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6OQ(d)

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Operations And Supply Chain Management
Found in: Page 345
Operations And Supply Chain Management

Operations And Supply Chain Management

Book edition 14th
Author(s) F. Robert Jacobs
Pages 800 pages
ISBN 9780078024023

Short Answer

Question: Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

d. What are the probability that an arriving student (just before entering the Administrative Services Office) will me and at least one other student waiting in line?

Answer

Probability is when a few clients ask for benefits at roughly the same time. This surge of clients incidentally over-burdens the benefits framework, creating a tube.

Holding up line models that survey benefit frameworks' execution ordinarily expect customers to arrive concurring to Poisson likelihood dissemination, and an exponential conveyance describes benefit times. The Poisson transportation indicates that many clients will come at a given time (per hour). The exponential passage portrays the benefit times as the probability that a specific benefit time will be less than or break even with a given time.

See the step by step solution

Step by Step Solution

Step 1: Probability formula  

Step 1: Probability formula

The required probability is calculated using the following formula:

Where   is the probability that n students waiting in the line

Step 2: Probability that an arriving student (just before entering the Administrative Services Office)    

Step 2: Probability that an arriving student (just before entering the Administrative Services Office)

The probability of at least one student standing in the line when another student arrives (which means there are total 2 students in the system) is

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