We will work in teams to develop a queuing model and some answers to common requests for information regarding queues. We will use real$-$world class data gathered in Field Study $4.$ You will work in teams and develop answers to Parts $1$ and $2.$ If you missed this class, you will need to do this work on your own time.

CLASS DATA SET: FS$4$ data queues$-1.$xlsxOpen this document with ReadSpeaker docReader Download FS$4$ data queues$-1.$xlsxOpen this document with ReadSpeaker docReader

Part $1.$ Post an answer for both items $($a$)$ and $($b$)$ in writing as a text entry in the response.

item $($a$).$ We need to determine an hourly average arrival rate $($lambda$)$ from the class data set. Develop an answer to the first significant digit $($e$.$g$.,26\mathrm{.}5).$ Be sure you have the right answer for this.

item $($b$).$ You need to derive the hourly average service rate $($mu$)$ from the class data set. Develop an answer to the first significant digit $($e$.$g$.,26\mathrm{.}5).$ There is a correct answer.

Part $2.$ You MUST post an Excel file to show your answers to Part $2.$

From the attached queuing MMk model, assume that Wawa has a three$-$server operation $($that is$,$ three persons working at the deli counter$)$ and, using your answers developed from Part $1,$ then answer the following questions:

a$.$ What is Po$?$ express as a percentage. Refer to Table $11\mathrm{.}4.$ Round the ratio of lambda to mu to two significant digits $($e$.$g$.,1\mathrm{.}56).$ Then, interpolate to develop a value to a percentage expressed to one significant digit $($e$.$g$.,9\mathrm{.}6\%).$

b$.$ What is the probability that one customer is waiting? You have already done the hard work for item $($a$)$ above. You simply need to enter a value in cell C$23.$ Your answer should be a percentage expressed to one significant digit $($e$.$g$.,9\mathrm{.}6\%).$

c$.$ If the waiting cost per hour is $$100,$ and the service cost per channel per hour is $$45,$ what is total cost per hour for this operation? Express as a dollar amount per unit of time.