$4.$ Assume the following pseudocode is run by two threads at approximately the same time on a

single processor machine.

do$\_$something$()$; $//$ takes T unit time to execute $($T is less than C$)$

mutex$\_$lock$()$;

do$\_$something$\_$else$()$; $//$ takes no time to execute

mutex$\_$unlock$()$;

exit$()$; $//$ takes no time to execute

Assume also that a simple spin lock is used. The time required for acquiring this lock

$($mutex$\_$lock$)$ is A unit time and the time required for releasing it $($mutex$\_$unlock$)$ is also A unit

time. Context switch time is B unit time. A thread works at most C unit time before the context

switch happens $($i$.$e$.,$ time slice $($quantum$)=$ C$).$

a$)$ What would be the total completion time of the two threads in the best possible case?

$(10$ points$)$

b$)$ What would be the total completion time of the two threads in the worst possible case?

$(10$ points$)$

Hint: In both answers, the completion time is equal to a numerical value plus $2$T $($you do not know hence

do not need to specify the value of T$).$

Note: In your answer, please