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2/21/2016Collection – MBA675T303 Operations & Logistics in the (...…1/32CollectionUsers can Collect posts into a printable, sortable format. Collections are a good way to organizeposts for quick reading. A Collection must be created to tag posts.More HelpThread:Q9 Single Server WaitPost:Q9 Single Server WaitAuthor:Posted Date:January 12, 2016 8:41 PMStatus:Published9. Suppose the arrival rate for a singleserver singlechannel (line) queuingoperation is 20 per hour. The service time for this operation is 2 minutes percustomer. Calculate the following: the average number in the queue, theaverage number in the waiting line, the average time in the system, the averagetime in the queue, and the probability that an arriving customer will have towait to be served. Provide your analysis.Here are the following values followed by the calculations & reasons:λ (arrival rate) = 20/hourμ (service rate) = 2 min/customer which is 30/hour1. average number in queue: Lq=λ*Wqa. Lq= 20*.0667 = 1.33 customers2. average number in the waiting line: L (or Ls) =λ*Wa. L = 20*.1 = 2 customers3. average time in system: W =1/(μλ)a.W = 1/(3020) = .1 hour or 6 minutes4. average time in queue:Wq=λ/(μ*(μλ))a.Wq=20/(30*(3020)) = .0667 hours orapproximately 4 minutes5. Probability of a customer having to wait: P0 =(1λ/μ)a. P0 =(120/30) = .33 or a 33% chance of havingto wait.It’s obvious they can’t be figured in this order, as some of the first items needthe figures from the lower items. I set up all my equations and then plugged inJana McLendon
2/21/2016Collection – MBA675T303 Operations & Logistics in the (...…2/32(Post is Read)the numbers I had and began to figure all of them until they were complete.Thread:Q9 Single Server WaitPost:RE: Q9 Single Server WaitAuthor:Posted Date:January 16, 2016 9:15 AMStatus:Published(Post is Read)Hi Jana,Great job on the problem. You are spot on and I always get confused when itcomes to these problems when you have to solve other variables before you canuse those variable in the first question asked. In this case you needed to solvefor Wq before you could solve for Lq. Collecting all the data and then solving theproblems based on the available data makes this type of problem seem simple.You made this appear very simple just like the book does. But when I read theproblem(s), I can’t seem to get my head around all the data to understand whatinfo I have and what I need.Again, you made this seem very simple. Great Job!BillWilliam DempseyThread:Neubauer Q1Post:Neubauer Q1Author:Posted Date:January 15, 2016 12:01 AMStatus:Published