A Car Wash takes a constant time of 9.1 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 6 per hour. The owner wants to know:
a) The average waiting time in line.
b) The average length of the line.
c) The average utilization rate.
d) The average time in the system.
e) The average number of customers in the system.

Question

salman salih · Accepted Answer

Final Answer :  a to e)    Arrival rate  ( λ ) 6  Service rate  ( μ ) 6.59341  Number of servers  1  Average server utilization  ( ρ )  C  0.910  Average number of customers in the queue  ( L q )  B  4.601  Average number of customers in the system  ( L s )  E 5.511   Average waiting time in the queue  ( W q )  A  0.767  Average time in the system  ( W s )  D  0.918 \begin{array}{l}\begin{array} { | l | r | } \hline 	ext { Arrival rate } ( \lambda )  &  6 \\hline 	ext { Service rate } ( \mu )  &  6.59341 \\hline 	ext { Number of servers }  &  1 \\hline\end{array}\\\begin{array} { | l | l | } \hline 	ext { Average server utilization } ( ho )  &  	ext { C } 0.910 \\hline 	ext { Average number of customers in the queue } \left( \mathrm { L } _ { q } ight)  &  	ext { B } 4.601 \\hline 	ext { Average number of customers in the system } \left( L _ { s } ight)  &  	ext { E 5.511 } \\hline 	ext { Average waiting time in the queue } \left( W _ { q } ight)  &  	ext { A } 0.767 \\hline 	ext { Average time in the system } \left( W _ { s } ight)  &  	ext { D } 0.918 \\hline\end{array}\end{array}  Arrival rate  ( λ )  Service rate  ( μ )  Number of servers  ​ 6 6.59341 1 ​ ​  Average server utilization  ( ρ )  Average number of customers in the queue  ( L q ​ )  Average number of customers in the system  ( L s ​ )  Average waiting time in the queue  ( W q ​ )  Average time in the system  ( W s ​ ) ​  C  0.910  B  4.601  E 5.511   A  0.767  D  0.918 ​ ​ ​

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