As  part  of  a  specific  disease  prevention  program,  a  clinic  is  considering  setting  up  a screening service in a town.  They are considering the following design:  After waiting in a single line, each walk-in patient is served by one of three available nurses.  Each nurse has their own booth, where the patient is first asked some medical health questions, then the patients vitals are taken, and finally, a glucose test is performed to check for the disease. In  this  design,  each  nurse  performs  the  tasks  in  sequence  for  the  patient.   If  the  glucose test indicates a chance of the disease, the patient is sent to a separate clerk to schedule an appointment for a follow-up at the clinic.  If the test is not positive, then the patient departs. Patients are eager to get tested but they are reluctant to wait for to screening operations.
To clarify, if the number of people waiting for nurses is larger than 4, they prefer to go to a park nearby the screening booths,  and spend 15 minutes therein.  After this 15 minute period they again return to booths to check if the number of people is acceptable or not. Noting that, there is no limit on the number of times for park visiting, i.e.  people are get screened eventually.
Patients  arrive  to  the  system  according  to  an  exponential  distribution  with  a  mean of  4  minutes.   Assume  that  there  is  a  5%  chance  that  the  glucose  test  will  be  positive.
For  the  given  design,  the  time  that  it  takes  to  have  the  paperwork  completed,  the  vitals taken,  and  the  glucose  tested  are  all  lognormally  distributed  with  means  of  6.5,  6.0,  and 5.5 minutes, respectively.  They all have a standard deviation of approximately 0.5 minutes. The  distribution  used  to  model  the  time  that  it  takes  to  schedule  a  follow-up  visit  is  a
WEIB(2.6, 7.3) distribution (in minutes).  Moreover, distance between park and screening booths requires a travel time of uniformly distributed between 1 and 2 minutes.
In addition, nurses are working based on a schedule (valid for just nurses, not the clerk). All breaks are given in a staggered manner that is, one nurse goes on break and immediately
upon  return  the  next  nurse  goes  on  break  until  all  nurses  have  had  their  breaks.   Nurses are  kind  people,  hence  they  wait  until  the  patient  they  are  testing  is  done  and  returns after  completing  their  scheduled  amount  of  time  for  the  breaks.   Assuming  the  screening
operations  start  at  8:00,  first  10  minute  breaks  should  be  given  starting  at  10:00.   Upon
completion  of  4  hours  of  work  (i.e.   at  12:00),  they  have  a  30  minute  lunch  break.   And
finally, at 15:00, they have one another small break session for 10 minutes.  The booths are
closed at 17:00.
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Collect statistics for queue length, queue time and utilization of the resources for 30
replications.
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State the average number of people screened as positive and negative.
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What are the average cycle times for positive and negative patients