The optimal situation (in terms of minimizing the average number of customers in the queue) in an M/M/1 queuing system is when the arrival rate λ exactly equals the service rate μ.

Question

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In an M/M/1 queuing system, the optimal situation for minimizing the average number of customers in the queue occurs when the arrival rate λ is less than the service rate μ, not when they are equal. When λ < μ, the system can keep up with incoming customers, preventing the queue from growing indefinitely.

The Optimal Situation (In Terms of Minimizing the Average Number