Erlang B Blocking Probability Calculator
Total traffic offered to the system (e.g., call arrival rate × average call holding time).
The number of available communication channels or resources.
Understanding the Erlang Calculator: Optimizing Telecommunication Systems
The Erlang calculator is a fundamental tool in telecommunications and queueing theory, used to predict the performance of systems where resources (like phone lines, customer service agents, or server capacity) are shared among multiple users. Named after A.K. Erlang, a Danish mathematician, these formulas help engineers and planners determine the number of resources needed to achieve a desired service level or to estimate the blocking or delay probability for a given system.
What is an Erlang?
An Erlang is a dimensionless unit of telecommunications traffic intensity. One Erlang represents the continuous use of one voice path or resource. For example, if a single phone line is busy for 30 minutes in an hour, it carries 0.5 Erlangs of traffic. More generally, it's calculated as:
Offered Traffic (Erlangs) = Call Arrival Rate (calls per unit time) × Average Call Holding Time (same unit of time)
For instance, if 10 calls arrive per hour, and each call lasts an average of 6 minutes (0.1 hours), the offered traffic is 10 × 0.1 = 1 Erlang.
The Erlang B Formula: Calculating Blocking Probability
The Erlang B formula is used in systems where calls are blocked (or lost) if all available resources (trunks/lines) are busy. There is no queueing; if a call cannot be immediately served, it is rejected. This is typical for traditional telephone networks where a busy signal is given.
Our calculator above uses the Erlang B formula to determine the probability that an incoming call will be blocked given a certain amount of offered traffic and a specific number of trunks.
Inputs Explained:
- Offered Traffic (Erlangs): This is the total amount of traffic that the system is expected to handle. It's a measure of how busy the system would be if it had infinite capacity.
- Number of Trunks/Lines: This refers to the number of parallel communication channels or resources available to serve the traffic.
Output Explained:
- Blocking Probability (Erlang B): This is the likelihood, expressed as a percentage, that an incoming call will find all trunks busy and therefore be blocked or lost. A lower percentage indicates better service.
Practical Applications of Erlang B:
- Telephony Network Design: Determining the optimal number of telephone lines or circuits required between exchanges to minimize call blocking.
- Call Center Capacity Planning (Outbound): Estimating how many outbound lines are needed to achieve a certain success rate for calls.
- Server Capacity Planning: For systems where requests are dropped if no server is immediately available.
Erlang C Formula (Brief Mention):
While our calculator focuses on Erlang B, it's important to know about Erlang C. The Erlang C formula is used for systems where calls are queued if all resources are busy, rather than being blocked. This is common in modern call centers where callers are put on hold until an agent becomes free. Erlang C helps calculate the probability of a call being delayed and the average waiting time.
Example Usage:
Imagine a small business with 10 Erlangs of offered traffic during its busiest hour. They currently have 12 telephone lines (trunks). Using the calculator:
- Offered Traffic: 10 Erlangs
- Number of Trunks/Lines: 12
The calculator would output a blocking probability. For these values, the blocking probability is approximately 10.48%. This means about 1 in 10 calls will get a busy signal. If the business wants to reduce this to, say, 5%, they would need to increase their number of trunks, and the calculator can help determine how many more are needed by iteratively testing values.
By understanding and utilizing the Erlang calculator, businesses and network administrators can make informed decisions to optimize their resource allocation, improve service quality, and manage costs effectively.