 48-hour threshold that matters most for arrest probability.

Scenario 4 — 24-hour lab operations. Runs sample prep, sequencing, and validation 24/7 while retaining standard CSI hours. Eliminates sample preparation and validation queues and substantially narrows the sequencer queue. Mean time falls to 2.4 days, though the upstream CSI bottleneck limits further gain.

Scenario 5 — Full 24/7 operations. Combines Scenarios 3 and 4. Eliminates every schedule-induced queue simultaneously. Mean time falls to 0.6 days (under 15 hours). All queue distributions compress to near-zero spread. In every simulation trial, 100% of samples were processed within 2 days.

Time in system across all scenarios

ROI analysis — two methods

The ROI metric is arrests per £1 million spent per year. Two independent methods were applied to assess investment effectiveness, motivated by the fact that average time in system alone is insufficient: arrest probability drops sharply at the 48-hour threshold, so the tail of the time distribution matters as much as the mean.

Method 1 — Average-based triangular distribution. The 500-trial mean time in system was used as the mode of a triangular distribution; the 95% CI bounds were used as upper and lower limits. Arrest probability was assigned by the golden-hour principle: 0.10 for matches within 0 days, 0.08 within 1 day, 0.05 within 2 days, and 0.02 for 3+ days. Assuming 5,000 DNA samples per year, expected arrests were divided by annual cost.

Method 2 — Monte Carlo simulation via @Risk. Matched-sample times-in-system from a single Simul8 trial were used directly. For each matched sample (2% match rate applied, reducing ~5,200 annual samples to ~100 matched cases), days elapsed were floored to determine the applicable arrest probability tier. A Bernoulli draw using RiskUniform(0,1) simulated whether arrest occurred. This was repeated for 10,000 @Risk iterations, producing a full ROI distribution per scenario including mean, median, and spread.

Method 1 and Method 2 use different units (Method 1 assumes all 5,000 samples match; Method 2 applies a realistic 2% match rate) but both consistently rank the scenarios in the same order. Scenario 1 is the only scenario that produces a lower ROI than the current process under both methods — the cost increase from £5m to £7m is not justified by Rapid DNA machines alone without the complementary operational changes that follow.

The @Risk distributions reveal a risk dimension absent from Method 1. The current process and Scenarios 1–2 retain significant probability mass near zero ROI, representing simulation iterations where almost all samples miss the golden-hour window entirely. Only Scenario 5 — where 100% of samples were processed within 2 days across every trial — eliminates this downside tail. Scenario 5 achieves a 5th–95th percentile range of 0.55–1.36 arrests/£m with no meaningful near-zero outcomes. An unreliable system is strategically harder to depend on than a consistently fast one.

Recommendation and practical considerations

Both methods consistently identify Scenario 5 as optimal. It delivers a 92% reduction in mean time in system (10,970 to 844 minutes), a maximum observed time under 30 hours compared to over 11 days currently, and a 127% improvement in arrest efficiency under Method 1. The cost increase from £5m to £11m is justified on both analytical and probabilistic grounds.

However, the report identifies several implementation constraints. 24/7 CSI and lab operations require approximately three rotating shifts, roughly tripling current headcount, with associated recruitment, training, and shift-premium costs not captured in the £11m annual operating figure. Rapid DNA machines carry significant capital expenditure plus per-cartridge running costs, and the 8-sample batch limit creates partial-batch inefficiency during low-crime periods. Rapid DNA is also explicitly less accurate than legacy sequencing, raising quality assurance requirements for evidence admissibility. The seasonal crime peak in early summer visible in the simulation data suggests flexible seasonal capacity planning would be more cost-effective than fixed 24/7 year-round staffing.

The recommended implementation path is phased: begin with Scenario 2 (£7.5m), add 24-hour lab coverage at Scenario 4 (£9.5m), then commit to full Scenario 5 (£11m) once operational confidence is established. This limits risk while delivering progressive ROI improvements at each stage.

Technical notes

All discrete-event simulations were run in Simul8 v31.0.4557 (licence 1106-8358-6492-9820-0241) for 500 trials with random number seed and random stream both set to 4517. The M/M/c analytical solution was derived by hand and verified against the Simul8 output. ROI Monte Carlo simulation used Palisade @Risk with 10,000 iterations. All comparison charts and boxplots were produced in R; scripts are available in the project GitHub repository. The baseline Simul8 file was provided by Dr. Mehdi Toloo as part of the coursework specification.