A generalized sustainment network at the level of public doctrine and textbooks: 24 generic platforms, 8 maintenance teams, a supply depot fed by convoys, a 12-channel radio net and five sensor sites. No real system, unit or operation is modelled — this is the operations research behind readiness.
What you will learn
What operational availability (Ao) measures and how spare parts and repair queues drive it.
How Erlang’s formula sizes a radio net, and why reserving channels protects priority traffic.
Why supply planners count in days of supply, and how a closed route turns into grounded platforms.
Simulator
Time 0 h
✓Mission capable
🔧In maintenance
⧗Waiting for parts
◯Sensor coverage
Controls
Operating hours per platform per day. More tempo, more failures and fuel.
Out of 8 maintenance teams; the rest work on platforms.
Take a part from a platform already waiting for parts. Faster, but doubles the work.
Hours between supply convoys (fixed load per convoy).
Range grows with the fourth root of power; fuel use grows linearly.
Routine calls may not take the last r free channels.
Books one priority shipment: up to 4 open orders land within 24 h. Only one shipment can be in the air at a time, and each one counts against the transport budget.
Adds 4 channels after 3 h of setup; uses a little fuel.
Indicators
Operational availability
100%
normal
Days of supply
3.2d
normal
Surveillance coverage
95%
normal
Priority call blocking
0.9%
normal
Waiting for parts
0
In maintenance
0
Spares on hand
6
Parts on order
0
Backorders (parts owed)
0
Priority shipments used
0
Priority shipment in flight (hours left)
0 h
Depot stock
500 u
Routine call blocking
0.9 %
Fleet operating hours
0.0 h
Sensor sites up
5
Trend
Crisis scenarios
Level 1 · Readiness surge
An exercise more than doubles the demand for operating hours for four days. Spares are thin, routine resupply takes four days, and the transport budget covers two priority shipments. Deliver the hours without wrecking readiness, piling up backorders or jamming the radio net.
At least 790 fleet operating hours during the surge
Average operational availability ≥ 86 % from hour 30
Average backorders ≤ 2 over the last day
No more than 2 priority shipments (transport budget)
Average priority blocking ≤ 2 %
Average routine blocking ≤ 35 %
Level 2 · Supply route closed
A flood closes the only road to the depot for 60 hours. Convoys queue up behind it. Make the stock last without letting surveillance coverage collapse.
Depot never runs empty (hard limit)
Average surveillance coverage ≥ 89 %
At least 60 operating hours of missions before the road is cut
At least 440 fleet operating hours in total
At least 255 operating hours after the road reopens
Level 3 · Radio interference and sensor faults
Interference knocks out half of the radio channels. Twelve hours later two sensor sites fail. Keep priority traffic flowing and restore coverage.
Average priority blocking ≤ 3 %
Average coverage ≥ 88 % after the sensor fault
Average routine blocking ≤ 40 % (do not shut routine traffic out)
Average operational availability ≥ 80 %
Basis — the model behind the numbers
Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.
Operational availability: the share of time a system is ready, including logistics delay.
Platforms fail at random with an exponential time-to-failure while operating.
P(fail during h operating hours) = 1 − e^(−h/MTBF), MTBF = 40 h[2]Assumption: MTBF, part probability, burn rates and traffic are generic planning numbers, not data on any real system.
Palm’s theorem: with one-for-one resupply, parts in the pipeline follow a Poisson distribution.
Repairs wait in a queue served by a fixed number of teams.
c teams serve the maintenance queue (M/M/c); site teams + fleet teams = 8[9]Assumption: MTBF, part probability, burn rates and traffic are generic planning numbers, not data on any real system.
Days of supply: how long the depot lasts at today’s consumption.
DOS = stock / daily consumption[10]Days of supply is a planning measure used in sustainment doctrine; the ratio itself is simple arithmetic.
Erlang B blocking, and its exact extension when channels are reserved for priority traffic.
MTBF 40 operating h · part needed 40 % · repair Exp(6 h) · sites MTBF 300 h, repair Exp(8 h) · convoy 200 u · burn 1 u per operating h + 0.5 u/h per site at full power · relay +4 channels after 3 h · priority shipment: ≤ 4 open orders, lands within 24 h, one in flight at a time · ≥2 channels always open to routine trafficAssumption: MTBF, part probability, burn rates and traffic are generic planning numbers, not data on any real system.
Boolean coverage model: the chance a point is seen by at least one of several sensor discs.
coverage = 1 − exp(−Σ πR_i² / A)[8]Assumption: MTBF, part probability, burn rates and traffic are generic planning numbers, not data on any real system.
Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.
C. Palm — Analysis of the Erlang traffic formulae for busy-signal arrangements (Palm’s theorem on (S−1,S) pipelines) — Ericsson Technics No. 4, pp. 39–58, 1938