CODEWITHSUNDEEP
mathcomputer-scienceprobabilitytheoryqueuing
ndr
ndr

Reputation: 21

Queuing Theory - I am not getting the correct answer to a question related to queuing theory. Please help :)

How come the answer to part (a) of the question (please refer to the link below) is 2.25?

[Question-related to queuing theory taken from the book "Operations Research Second Edition Richard Bronson Govindasami Naadimuthu"] [1]: https://i.sstatic.net/MJL36.png

When I am working out part (a) of this question I am getting 4 customers. Below is my workings:

λ = 30 per hr

μ = 40 per hr

p = 3/4

The average number of customers waiting for service = 1/ (1-p)

= 1/ (1 - 3/4) = 4 customers

What am I doing wrong? Can anybody please help me out?

Upvotes: 0

Views: 89

Answers (1)

Beta
Beta

Reputation: 99172

I don't know where you're getting that p formula, but it doesn't apply here, as you can tell by looking at an extreme case: suppose the clerk were extremely fast, making μ about 10^6. So nobody stays in the queue longer than the blink of an eye, it is almost always empty, the average number of people in it is barely above zero. But your p formula says it's just a sliver above 1.

The formula I find with a quick web search for the average number of customers waiting for service is:

L = λ2/[μ (μ - λ)]

I haven't figured out the derivation yet, but it passes a couple of sanity checks. And in this case it gives L=9/4.

Upvotes: 0

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