Call Center Modeling

Probability · Axiom Academy

REAL WORLD Call Center Modeling Using the Poisson distribution to optimize staffing and customer service You're the operations manager for a customer service call center. Every day, you face a critical question: How many agents do you need on duty? Too few agents means long wait times and frustrated customers. Too many means wasted money on unnecessary staff. The answer lies in understanding when calls arrive—and that's where the Poisson distribution comes in. Live Call Arrivals (Next Minute) Notice how the number of calls varies even though the average rate stays constant. This randomness is exactly what the Poisson distribution models! Call arrivals are a classic example of a Poisson process . Each call arrives independently, at random times, with a constant average rate. The Poisson distribution tells us the probability of exactly k calls in a given time period. where λ (lambda) is the average arrival rate and k is the number of events Mean = λ: On average, λ calls per minute Variance = λ: The spread also equals λ Events are independent: One call doesn't affect the next Constant rate: Average doesn't change over the time period Probability of k calls in one minute The Poisson distribution assumes a constant rate λ. But in reality, call centers experience different volumes throughout the day. During peak hours, λ might be 8 calls per minute. Late at night, it might drop to 1 call per minute.

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