All patients who arrive to the Emergency Department $($ED$)$ of Cleveland Clinic first go to Registration and then to Triage. Triage is staffed by two nurses: Alex and Dave. Triage is using a single line and patients are served on a first$-$come$-$first$-$serve basis.

a$.$ Patients arrive at an average of one every $20$ minutes, and their requests take on average $35$ minutes to be processed at Triage. Assume Poisson arrivals and exponential service times. What is the average waiting time for a patient?

Prepare for the VUT calculation.

$\backslash$table$[[\backslash$table$[[$a $($avg$.$ inter$-],[$arrival time$)]],\backslash$table$[[$s $($avg$.$ service$],[$time$)]],\backslash$table$[[m($number$],[$of servers$)]],\backslash$table$[[u($avg$.],[$utilization$)]],\backslash$table$[[C{V}_a($coef$.$ of$],[$var$.-$ arrival$)]],\backslash$table$[[C{V}_s($coef$.$ of$],[$var$.-$ service$)]]],[,,,,,]]$

Show the VUT calculation and final answer to the question:

b$.$ How many patients are waiting in line on average?

c$.$ Triage is considering creating two separate lines, the first for patients with surnames starting with a letter in the range A$-$M$,$ the second for N$-$Z$.$ Each line would have a Triage nurse dedicated to serving only that line of patients. What effect do you think creating these dedicated lines will have on the average waiting time experienced by patients at Triage? $($i$.$e$.,$ will the waiting time remain the same, increase or decrease?$)$ You may assume that the average patient arrival rates to each line would be roughly the same. Justify your answer.