Calculator inputs
Model four unknown cloud traffic links with a 4 × 4 coefficient matrix and deployment planning options.
Example data table
Use this sample to validate the solver. It represents four cloud links constrained by balance equations and capacity planning assumptions.
| Equation or link | x1 | x2 | x3 | x4 | Target / capacity |
|---|---|---|---|---|---|
| Gateway A balance | 1 | 1 | -1 | 0 | 110 |
| Gateway B transfer | 0 | 1 | 1 | -1 | 60 |
| Region C conservation | 1 | -1 | 0 | 1 | 30 |
| Backbone demand equation | 2 | 0 | 1 | 1 | 200 |
| x1 capacity | Edge ingress link | 110 Gbps | |||
| x2 capacity | Core transit link | 130 Gbps | |||
| x3 capacity | Cache distribution link | 90 Gbps | |||
| x4 capacity | Egress delivery link | 95 Gbps | |||
Formula used
Core linear algebra model: A × x = b, where A is the traffic coefficient matrix, x is the unknown link-flow vector, and b is the demand or balance vector.
Solution method: x = A-1b when det(A) ≠ 0. This page uses Gauss-Jordan elimination to solve the matrix safely without requiring manual inversion.
Adjusted design flow: Adjusted flow = Raw flow × Peak multiplier × (1 + protocol overhead) × (1 + reserve margin).
Utilization: Utilization (%) = (Adjusted flow ÷ Link capacity) × 100.
Transfer estimate: Transfer (TB) = Adjusted flow × hours × 3600 ÷ 8 ÷ 1000.
Cost estimate: Estimated cost = Adjusted flow × cost per Gbps.
How to use this calculator
- Enter the 4 × 4 coefficient matrix that represents your traffic conservation or routing equations.
- Enter the right-side balance targets for each equation.
- Set link capacities, protocol overhead, reserve margin, peak multiplier, cost, and time horizon.
- Click Solve traffic network to compute unknown flows and design values.
- Review determinant, utilization, residual checks, and the chart to confirm model quality.
- Export the final report as CSV or PDF for planning, review, or stakeholder sharing.
Frequently asked questions
1) What does this calculator solve?
It solves four unknown traffic-link values from four simultaneous linear equations. This fits cloud routing, bandwidth balancing, peering analysis, cache distribution, and capacity planning scenarios.
2) Why is the determinant important?
A non-zero determinant means the matrix has one unique solution. If it is zero or nearly zero, your traffic equations are dependent or conflicting.
3) What are residuals telling me?
Residuals measure equation error after solving. Values near zero show the calculated traffic flows satisfy the original balance equations accurately.
4) Why add protocol overhead and reserve margin?
Raw flows rarely represent final design demand. Overhead covers framing or tunneling costs, while reserve margin adds headroom for resilience, scaling, and burst tolerance.
5) Can I use negative coefficients?
Yes. Negative coefficients are normal when one link removes traffic from a junction balance equation or represents traffic leaving a node.
6) What if utilization exceeds 100%?
That means the adjusted design flow is higher than the configured link capacity. Increase capacity, reroute demand, or change reserve assumptions before deployment.
7) Is this only for hosting networks?
No. The same matrix model also works for road traffic, logistics, power-flow simplifications, packet routing, and other conservation-based network problems.
8) When should I trust the output?
Trust it when the matrix is invertible, the inputs match your real network topology, residuals are near zero, and the utilization pattern looks operationally realistic.