Trio has two unique features: (1) it enables users to control shares of CPU time for any thread or group of threads (e.g., a process, an application, etc.), and (2) it enables fair sharing of CPU time across multiple CPUs. For example, with ten tasks running on eight CPUs, Trio allows each task to take an equal fraction of the total CPU time, whereas no existing scheduler achieves such fairness. These features enable Trio to complement the mainline scheduler and other proposals such as CFS and SD to enable greater user flexibility and stronger fairness.
Over the years, there has been a lot of criticism that conventional Unix priorities and the nice interface provide insufficient support for users to accurately control CPU shares of different threads or applications. Many have studied scheduling algorithms that achieve proportional fairness. Assuming that each thread has a weight that expresses its desired CPU share, informally, a scheduler is proportionally fair if (1) it is work-conserving, and (2) it allocates CPU time to threads in exact proportion to their weights in any time interval. Ideal proportional fairness is impractical since it requires that all runnable threads be running simultaneously and scheduled with infinitesimally small quanta. In practice, every proportional-share scheduling algorithm approximates the ideal algorithm with the goal of achieving a constant error bound. For more theoretical background, please refer to the following papers:
 A. K. Parekh and R. G. Gallager. A generalized processor sharing approach to flow control in integrated services networks: The single-node case. IEEE/ACM Transactions on Networking, 1(3):344-357, June 1993.
 C. R. Bennett and H. Zhang. WF2Q: Worst-case fair weighted fair queueing. In Proceedings of IEEE INFOCOM '94, pages 120-128, Mar. 1996.
Previous proportional-share scheduling algorithms, however, suffer one or more of the following problems:
Since the Linux scheduler has been successful at avoiding problems 2 to 4, this design attempts to extend it with support for accurate proportional fairness while retaining all of its existing benefits.
By default, each thread is assigned a weight proportional to its static priority. A set of system calls also allow users to specify a weight or reservation for any thread. Weights are relative. For example, for two threads with weights 3 and 1, the scheduler ensures that the ratio of their CPU time is 3:1. Reservations are absolute and in the form of X% of the total CPU time. For example, a reservation of 80% for a thread means that the thread always receives at least 80% of the total CPU time regardless of other threads.
The system calls also support specifying weights or reservations for groups of threads. For example, one can specify an 80% reservation for a group of threads (e.g., a process) to control the total CPU share to which the member threads are collectively entitled. Within the group, the user can further specify local weights to different threads to control their relative shares.
The scheduler keeps a set data structures, called Trio groups, to maintain the weight or reservation of each thread group (including one or more threads) and the local weight of each member thread. When scheduling a thread, it consults these data structures and computes (in constant time) a system-wide weight for the thread that represents an equivalent CPU share. Consequently, the scheduling algorithm, DWRR, operates solely based on the system-wide weight (or weight for short, hereafter) of each thread.
For each processor, besides the existing active and expired arrays, DWRR keeps one more array, called round-expired. It also keeps a round number for each processor, initially all zero. A thread is said to be in round R if it is in the active or expired array of a round-R processor. For each thread, DWRR associates it with a round slice, equal to its weight multiplied by a scaling factor, which controls the total time that the thread can run in any round. When a thread exhausts its time slice, as in the existing scheduler, DWRR moves it to the expired array. However, when it exhausts its round slice, DWRR moves it to the round-expired array, indicating that the thread has finished round R. In this way, all threads in the active and expired array on a round-R processor are running in round R, while the threads in the round-expired array have finished round R and are awaiting to start round R+1. Threads in the active and expired arrays are scheduled the same way as the existing scheduler.
When a processor's active array is empty, as usual, the active and expired arrays are switched. When both active and expired are empty, DWRR eventually wants to switch the active and round-expired arrays, thus advancing the current processor to the next round. However, to guarantee fairness, it needs to maintain the invariant that the rounds of all processors differ by at most one (when each processor has more than one thread in the run queue). Given this invariant, it can be shown that, during any time interval, the number of rounds that any two threads go through differs by at most one. This property is key to ensuring DWRR's constant error bound compared to the ideal algorithm (formal proofs available upon request).
To enforce the above invariant, DWRR keeps track of the highest round (referred to as highest) among all processors at any time and ensures that no processor in round highest can advance to round highest+1 (thus updating highest), if there exists at least one thread in the system that is in round highest and not currently running. Specifically, it operates as follows:
On any processor p, whenever both the active and expired arrays become empty, DWRR compares the round of p with highest. If equal, it performs idle load balancing in two steps: (1) It Identifies runnable threads that are in round highest but not currently running. Such threads can be in the active or expired array of a round highest processor, or in the round-expired array of a round highest - 1 processor. (2) Among those threads from step 1, move X of them to the active array of p, where X is a design choice and does not impact the fairness properties of DWRR. If step 1 returns no suitable threads, DWRR proceeds as if the round of processor p is less than highest, in which case DWRR switches p's active and round-expired arrays, and increments p's round by one, thus allowing all threads in its round-expired array to advance to the next round.
Whenever the system creates a new thread or awakens an existing one, DWRR inserts the thread into the active array of an idle processor and sets the processor's round to the current value of highest. If no idle processor exists, it starts the thread on the least loaded processor among those in round highest.
Whenever a processor goes idle (i.e., all of its three arrays are empty), DWRR resets its round to zero. Similar to the existing scheduler, DWRR also performs periodic load balancing but only among processors in round highest. Unlike idle load balancing, periodic load balancing only improves performance and is not necessary for fairness.Tong Li