Industry: Telecommunications and IT
Product: ModelRisk
Application: Network Capacity Planning

Pricing the year-3 backbone overflow: 800 Gbps today, but how much tomorrow?

A regional ISP runs an 800 Gbps backbone link carrying a 410 Gbps busy-hour mean. Demand has been growing at 18% per year and the team has to commit a three-year CapEx plan: hold the link, deploy a +400 Gbps upgrade to 1.2 Tbps, or jump straight to 1.6 Tbps. The deterministic forecast multiplied the mean load by 1.18³ × 1.7 and concluded that the year-3 peak would be roughly 1,145 Gbps — close enough to 1.2 Tbps that the engineering board nearly approved the +400 G plan and moved on. The Monte Carlo run told the board the peak's mean was 1,151 Gbps, the P90 was 1,402 Gbps, and that a 38% probability of busy-hour overflow remained even after the +400 G upgrade. The +800 G option moved that probability to under 2% for an extra $3.2M of CapEx — a number the deterministic forecast literally could not compute.

Two independent uncertainties compound

Capacity planning multiplies a growth uncertainty by a traffic-shape uncertainty, and both deserve a distribution:

• CAGR per year — Normal with mean 18% and standard deviation 5%. The 18% point estimate is the trailing-three-year average; the 5% spread is the year-to-year noise driven by streaming-product launches, IPTV penetration, and large-customer churn. Compounded over three years, the growth multiplier ranges from roughly 1.3× to 2.0× at the P10–P90.
• Peak-to-mean factor — Normal(1.70, 0.18), clipped to [1.1, 2.6]. Busy-hour peak is a multiple of mean load, but the multiple itself moves with the user mix: more streaming pushes the ratio higher and more elastic web traffic pushes it lower. Carriers commonly assume 1.7 deterministically; in our sample of 36 monthly observations the standard deviation was 0.18.

The two effects multiply, and multiplying two roughly-Normal random variables produces a right-skewed product. The deterministic mean × mean = 1,145 Gbps point estimate sits just above the P50 of 1,140 Gbps but well below the P90 of 1,402 Gbps, where the right tail of the product distribution lives.

What the headroom CDF says that the point estimate cannot

Headroom — deployed capacity minus the year-3 peak — is the operational metric the NOC actually cares about. Plotting the headroom CDF for each candidate deployment makes the trade-off direct.

• Hold at 800 Gbps — P(overflow) ≈ 98%; the P10 headroom is about −600 Gbps (i.e., the link is 600 Gbps short in the worst tenth of futures). Not a serious option.
• Upgrade to 1.2 Tbps — P(overflow) ≈ 38%; P10 headroom is about −200 Gbps. The link spends roughly two busy hours in five over the new limit.
• Upgrade to 1.6 Tbps — P(overflow) ≈ 2%; P10 headroom is about +200 Gbps. Comfortable for three years.

A deterministic comparison would have said "1.2 Tbps gives 55 Gbps headroom; that is enough." The Monte Carlo comparison says "1.2 Tbps still overflows nearly two busy hours in five, and you are buying a fix that does not fix the problem."

What actually drives the year-3 peak

Sensitivity ranking on the P90 peak load tells the team where to invest in forecasting accuracy.

The dominant lever is CAGR mean itself — moving the central forecast from 12% to 24% shifts the year-3 P90 by roughly 410 Gbps, more than one full 400-G upgrade increment. The peak-to-mean factor ranks second, at about 305 Gbps across its 1.5–1.9 range. A rare-event spike — a live sports rights launch or a new streaming service onboarding — adds another 80 Gbps to P90 even at a modest 8% per-year probability. The data investment that buys most P90 accuracy is therefore the one most ISPs do not make: a structured forecast of large-customer growth, not just port-utilisation extrapolation.

Mapping headroom to dollars

SLA credits to enterprise customers are linear in Gbps-hours of overflow at busy hour, at roughly $18 per Gbps-hour for this carrier. Multiplying simulated overflow by 1,800 busy hours per year, amortising CapEx over five years, and adding annual OpEx gives a total-annual-cost distribution for each option.

• Hold at 800 Gbps: mean annual cost ≈ $11.4M, P95 ≈ $22.2M — almost entirely SLA credit.
• +400 Gbps to 1.2 Tbps: mean ≈ $3.2M, P95 ≈ $10.6M. CapEx amortisation dominates the mean; the tail is the overflow that still occurs in adverse futures.
• Phased +400 G in y1, +400 G in y2: mean ≈ $2.6M, P95 ≈ $7.7M. Deferring half the CapEx avoids over-buying in the optimistic futures.
• +800 Gbps to 1.6 Tbps: mean ≈ $2.5M, P95 ≈ $2.5M. The tightest tail of the four — its mean is essentially its P95, because it removes nearly all overflow risk.

The decision the model framed: the phased option and the +800 G option have nearly identical means, but the +800 G option's P95 is $5.2M lower because it eliminates the futures where year-2 traffic explodes before the second upgrade lands. For an SLA-anchored carrier whose CFO penalises P95 surprises, the +800 G option is the dominant choice — and it is the choice the deterministic mean-only comparison would not have selected.

What changed

• Approved deployment switched from +400 G to +800 G after the P95 cost number replaced the mean-cost comparison.
• Quarterly CAGR re-forecast introduced, with the same Monte Carlo model re-run each quarter so the trigger for the next upgrade is a posterior-probability threshold (P(year-3 peak > 1.5 Tbps) crosses 25%) rather than a calendar date.
• Forecast investment redirected to large-customer growth modeling — the variable the tornado identified as the biggest mover of P90 peak.

ModelRisk functionality used

• Compounded normal growth with VoseNormal on per-year CAGR and explicit three-year compounding, so the year-3 multiplier inherits the right-skew that point-estimate multiplication erases.
• Two-factor multiplicative load model (mean load × peak-to-mean factor), each factor drawn independently, capturing the second-order variance that one-factor traffic forecasts ignore.
• Bernoulli × multiplier rare-event spike for the streaming-launch / live-event risk, sized from carrier history.
• Headroom CDF as the primary decision visual, so the comparison between deployments is read off the same axis the NOC monitors in production.
• Total-cost simulation combining amortised CapEx, OpEx, and overflow-driven SLA credit, returning a P95-vs-mean comparison the CFO recognises.

Backbone capacity is not a forecast number — it is a probability distribution that compounds growth uncertainty with traffic-shape uncertainty. Monte Carlo simulation in ModelRisk is what turns "we will probably be fine at 1.2 Tbps" into "we overflow one busy hour in three at 1.2 Tbps, and $3M more buys the tail."