In theory, for a single server Poisson arrival exponential service waiting line system with server utilization less than 1 and unlimited source, the number of units in the system can be infinite.

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In a single server queue with Poisson arrivals, exponential service times, and server utilization (ρ) less than 1, the system can theoretically accommodate an infinite number of units because the probability of the system having a certain number of units decreases exponentially with the number of units, but never reaches zero. This means there's always a non-zero probability for the system to have any number of units, no matter how large.

In Theory, for a Single Server Poisson Arrival Exponential Service