Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 04 customers per minute (exponential service times). If there are 4 servers, what is the probability of three or fewer customers in the system?

Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 04 customers per minute (exponential service times). If there are 4 servers, what is the probability of three or fewer customers in the system?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

please answer this for my review

Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 04
customers per minute (exponential service times).
If there are 4 servers, what is the probability of three or fewer customers in the system?

Expert Solution

Step 1

Given that,

Clients show up at a pace of one every moment. That is, $2 = 1$
The server can deal with 0.4 clients each moment. That is, $μ = 0.4$

The quantity of servers is 4. That is, $s = 4$

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