A single server Poisson arrival exponential service system with $\lambda / \mu

Question

A single server Poisson arrival exponential service system with $\lambda / \mu<1.0$ will always have a smaller queue length, as compared to a single server Poisson arrival exponential service system with same $\lambda$ and $\mu$ but limited system capacity.

Quizplus · Accepted Answer

A single server Poisson arrival exponential service system with $\lambda / \mu<1.0$ but unlimited capacity can potentially have a larger queue length compared to a system with the same $\lambda$ and $\mu$ but limited capacity, because the limited capacity system restricts the maximum number of entities in the system, thereby capping the queue length.

A Single Server Poisson Arrival Exponential Service System With λ/μ<1.0\lambda / \mu<1.0λ/μ<1.0

A Single Server Poisson Arrival Exponential Service System With $\lambda / \mu<1.0$