Erlang C Calculator With Shrinkage

Erlang C Formula with Shrinkage Adjustment:

\[ \text{Effective Agents} = \frac{\text{Total Agents}}{1 - \text{Shrinkage}/100} \] \[ PW = \frac{\frac{A^{\text{Effective Agents}}}{\text{Effective Agents}!}}{\sum_{k=0}^{\text{Effective Agents}-1} \frac{A^k}{k!} + \frac{A^{\text{Effective Agents}}}{\text{Effective Agents}!}} \]

Wait Probability (PW):

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1. What is the Erlang C Calculator With Shrinkage?

The Erlang C Calculator With Shrinkage estimates the probability that a customer will have to wait for service in a call center or service system, accounting for agent unavailability due to shrinkage factors such as breaks, training, and absenteeism.

2. How Does the Calculator Work?

The calculator uses the Erlang C formula with shrinkage adjustment:

Where:

\( \text{Total Agents} \) — Number of scheduled agents
\( \text{Shrinkage} \) — Percentage of time agents are unavailable
\( A \) — Traffic intensity in Erlangs
\( \text{Effective Agents} \) — Adjusted number of available agents
\( PW \) — Probability of waiting

Explanation: The formula first adjusts the agent count for shrinkage, then calculates the probability that an incoming call will find all agents busy and have to wait in queue.

3. Importance of Wait Probability Calculation

Details: Accurate wait probability estimation is crucial for call center staffing, service level management, and customer satisfaction optimization in service systems.

4. Using the Calculator

Tips: Enter total scheduled agents (count), shrinkage percentage (0-99.99), and traffic intensity in Erlangs. All values must be valid positive numbers with shrinkage less than 100%.

5. Frequently Asked Questions (FAQ)

Q1: What is shrinkage in call center terms?
A: Shrinkage refers to the percentage of time that agents are not available to handle calls due to breaks, meetings, training, absenteeism, or other non-productive activities.

Q2: How is traffic intensity (A) calculated?
A: Traffic intensity in Erlangs is calculated as (call arrival rate × average handling time) / 3600, when time is measured in seconds.

Q3: What is a reasonable wait probability target?
A: Typical service level targets aim for 80% of calls answered within 20 seconds, which corresponds to a wait probability usually below 10-20% depending on the specific system.

Q4: Are there limitations to the Erlang C formula?
A: The formula assumes Poisson arrivals, exponential service times, infinite queue capacity, and that abandoned calls are negligible, which may not hold in all real-world scenarios.

Q5: How does shrinkage affect staffing requirements?
A: Higher shrinkage requires more total agents to maintain the same service level, as fewer agents are actually available to handle calls at any given time.