The Erlang Loss Formula Calculator estimates the probability that a call or request is blocked in a system with a limited number of servers or lines, assuming there is no queue. This is also known as the Erlang B formula, commonly used in telecommunications, call centers, network design, and even traffic engineering. The calculator helps determine the efficiency and capacity needs of systems by identifying how likely it is for a user to experience service denial due to full capacity.
This calculator is especially useful for engineers and planners when designing infrastructure that must handle high volumes of demand without causing too much service disruption. Rather than guessing how many servers are enough, users can make data-backed decisions based on actual traffic patterns and acceptable loss thresholds.
formula of Erlang Loss Formula Calculator
Where:
B(E, N) = blocking probability (Erlang B)
E = total traffic offered (in Erlangs)
N = number of available servers or lines (integer)
n! = factorial of N
Σ = sum of all terms from k = 0 to N
This formula assumes:
- Calls are lost if all servers are busy (no queue)
- Traffic arrives randomly (Poisson process)
- Service times follow an exponential distribution
The output value, B(E, N), ranges from 0 to 1, where a lower value indicates better service availability.
Helpful Reference Table
Here’s a table with common traffic levels and the required number of servers to maintain a target blocking probability.
| Traffic (Erlangs) | Blocking Probability (B) | Required Servers (N) |
|---|---|---|
| 10 | 1% | 14 |
| 20 | 1% | 24 |
| 30 | 1% | 33 |
| 10 | 0.1% | 17 |
| 20 | 0.1% | 28 |
| 30 | 0.1% | 38 |
Use this as a quick guide when designing systems with specific service level targets. It avoids repeated manual calculations and gives a sense of how resources should scale with traffic.
Example of Erlang Loss Formula Calculator
Suppose you have a call center receiving an average of 12 Erlangs of traffic and want to know the blocking probability if there are 15 operators available.
Using the formula:
B(12, 15) = (12¹⁵ / 15!) / Σ (12ᵏ / k!) from k = 0 to 15
To solve this, you calculate:
- Numerator: 12¹⁵ / 15!
- Denominator: sum of (12ᵏ / k!) from k = 0 to 15
This results in:
B(12, 15) ≈ 0.0501
So, the probability that a caller will be blocked is about 5%. If this is too high for your service standards, you may need to add more operators.
Most Common FAQs
Erlang B shows the chance that a call or request will be blocked in a system with no waiting line. It is a common metric in telecom and customer service industries.
To lower the blocking probability, you can either reduce the incoming traffic (Erlangs) or increase the number of available servers or lines (N).
Erlang B assumes no queue — if all lines are busy, calls are lost. Erlang C assumes calls can wait in a queue until a server becomes available. Choose based on your system’s design.