GATE Papers >> Mechanical >> 2016 >> Question No 130

Question No. 130 Mechanical | GATE 2016
In a single-channel queuing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is _______ minutes.

Answer : 2.4 : 2.6


Solution of Question No 130 of GATE 2016 Mechanical Paper

$ \begin{array}{l}\mathrm\lambda=12\\\mathrm\mu=24\\\mathrm\rho=\frac{\mathrm\lambda}{\mathrm\mu}=\frac{12}{24}=0.5\end{array} $

Little's law,

$ \begin{array}{l}{\mathrm L}_\mathrm q={\mathrm{λW}}_\mathrm q\\{\mathrm W}_\mathrm q=\frac{{\mathrm L}_\mathrm q}{\mathrm\lambda}\\{\mathrm W}_\mathrm q=\frac{\mathrm\rho^2}{\mathrm\lambda\left(1-\mathrm\rho\right)}\\{\mathrm W}_\mathrm q=\frac{\left(0.5\right)^2\times60}{12\times\left(1-0.5\right)}=2.5\mathrm{minutes}\end{array} $

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