In a single server waiting line system with Poisson arrival and exponential service, as the average utilization increases, the average number in the system will increase.

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Quizplus · Accepted Answer

In a single server queue with Poisson arrivals and exponential service times (an M/M/1 queue), as the average utilization (ρ) increases, the average number of customers in the system (L) increases. This is because the system is busier, leading to longer queues and wait times. The relationship is given by L = ρ / (1 - ρ), showing that L increases as ρ approaches 1.

In a Single Server Waiting Line System with Poisson Arrival