The expected waiting time is 1.2 minute
According the statement
We know that the kingman formula is
[tex]{ E(W) = \left ( \frac{p}{1-p} \right )\cdot \left ( \frac{ C_{a}^{2}+ C_{s}^{2} }{2} \right ) \cdot \mu_{s} }[/tex]
According to statement the mean value μs is 6 min.
Here the value of P is 6/36 = 1/6
And the value of ca and cs is 1
Substitute the values in formula then
[tex]{ E(W) = \left ( \frac{0.17}{1-0.17} \right )\cdot \left ( \frac{ 1^{2}+ 1^{2} }{2} \right ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( \frac{0.17}{0.83} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( 0.20} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = 1.22[/tex]
So, the expected waiting time is 1.2 minute
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