A Categorization of Real-Time Multiprocessor Scheduling Problems and Algorithms Presentation by Tony DeLuce CS 537 Scheduling Algorithms Spring Quarter Dr. Gilbert Young

Agenda Introduction Classification Relationships Conclusion

Introduction - Preliminary Real-time multiprocessor systems are now commonplace Problem of ensuring that deadline constraints of Uniprocessor systems has been widely studied In contrast, researchers are just beginning to understand the tradeoffs that exist in multiprocessor systems This presentation will present a classification and taxonomy for scheduling independent, periodic real-time tasks on a multiprocessor

Introduction

Introduction – Liu and Layland model Simplist model of a recurring process Task T is characterized by two parameters e – a worse case execution requirement p – a period Task T is invoked (known as a Job Release) at each non negative integer p Requires at most e units of processor time Must complete its execution in p units of time Collection of Periodic tasks is known as a Periodic Task System (denoted t)

Liu and Leyland - definitions Task system t is schedulable by an algorithm A if A ensures that the timing constraints of all tasks in t are met. t is said to be feasible under a class C of scheduling algorithms if t is schedulable by some algorithm A that is a member of C An algorithm A is said to be optimal with respect to class C if A is a member of C and A correctly schedules every task that is feasible under C Note: When C is not specified, it should be assumed to include all possible scheduling algorithms.

Classification of Scheduling Approaches

Two Traditional Approaches Partitioning Each task is assigned to a single processor Processors are scheduled independently Main advantage is reduces problem to a uniprocessor problem Problem is NP-HARD! Global Scheduling All eligible tasks are stored in single priority-ordered queue Global Scheduler selects highest priority tasks from this queue Unforunately using this with optimal uniprocessor algorithms may result in very low processor utilization But recent research on Pfair scheduling has shown considerable progress – optimal!

New “Middle” Approach also considered Each job is still assigned to a processor but tasks are allowed to migrate Interprocessor task migration is permitted only at job boundaries Resolves issue of low processor utilization to some extent In effort to understand cost of migration a classification was created that ranks scheduling schemes along two dimensions: Complexity of the Priority Scheme Degree of Migration Allowed

New Classification of Scheduling Approaches Complexity of the Priority Scheme Static Dynamic but fixed within a job Fully Dynamic Degree of Migration Allowed No Migration Migration allowed, but only at job boundaries Unrestricted Migration

9 Different Classes of Scheduling Algorithms Job preemption is permitted Two Axes of of Classification are orthogonal to each other in the sense that restricting an algorithm along one axis does not restrict freedom along the other Thus there are 3 x 3 = 9 different classes of Scheduling Algoithms in this Taxonomy

Migration-Based Classification Axis Interprocessor migration was traditionally forbidden in real-time systems for a number of reasons In many systems the cost of transferring a job from one processor to the next can be prohibitive (recent developments in very fast interconnection networks over small areas have reduced this concern somewhat) Until recently, traditional real-time scheduling lacked the techniques and tools to permit a detailed analysis Therefore Partitioning was preferred approach solely due to the nonexistence of viable alternative approaches

Degrees of Migration-Based Classification Axis No Migration Set of tasks partitioned into as many disjoint subsets as processors available Each subset is associated with a unique processor All jobs generated by the tasks in a subset must execute on the corresponding processor Same as Partition problem Restricted Migration Each job must execute entirely upon a single processor However, different jobs of the same task may execute upon different processors Job level context on unique processor but task-level context may be migrated Full Migration no restrictions of any kind

Degrees of Priority-Based Classification Static Priorities Unique Priority is associated with each task All jobs generated by a task have the priority associated with that task Job-level Dynamic Priorities for any pair of jobs Ji and Jj, if Ji has a higher priority than Jj at some instant in time, then Ji always has higher priority than Jj Unrestricted Dynamic Priorities No restrictions placed on priorities that may be assigned to jobs Relative Priority between jobs may change at any time

Two Definitions A scheduling algorithm is (x,y)-restricted for x is a member of {1,2,3} and y is a member of {1,2,3}, if it is in priority class x and migration class y An ordered pair denoted by denotes the set of task systems that are feasible under (x,y)-restricted scheduling

Table of Classification of Algorithms

Schedulability Relationships

Schedulability Relationships - Definitions The class of (w,x)-restricted algorithms is strictly more powerful than the class of (y,z)-restricted algorithms That is, any task system that is feasible under (y,z)-restricted class is also feasible under the (w,x)-restricted class Furthermore, there exists at least one task system that is feasible under the (w,x)-restricted class but not under the (y,z)-restricted class

Schedulability Relationships Definitions The class of (w,x)-restricted algorithms and the class of (y,z)- restricted algorithms are equivalent That is, a task system is feasible under the (w,x)-restricted class if and only if it is feasible under the (y,z)-restricted class The class of (w,x)-restricted algorithms and the class of (y,z)- restricted algorithms are incomparable That is, there exists at least one task system that is feasible under the (w,x)-restricted class but not under the (y,z)-restricted class, and vice-versa

Table of Scheduling Relationships

Relationships among Classes

Conclusion

This presentation detailed a new taxonomy of scheduling algorithms for scheduling preemptive tasks on multiprocessors. We described new classes of scheduling algorithms and considered the relationship of these classes to each other