Question

Pop-up Restaurant

Answer 1

Answer:

The answer is "Option F".

Explanation:

The arrival rate$(\lambda) = 10 \ / \ hour$

The service rate $(\mu) = 1 \ in \ 5 \ minutes = 12\ /\ hour$

The time of waiting at queue

$\frac{M}{\frac{M}{1}} \ queue, \ W_q, \\\\ \frac{M}{\frac{M}{1}} = \frac{\lambda}{ \mu \times (\mu - \lambda)}$

   $= \frac{10}{(12 \times (12 - 10))} \\\\ = 0.4167 \ hours \\\\ = 25 \ minutes$

 It was not a queue for $\frac{M}{\frac{M}{1}}$. This is a $\frac{G}{\frac{G}{1}}$ queue so because intercom or time intervals differ coefficient is given.

$\to c_a = 2.58\\\\\to c_e = 0.75$

$\to W_q , \frac{G}{\frac{G}{1}} = \frac{(c_{a}^2 + c_{e}^2)}{2} \times W_q \frac{M}{\frac{M}{1}}$

             $= \frac{(2.58^2 + 0.75^2)}{2} \times 25 \\\\ = \frac{(6.6564 + 0.5625)}{2} \times 25 \\\\ = 3.60945 \times 25\\\\ = 90.23625\\\\ = 90 \ minutes$

Therefore, the entire waiting time even before order is issued,

$\to W_s , \frac{G}{\frac{G}{1}} = W_q \frac{G}{\frac{G}{1}} + \text{Avg service time}$

             $=90+5\\\\=95 \ minutes$