$\begin{array}{l}
\begin{array}{|l|l|}
\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\
\hline \text { High } & 3 \text { per hour } \
\hline \text { Low } & 5 \text { per hour } \
\hline
\end{array}
\end{array}$
$\begin{array}{|l|l|}
\hline Nurrber~ of~ servers:&5\
\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\
\hline
\end{array}$
What is the average time in line (in minutes) for a low priority item?
A) 2
B) 5
C) 24
D) 35
E) 54

Question

$\begin{array}{l}
\begin{array}{|l|l|}
\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\
\hline \text { High } & 3 \text { per hour } \
\hline \text { Low } & 5 \text { per hour } \
\hline
\end{array}
\end{array}$
$\begin{array}{|l|l|}
\hline Nurrber~ of~ servers:&5\
\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\
\hline 
\end{array}$
What is the average time in line (in minutes) for a low priority item?
A) 2
B) 5
C) 24
D) 35
E) 54

Quizplus · Accepted Answer

The average time in line for a low priority item is given by:$W_q = \frac{\lambda_L}{\mu(\mu - \lambda_H - \lambda_L)}$where:$\lambda_L$ is the average arrival rate for low priority items$\lambda_H$ is the average arrival rate for high priority items$\mu$ is the service ratePlugging in the given values, we get:$W_q = \frac{5}{2(2 - 3 - 5)} = 24$ minutes

Nurrber of servers:5Service rate:2 per hour (exponential service times)\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}Nurrber of servers:Service rate:​52 per hour (exponential service times)​​

$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$