In the M/M/1 model, is it true that the probability of exactly k customers in the system always e...

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Question

In the M/M/1 model, is it true that the probability of exactly k customers in the system always exceeds the probability of ex

Answer 1

Answer #1

In M/M/1:

Considering λ as the arrival rate and µ as the service rate.

λ /µ gives us the ρ.

We know,

P_n=(ρ)P_n-1

In general , ρ is always <1.

So you can observe, P_k+1 will be ρ*P_k which clearly tells us that the probability of k customers always exceed the probability of k+1 customers.

Note: I tried my best in answering the question. It'd be appreciated if you leave an upvote.Thanks in advance.

Answer 2

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