$.$ Suppose you have a real$-$time OS on some computer controlling an autonmous train operating in

Vermont. The computer running this OS uses interrupts to interact with devices; it has $8$ priority

levels, $0.\mathrm{.}7,$ with $7$ the highest priority. One of the hard real$-$time requirements is that when a cow

event is detected, i$.$e$.,$ a foreign body of significant size on the tracks, the code that decelerates the

train must begin executing not later than $20$ ms after detection, and finish executing not later than

$1600$ ms after detection. The handler, itself, needs $1340$ ms to run. The detection is made known

first to the CPU via a priority $7$ interrupt.

$($a$)$ Assume the CPU has just finished an instruction, so is checking if there are any pending higher

priority interrupts and so instantly sees there is a priority $7$ interrupt to handle. If the OS takes

$14$ ms to save the current process context before beginning the handler for the interrupt, and

then x ms to switch to and begin executing the handler, what is the largest permitted value for

x if the start deadline is to be met?

$($b$)$ Suppose someone in management made a poor decision and chose to implement this realtime system on a general$-$purpose OS that uses virtual memory. This computer uses an ssd $($as

opposed to a hard drive$).$ The maximum time to service a page fault is $250$ ms$.$ For a worst$-$case

plan $($i$.$e$.,$ page fault$($s$)$ all take the maximum time$),$ how many page faults can be tolerated and

have the handler still meet its finish$-$by deadline?

$($c$)$ If the train is moving at $60$ mph when the event is first detected, how far does it move in the $20$

ms before the handler begins executing? $($or$,$ if you prefer, suppose the train is moving at $100$

kph$).$ Remember to provide correct units with your answer.