Blocking Probability Calculator

Interpreting blocking probability

Blocking probability B is the fraction of calls or jobs rejected immediately when all N circuits are busy. In a pure loss system, there is no queue, so B directly represents the lost-at-arrival rate. For example, B=0.02 means roughly 2 out of every 100 attempts are blocked under steady offered load.

Offered traffic and Erlangs

Offered traffic A in Erlangs measures average concurrent demand. It can be estimated as arrival rate × mean holding time. If 120 calls per hour arrive and the mean holding time is 3 minutes, then A ≈ 120×3/60 = 6 Erlangs. Increasing A raises congestion pressure nonlinearly, which is why small load growth can noticeably increase blocking.

Capacity sensitivity by circuits

Adding circuits reduces blocking, but the improvement depends on where you are on the curve. When N is small relative to A, each additional circuit can drop B sharply. When N is already generous, incremental circuits yield diminishing returns. The “Blocking vs circuits” plot helps you see where extra capacity still buys meaningful service quality.

Target grade of service benchmarks

Network engineering often uses target blocking levels such as 1%, 2%, or 0.5% depending on service expectations. A busy-hour voice trunk group may accept 2% blocking, while premium or safety-critical services push lower. Use the target field to evaluate whether your current A and N meet the desired grade of service before expanding capacity.

Planning with reverse solves

This calculator supports reverse planning in both directions. “Find circuits” returns the smallest N that achieves the chosen target blocking for a fixed A. “Find traffic” estimates the maximum A you can carry at fixed N while staying near the target. These modes convert service goals into concrete capacity or load limits for design reviews.

Exporting and auditing results

CSV exports preserve numeric precision for spreadsheets, sensitivity tables, and scenario comparisons. The PDF export produces a compact one-page summary suitable for approvals and documentation. For audits, record A, N, target, and computed B with a timestamp, then rerun the same inputs to reproduce results. Stable recursion prevents overflow at larger N, improving reliability for high-capacity planning cases.

FAQs

1) What assumptions does Erlang B make?

It assumes Poisson arrivals, exponential holding times, identical circuits, and no waiting room. If all circuits are busy, the arrival is blocked and lost immediately.

2) Why can blocking rise quickly with small traffic increases?

Congestion effects are nonlinear. Near capacity, a small increase in offered traffic pushes utilization higher and the probability of “all circuits busy” rises sharply.

3) What is “carried traffic” in the results?

Carried traffic approximates the successful load: A × (1 − B). It is the portion of offered demand that finds an available circuit in a loss system.

4) When should I use “Find circuits” mode?

Use it when you know expected offered traffic A and a blocking target. It returns the smallest circuit count that meets the target under the Erlang B model.

5) When should I use “Find traffic” mode?

Use it when circuits N are fixed and you need an estimated traffic limit for a chosen blocking target. It helps define safe operating load before upgrades.

6) Does this calculator work for queued systems?

No. Queued systems need waiting-time models such as Erlang C. This tool is for pure loss systems where blocked arrivals are cleared immediately.