Correct Answer - Option 1 : 3 Customer
Concept:
No. of customers in the system, \({L_S} = \frac{λ }{{μ - λ }}\)
No. of customers in the queue, \({L_q} = \frac{{{λ ^2}}}{{μ \left( {μ - λ } \right)}}\)
λ = arrival rate, μ = service rate
Calculation:
Given:
λ = 1/8 per minute, μ = 1/6 per minute
Number of customers in the queue,
\({L_q} = \frac{{{λ ^2}}}{{μ \left( {μ - λ } \right)}}\)
\({L_q} = \frac{{{(\frac18) ^2}}}{{\frac16 \left( {\frac16 - \frac18 } \right)}}\)
\(L_q= \frac{\frac{1}{64}}{\frac{1}{6}\times\frac{1}{24} }\)
\(L_q=\frac{24\times6}{64}=2.25\) (rounding off to next integer we get Lq = 3)
