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Question

For a single server with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?

A
6 per hour
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B
10 per hour
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C
12 per hour
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D
24 per hour
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Solution

The correct option is D 24 per hour Lq=queue length =ρ21−ρ = finite only when ρ<1 so using options (d), ρ=λμ=Arrival rateService rate=1224=12<1 For other options ρ≥1 & Lq can not be finite because when arrival rate is more than service rate queue will keep on increasing.

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