1. Consider a system of 9 processes, P = {p1, ..., p10} Associated with the system are 6 memory cells, M = {M1, .., M6}. The domain and range for each process is given in the following table:

In addition, you are given the following precedence relation:

→ = {(1,2),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(4,7),(5,7),(5,8),(6,8),(6,9),(7,9),(8,9), (9,10)}

a. Construct the Precedence Graph (not containing any redundant edges)

b. Determine if the system above is determinate. If it is not, add to → necessary elements to make it determinate

c. Find the Maximally Parallel System

2. Linux Task Scheduling

The Linux scheduler repeatedly switches between all the running tasks on the system, attempting to give a fair amount of CPU time to each task. Fair-share scheduling is a strategy that shares the CPU among sets of processes according to the groups that own those processes. For example, suppose that Mary, Jane, and Sam belong to different groups and are logged in to a machine that uses fair-share scheduling. Suppose Mary has one runnable process, Jane has three, and Sam has six. Fair-share scheduling views the ten runnable processes in three groups, and each group receives one-third of the CPU

cycles allocated to the processes that it owns. Mary's single process would therefore get about 33% of the available CPU cycles, each of Jane's three processes would get roughly 11% of the available CPU cycles, and each of Sam's six processes would get about 5.5% of the CPU cycles. Suppose Jim belongs to Jane's group and he logs in to the machine and creates two more processes. Then Mary's single process would still get its 33% of the CPU and each of Sam's six processes would still get about 5.5% of the CPU. Jim and Jane together would have five processes that in total receive one-third of the CPU, so that each process would get about 6.7% of the CPU.

You are required to develop a new scheduling policy to support fair-share scheduling. It is called GRR, for group weighted round-robin scheduling. GRR should use fair-share scheduling based on each process's Linux group identification. At each invocation of the scheduler, we will use a hierarchical scheme to choose which task to run: first, a group is chosen, then, a task within that group's set is chosen. If we allow each group's chosen task the same amount of time on the CPU, each group should be represented equally.

Since we have to make two choices in each scheduling decision, we need two algorithms: one to choose the group and one to choose one of that group's tasks. Let's start by assuming we will use a Round-Robin scheme to decide which group to choose. We keep a queue of groups, and whichever group was chosen last time we scheduled, we choose the next group in the queue for this schedule. We then choose a task within this group's set of tasks (more on this later), and let it run for a fixed amount of time. Now every group gets an equal amount of CPU time at a relatively fine grain.

Now let's say that some groups are more equal than others. Imagine that we associate an integer, which we'll call a weight, with each group. We then modify the round-robin algorithm above so that we pick the same group for W time quanta (instead of a single time quantum), where W is the group's weight, before moving on to the next group in the queue. In this way, we can specify that some groups get more CPU time than others, and also how much more. A group with a weight of 3 will get 50% more CPU time than a group with weight 2. This is called proportional sharing. More specifically, this implementation of proportional sharing is called Weighted Round-Robin.

We still haven't specified how a task is to be chosen once we choose a group. For simplicity, use a simple round-robin (RR) scheduling algorithm to do that. The intragroup RR scheduler should use the same default timeslice as the Linux scheduler uses for a task with the default nice value. Otherwise, the RR scheduler should work the same as GRR except that it schedules tasks, not groups, and there are no different task weights.

In this homework, you are asked to implement a new task scheduler GRR as described above:

- Most of the code of interest for this assignment is in kernel/sched.c and include/linux/sched.h, and the main scheduler entry point is/are schedule() and pick_next_task(). These are probably not the only files you will need to look at, but they're a good start.

While there is a fair amount of code in these files, a key goal of this assignment is for you to understand how to abstract the scheduler code so that you learn in detail the parts of the scheduler that are crucial for this assignment and ignore the parts that are not.

- Implement group weights. Add two system calls, getgroupweight() and setgroupweight(), with the following prototypes:

int getgroupweight(int gid);

int setgroupweight(int gid, int weight);

getgroupweight() should return the weight of the specified group, or -1 on error. The default group weight should be 10.setgroupweight() should give the specified group the specified weight, and return 0, or -1 on error.

- Your scheduler should operate alongside the existing Linux scheduler. Therefore, you should add a new scheduling policy, SCHED_GRR. Only tasks whose policy is set to SCHED_GRR (normally done via the system callsched_setscheduler()) should be considered for selection by your new scheduler. Your scheduler and the existing scheduler should interoperate as follows:

o If there are any running tasks whose policy is SCHED_RR or SCHED_FIFO (these are real-time tasks), one of them should be chosen before any other, according to the existing Linux scheduler rules.

o If there are any running tasks whose policy is SCHED_NORMAL (the default scheduler), one of them should be chosen before any SCHED_GRR (your scheduler) tasks, according to the default scheduler's rules.

o If all running tasks have a policy of SCHED_GRR, your scheduler should be used to choose a task, according to the rules outlined.

In other words, there should be a strict priority relationship where SCHED_RR and SCHED_FIFO are first, SCHED_NORMAL andSCHED_BATCH are second, and SCHED_GRR is last.

- The user_struct structure in include/linux/sched.h is used for tracking users. This structure may be helpful in creating a useful way to keep track of user groups.

Create five users: Mary, Jane, Sam, Jim, and Pat. Assign Mary and Jane to the same group, Sam and Jim to the same group, and Pat to a separate group. Assign weights of 30, 10, and 10 to the respective groups. Create a simple test program that measures its own CPU usage as it runs and use it to show that your GRR scheduler behaves properly.

Prepare the tests before the demo and document your results in a writeup taken to the demo.