A process flow map for a hospital emergency room is given below. $($This example is closely based on an example in Introduction to Simulation and Risk Analysis by J$.$ R$.$ Evans and D$.$ L$.$ Note: Because there are only $10$ phone lines, the number of CS people plus the capacity of Line must be $10.$ Olson, Prentice Hall, $1998.)$ To simplify the map, a number of details have been left out, hence all the boxes in the map do not directly correspond to SimQuick elements. For this model, we focus on the night shift, from midnight to $8$ A$.$M$.$ During this time, patients arrive at the emergency room according to a fairly stable pattern: on average, they arrive every $15$ minutes according to an exponential distribution. A patient$$s first stop is the check$-$in desk. After describing their situation to the nurse, patients are sent to one of four locations: historically, $30\%$ are sent to the ambulatory area for immediate care, $20\%$ are sent for x$-$rays, $5\%$ are admitted directly to the hospital, and $45\%$ are sent for lab tests. Patients finishing at the ambulatory area are all released. Of patients finishing with their x$-$rays, $60\%$ are released, $10\%$ are sent for lab work, and $30\%$ are admitted to the hospital. Of patients finishing with their lab work, $10\%$ are admitted to the hospital and $90\%$ are released. In order to build a model for this process with SimQuick elements, we must add some detail to the process map. Clearly Door is an Entrance, and Release and Hospital are large Buffers. Ambulatory represents a Buffer, followed by a single Work Station. Each of the other three boxes represents a sequence of three elements: a large Buffer, followed by a single Work Station, followed by a Decision Point. These Buffers represent waiting areas. Work Stations are, of course, where the services are performed. The working times can be approximated as follows $($where we let time units represent minutes$)$: Work Stations Working Times Desk Nor$(3,\mathrm{.}1)$ Ambulatory Nor$(15,6)$ X$-$ray Nor$(15,3)$ Lab Nor$(30,6)$ Exercise $9$: a$.$ Build a SimQuick model for the emergency room process. Based on historical observations, we can assume there is initially one object in the Buffer before the lab Work Station and zero objects in the other Buffers. This model has a lot of uncertainty, so do $100$ simulations $($this will go faster if you click $$Other Features$$ and $$Hide Results Details$$; SimQuick will then write only the overall means on the Results worksheet$).$ Report the overall mean fraction time working $($also called the utilization$)$ for each Work Station and the overall mean cycle time for each Buffer in front of a Work Station. Which Work Station is a bottleneck according to these statistics $($i$.$e$.,$ has the highest values$)?$ b$.$ Management wants to know the effect of doubling the capacity of the bottleneck, that is$,$ adding an identical Work Station next to the exiting one in the model. With this additional element, rerun the model as in part a and report the same statistics. How has the bottleneck been affected? c$.$ Management also wants to know the effect on the original model of an increase in demand, where the time between arrivals drops to $10$ minutes, on average. Rerun the model as in part a and report the same statistics. How has the bottleneck Work Station been affected? Process Flow Map for a Hospital Emergency Room Door Desk Lab Ambulatory Hospital X$-$ray Release