Question

Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of two jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 3.2 hours and a standard deviation of 2 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs:

1. What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places.
   
   per hour
   
2. What is the mean service rate in jobs per hour? If required, round your answer to four decimal places.
   
   per hour
   
3. What is the average number of jobs waiting for service? If required, round your answer to three decimal places.
   
   
   
4. What is the average time a job waits before the welder can begin working on it? If required, round your answer to one decimal place.
   
   hours
   
5. What is the average number of hours between when a job is received and when it is completed? If required, round your answer to one decimal place.
   
   hours
   
6. What percentage of the time is Gubser's welder busy?
   
   % of the time the welder is busy.

Answer 1

a) mean arrival rate = 2/8 = 0.25
b) mean service rate = 1/3.2 = 0.3125
c)
L_q =

The average numberofjobs waiting for service: L2 2 1

= (0.25^2 * 2^2 + (0.25/ 0.3125)^2)/(2*(1 - 0.25/ 0.3125)

= 2.225

d)
Average time a job waits = L_q/lambda = 2.225 /0.25 = 8.9

e)

W_s = W_q + 1/mu

= 8.9 + 3.2

= 12.1

f)

lambda/mu = 0.8

hence 80%

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