Pricing a 48-hour deadline: DNA forensics simulation for West Yorkshire Police

01 · THE PROBLEMEvidence has a half-life

In a criminal investigation, time is not neutral. While a DNA sample sits in a queue, suspects move, witnesses' memories blur, connected evidence goes cold and cases lose momentum. That's why West Yorkshire Police set a target of returning DNA results within 48 hours — the window where a result still changes the outcome of an investigation rather than merely documenting it.

The trouble is that "be faster" is easy to say and expensive to buy. Rapid DNA machines promise quicker processing. Dedicated couriers promise quicker transport. Extending crime-scene investigator (CSI) shifts or running the laboratory around the clock promises fewer dead hours. Each lever costs real, recurring money — and nobody could say which combination actually delivers the deadline, because a forensics operation is a queueing system, and queueing systems punish intuition.

Why 48 hours matters

Arrest probability as a function of result turnaround — the curve the ROI model is built on

The 48-hour target sits on the steep part of the curve: every hour saved there buys real arrest probability, while hours saved past ~80 buy almost nothing. Curve shape representative of the study's objective function.

So the question was framed properly before any tool was opened: which configuration of equipment, staffing and shifts reliably hits 48 hours at the lowest cost per arrest? Not an opinion question. A simulation question.

02 · WHY SIMULATIONAverages lie about queues

You cannot answer this with averages. A lab where every stage averages comfortably under target can still miss the deadline constantly, because delay in a queueing system lives in the interactions — samples arriving in bursts, machines waiting for batches to fill, evidence collected at 11pm waiting for a shift that starts at 8am. The variance is the system.

The pipeline was therefore modelled as a discrete-event simulation in Simul8: every stage a sample passes through, and crucially, every queue it waits in between stages. Each simulated sample was tracked individually — time in each queue, time in each activity, total time in queues, total time in activities, overall time in system — because averages hide exactly the bottlenecks the study existed to find.

The forensics pipeline as a queueing system

Stages and queues from crime scene to usable result · bottleneck stages flagged

The two flagged stages — CSI shift coverage and sequencer batching — turned out to dominate total delay. Neither is the "slow machine" the procurement debate was nominally about.

Each scenario ran for 5,000 trials, enough for the min, max, mean and 95% confidence intervals of every metric to stabilise — so differences between scenarios reflect the system, not the dice. Sample-level results were exported to Excel for every run, and queue distributions visualised in Python with consistent axes, so a fat queue in one configuration couldn't hide behind a rescaled chart in another.

03 · SCENARIOSSix ways to run a forensics operation

#	Scenario	What changes	Cost profile
S1	Current process	The baseline — existing equipment, shifts and transport	—
S2	Rapid DNA machine	Faster processing technology, everything else unchanged	Equipment capex
S3	Rapid DNA + courier	Adds dedicated evidence transport	+ ongoing transport
S4	Rapid DNA + 24hr CSI	Crime-scene investigator coverage around the clock	+ staffing
S5	Rapid DNA + 24hr lab	Laboratory operation around the clock	+ staffing
S6	Full 24/7 operation	Both CSI and lab run continuously	Maximum

04 · RESULTSWhat 30,000 simulated samples revealed

The headline output is the distribution of total time-in-system per scenario — not the average, the whole shape, because the 48-hour target is a question about the tail:

Time-in-system distributions, all six scenarios

Density of total turnaround time across 5,000 trials per scenario · dashed line = 48-hour target

Illustrative 5,000-trial reconstruction of the study design — scenario orderings and findings match the original analysis; exact values live in the project outputs.

Probability of hitting the 48-hour target

Share of simulated samples completing within 48 hours, by scenario

The current process misses the deadline almost half the time. The Rapid DNA machine alone lifts that only modestly — the decisive jumps come from extending coverage at the binding constraints (S4, S5). Illustrative 5,000-trial reconstruction of the study design — scenario orderings and findings match the original analysis; exact values live in the project outputs.

Read those two charts together and the study's first big finding falls out: buying the fast machine, by itself, barely moves the tail. S2's distribution shifts left a little, but the long right tail — the missed deadlines — survives almost intact. Something other than processing speed was holding the system hostage.

05 · BOTTLENECKSThe queue forms before the machine

Decomposing time-in-system by stage shows exactly where the hours live, and why:

Where the hours go

Mean time per stage (including its queue), selected scenarios

In the current process, sequencing dominates — not because the machine is slow, but because samples wait for a batch to fill before anything runs. Add the Rapid DNA machine (S2) and most of that bar survives: the batching policy, not the chemistry, was the constraint. Illustrative 5,000-trial reconstruction of the study design — scenario orderings and findings match the original analysis; exact values live in the project outputs.

Two bottlenecks emerged, and neither was the headline technology:

Sequencer batching. Samples queue waiting for a batch to fill. A faster machine processes a full batch faster — but does nothing for the sample that waits twelve hours for the batch to exist. This is why S2 disappoints and why the 24-hour lab (S5) transforms the picture: continuous operation means batches fill and run around the clock.
CSI shift coverage. Evidence that can't be collected outside working hours can't be processed, however fast the lab is. A sample generated at 11pm has lost nine hours before the pipeline even sees it — which is what 24-hour CSI coverage (S4) buys back.

It's the oldest lesson in operations, rediscovered in a forensics lab: improving a non-bottleneck resource improves nothing.

06 · SENSITIVITYWhat actually moves the clock

Sensitivity analysis made the diagnosis quantitative, two ways: correlation-based tornado plots (which input variations correlate most with total system time) and parameter-sweep spider plots (how the outcome bends as each input moves through its range). Both agreed on the ranking:

Sensitivity of total time-in-system

Effect of varying each driver ±30% · ranking per the study's tornado & spider analysis, magnitudes representative

The punchline sits in the last bar: raw processing speed — the variable the procurement debate was about — ranked behind three logistics variables. Evidence in transit, results awaiting sign-off and collection hours bound the system.

07 · ROIFrom hours saved to arrests bought

Hitting 48 hours is a proxy; the real objective is arrests. So every scenario's 5,000 turnaround times were pushed through the arrest-probability curve from section 01 and a cost model, using Monte Carlo simulation in AtRisk — producing a distribution of returns per scenario rather than a single misleading point. The metric: additional arrests per additional £m spent, against the current process.

Return on each operating model

Additional arrests per 1,000 cases, per additional £m vs current process · bars = 25th–75th percentile, whisker dots = median, range = 5th–95th

S5 and S4 lead: they buy time exactly where the bottlenecks are. S6 delivers the most arrests in absolute terms but pays for capability the system doesn't fully convert. S2 — the machine alone — is the weakest investment in the set. Illustrative 5,000-trial reconstruction of the study design — scenario orderings and findings match the original analysis; exact values live in the project outputs.

The call

The recommendation was the mid-tier: pair Rapid DNA with extended coverage at the binding constraint (S4/S5), rather than buying the full 24/7 operation. The simulation's job was to stop the decision being framed as "fast machine: yes or no?" and reframe it as "which constraint is binding, and what does relaxing it return per pound?" That reframing is the deliverable.

08 · METHODThe analysis chain

From simulated queues to investable ROI

Three tools, each doing the one job it's best at

09 · TRANSFERWhy this matters beyond forensics

Swap "DNA samples" for "support tickets", "seller onboarding applications" or "order fulfilment" and the method transfers untouched: model the flow, find where the queue actually forms, price each intervention by its return — under uncertainty, not under best-case assumptions. It's the same discipline I use on growth funnels: the stage with the worst conversion isn't always the stage worth fixing; the binding constraint is. And the same humility applies — report distributions and confidence intervals, because a single-point ROI from a stochastic system is a fiction with a decimal place.

Stack: Simul8 (discrete-event simulation) · Excel · AtRisk / Palisade (Monte Carlo ROI) · Python (pandas, matplotlib, seaborn) · University of Surrey, Operational Analytics (MANM304)