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

The correct option is A 24 per hour
λ=Arrival rate, μ=Service rate

When λ>μ,

queue length will keep on increasing and alternatively the system will fail.

When the λ<μ, system works and provides a steady state, finite queue length.

So μ>λ then only option (d) μ=24 per hour is correct.

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