Consider a FOG node that has a number of virtual machines allocated to multicore. Core $1$ has three different virtual machines VM$1,$ VM$2$ and VM$3.($Q$1=2,$ P$1=4),($Q$2=3,$ P$2=8)$ and $($Q$3=2,$ P$3=16)$ where Q$1,$ Q$2,$ Q$3$ are budgets for VM$1,$ VM$2,$ VM$3$ respectively and P$1,$ P$2,$ P$3$ are periods of VM$1,$ V$2,$ VM$3.$ VM$1$ has three periodic tasks $\backslash$tau $1,\backslash$tau $2,\backslash$tau $3$ and each task is characterized by C$=$execution time, T$=$period and D$=$deadline. C$1=2,$ T$1=$D$1=8,$ C$2=3,$ D$2=$T$2=16,$ C$3=2,$ D$3=$T$3=32$ VM$2$ has two periodic tasks $\backslash$tau $4,\backslash$tau $5$ with parameters C$4=3,$ T$4=16,$ D$4=10,$ C$5=3,$ T$5=16$ and D$5=15.$ VM$3$ has one periodic task $\backslash$tau $6$ with parameters C$6=2,$ T$6=16,$ D$6=14$ Assume that the fixed priority$-$scheduling algorithm is used for all schedulers $($global and local$)$ and priorities are selected based on the deadline monotonic approach.

a$)$ Will all tasks meet their deadlines? Motivate your answer by drawing the execution trace of VMs and tasks.

b$)$ If we change the global level scheduler to EDF what will happen?

c$)$ If there are some tasks that miss their deadlines, what can be done to make them meet their deadlines without changing the given parameters of tasks and VMs$?$

d$)$Suppose that there is one more copy of VM$2$ and another one of VM$3$ and there are two cores available to execute the $5$ VMs$.$ How will you distribute the VMs so that all tasks meet their deadlines? Please

motivate your design.