If the customer population of a service system generates customers according to a Poisson distribution, the exponential distribution describes the probability that the next customer will arrive in the next T time periods.

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This statement is true. The Poisson distribution is often used to model the arrival rate of customers in a service system, while the exponential distribution describes the time between consecutive customer arrivals. Specifically, if the arrival rate of customers follows a Poisson distribution with parameter λ, the time between consecutive arrivals follows an exponential distribution with parameter λ. This makes the exponential distribution a natural choice for modeling the interarrival times in many service systems.

If the Customer Population of a Service System Generates Customers