Teaching CSIR NET Mock Test Series Mathematical Science Limited Waiting Space M/M/1, M/M/1, M/M/C, M/M/C, M/G/1
Consider an M/M/1 queuing model with arrival rate λ = 15 per hour and service rate μ = 45 per hour. Let N(t) denote the number of customers in the system at time t ∈ (0, ∞). Also let T1 and T2 be the amounts of time a customer spends in the queue and in the system, respectively. Then which of the following statements are true?
1
\(\displaystyle \lim _{t \rightarrow \infty} P(N(t)=1)=\frac{2}{9} \)
2
\(P\left(T_1>0\right)=\frac{1}{3} \)
3
\(E\left(T_1\right)=\frac{1}{90} \)
4
\(E\left(T_2\right)=\frac{1}{35}\)