Waiting Line Design: A pediatric practice has $5$ physicians. Historically, patients were assigned to one physician and the same physician always treated these patients. For example, Alice$$s patients always visited her $($for $$well visits$$ and $$sick visits$)$ and never interacted with the other physicians. However, they have decided to change how they see patients. Now patients will be seen by whoever is available $($i$.$e$.,$ a working physician who is not busy treating other patients$).$ Assume that this "pooling" of physicians is ceteris paribus, that is$,$ it is the only change and there are no other changes. Based on our discussion of waiting lines, which of the three outcomes below are likely to occur due to this change?

i$)$ The coefficient of variation of patient inter$-$arrival times will increase

ii$)$ The utilization of each physician, u$,$ will increase

iii$)$ The average number of patients actually with a physician $($that is$,$inventory in process$,$ Ip$)$ will increase

Notes: This can be a challenging question. When you answer this question, think, ceteris paribus, how the proposed "pooling" change affects different parts of the system including the inter$-$arrival times, queues, service durations, and servers. $[$FYI$,$ c eteris paribus means other things remaining equal. So when the question talks about pooling physicians, we assume that this does not change anything else.$]$