In a single server, Poisson arrival, constant service time system with $\lambda=9$ per hour and ${ }^{\mu}=10$ per hour, $\mathrm{L}_{\mathrm{q}}$ will be equal to
A) 8.1
B) 4.05
C) 5.0
D) 9.0

Question

Quizplus · Accepted Answer

In a single server queue with Poisson arrivals and constant service time, the average number of customers in the queue ($L_q$) is given by $\frac{\lambda^2}{2\mu(\mu-\lambda)}$. Substituting $\lambda=9$ and $\mu=10$, we get $L_q = \frac{9^2}{2 \times 10 \times (10-9)} = 4.05$.

In a Single Server, Poisson Arrival, Constant Service Time System λ=9\lambda=9λ=9

In a Single Server, Poisson Arrival, Constant Service Time System $\lambda=9$