Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning real-time tasks on a heterogeneous multiprocessor platform comprising two different types of processors — such a platform is referred to as two-type platform. We present two linearithmic timecomplexity algorithms, SA and SA-P, each providing the follow- ing guarantee. For a given two-type platform and a given task set, if there exists a feasible task-to-processor-type assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type, then (i) using SA, it is guaranteed to find such a feasible task-to- processor-type assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding 2 a feasible task-to-processor assignment where tasks are not allowed to migrate between processors but given a platform in which processors are 1+α/times faster, where 0<α≤1. The parameter α is a property of the task set — it is the maximum utilization of any task which is less than or equal to 1.

A conjecture about provably good task assignment on heterogeneous multiprocessor platforms but with a stronger adversary

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a heterogeneous multiprocessor platform. We use an algorithm proposed in [1] (we refer to it as LP-EE) from state-of-the-art for assigning tasks to heterogeneous multiprocessor platform and (re-)prove its performance guarantee but for a stronger adversary.We conjecture that if a task set can be scheduled to meet deadlines on a heterogeneous multiprocessor platform by an optimal task assignment scheme that allows task migrations then LP-EE meets deadlines as well with no migrations if given processors twice as fast. We illustrate this with an example.

Provably good task assignment on heterogeneous multiprocessor platforms for a restricted case but with a stronger adversary

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a heterogeneous multiprocessor platform. We consider a restricted case where the maximum utilization of any task on any processor in the system is no greater than one. We use an algorithm proposed in [1] (we refer to it as LP-EE) from state-of-the-art for assigning tasks to heterogeneous multiprocessor platform and (re-)prove its performance guarantee for this restricted case but for a stronger adversary. We show that if a task set can be scheduled to meet deadlines on a heterogeneous multiprocessor platform by an optimal task assignment scheme that allows task migrations then LP-EE meets deadlines as well with no migrations if given processors twice as fast.

Task assignment algorithms for two-type heterogeneous multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising two different types of processors—such a platform is referred to as two-type platform. We present two low degree polynomial time-complexity algorithms, SA and SA-P, each providing the following guarantee. For a given two-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then (i) using SA, it is guaranteed to find such an assignment where the same restriction on task migration applies but given a platform in which processors are 1+α/2 times faster and (ii) SA-P succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which processors are 1+α times faster. The parameter 0<α≤1 is a property of the task set; it is the maximum of all the task utilizations that are no greater than 1. We evaluate average-case performance of both the algorithms by generating task sets randomly and measuring how much faster processors the algorithms need (which is upper bounded by 1+α/2 for SA and 1+α for SA-P) in order to output a feasible task assignment (intra-migrative for SA and non-migrative for SA-P). In our evaluations, for the vast majority of task sets, these algorithms require significantly smaller processor speedup than indicated by their theoretical bounds. Finally, we consider a special case where no task utilization in the given task set can exceed one and for this case, we (re-)prove the performance guarantees of SA and SA-P. We show, for both of the algorithms, that changing the adversary from intra-migrative to a more powerful one, namely fully-migrative, in which tasks can migrate between processors of any type, does not deteriorate the performance guarantees. For this special case, we compare the average-case performance of SA-P and a state-of-the-art algorithm by generating task sets randomly. In our evaluations, SA-P outperforms the state-of-the-art by requiring much smaller processor speedup and by running orders of magnitude faster.

Task Assignment Algorithms for Heterogeneous Multiprocessors

Consider the problem of assigning implicit-deadline sporadic tasks on a heterogeneous multiprocessor platform comprising a constant number (denoted by t) of distinct types of processors—such a platform is referred to as a t-type platform. We present two algorithms, LPGIM and LPGNM, each providing the following guarantee. For a given t-type platform and a task set, if there exists a task assignment such that tasks can be scheduled to meet their deadlines by allowing them to migrate only between processors of the same type (intra-migrative), then: (i) LPGIM succeeds in finding such an assignment where the same restriction on task migration applies (intra-migrative) but given a platform in which only one processor of each type is 1 + α × t-1/t times faster and (ii) LPGNM succeeds in finding a task assignment where tasks are not allowed to migrate between processors (non-migrative) but given a platform in which every processor is 1 + α times faster. The parameter α is a property of the task set; it is the maximum of all the task utilizations that are no greater than one. To the best of our knowledge, for t-type heterogeneous multiprocessors: (i) for the problem of intra-migrative task assignment, no previous algorithm exists with a proven bound and hence our algorithm, LPGIM, is the first of its kind and (ii) for the problem of non-migrative task assignment, our algorithm, LPGNM, has superior performance compared to state-of-the-art.

CPMD-mindful task assignment for NPS-F

The multiprocessor scheduling scheme NPS-F for sporadic tasks has a high utilisation bound and an overall number of preemptions bounded at design time. NPS-F binpacks tasks offline to as many servers as needed. At runtime, the scheduler ensures that each server is mapped to at most one of the m processors, at any instant. When scheduled, servers use EDF to select which of their tasks to run. Yet, unlike the overall number of preemptions, the migrations per se are not tightly bounded. Moreover, we cannot know a priori which task a server will be currently executing at the instant when it migrates. This uncertainty complicates the estimation of cache-related preemption and migration costs (CPMD), potentially resulting in their overestimation. Therefore, to simplify the CPMD estimation, we propose an amended bin-packing scheme for NPS-F allowing us (i) to identify at design time, which task migrates at which instant and (ii) bound a priori the number of migrating tasks, while preserving the utilisation bound of NPS-F.

Provably Good Task Assignment for Two-Type Heterogeneous Multiprocessors Using Cutting Planes

Consider scheduling of real-time tasks on a multiprocessor where migration is forbidden. Specifically, consider the problem of determining a task-to-processor assignment for a given collection of implicit-deadline sporadic tasks upon a multiprocessor platform in which there are two distinct types of processors. For this problem, we propose a new algorithm, LPC (task assignment based on solving a Linear Program with Cutting planes). The algorithm offers the following guarantee: for a given task set and a platform, if there exists a feasible task-to-processor assignment, then LPC succeeds in finding such a feasible task-to-processor assignment as well but on a platform in which each processor is 1.5 × faster and has three additional processors. For systems with a large number of processors, LPC has a better approximation ratio than state-of-the-art algorithms. To the best of our knowledge, this is the first work that develops a provably good real-time task assignment algorithm using cutting planes.

Task assignment optimization in SAP Extended WarehouseManagement

Nowadays in the world of mass consumption there is big demand for distributioncenters of bigger size. Managing such a center is a very complex and difficult taskregarding to the different processes and factors in a usual warehouse when we want tominimize the labor costs. Most of the workers’ working time is spent with travelingbetween source and destination points which cause deadheading. Even if a worker knowsthe structure of a warehouse well and because of that he or she can find the shortest pathbetween two points, it is still not guaranteed that there won’t be long traveling timebetween the locations of two consecutive tasks. We need optimal assignments betweentasks and workers.In the scientific literature Generalized Assignment Problem (GAP) is a wellknownproblem which deals with the assignment of m workers to n tasks consideringseveral constraints. The primary purpose of my thesis project was to choose a heuristics(genetic algorithm, tabu search or ant colony optimization) to be implemented into SAPExtended Warehouse Management (SAP EWM) by with task assignment will be moreeffective between tasks and resources.After system analysis I had to realize that due different constraints and businessdemands only 1:1 assingments are allowed in SAP EWM. Because of that I had to use adifferent and simpler approach – instead of the introduced heuristics – which could gainbetter assignments during the test phase in several cases. In the thesis I described indetails what ware the most important questions and problems which emerged during theplanning of my optimized assignment method.

The influence of memory in a threshold model for distributed task assignment

A nature inspired decentralised multi-agent algorithm is proposed to solve a problem of distributed task selection in which cities produce and store batches of different mail types. Agents must collect and process the mail batches, without a priori knowledge of the available mail at the cities or inter-agent communication. In order to process a different mail type than the previous one, agents must undergo a change-over during which it remains inactive. We propose a threshold based algorithm in order to maximise the overall efficiency (the average amount of mail collected). We show that memory, i.e. the possibility for agents to develop preferences for certain cities, not only leads to emergent cooperation between agents, but also to a significant increase in efficiency (above the theoretical upper limit for any memoryless algorithm), and we systematically investigate the influence of the various model parameters. Finally, we demonstrate the flexibility of the algorithm to changes in circumstances, and its excellent scalability.

Genetic Algorithm Approach for Solving the Task Assignment Problem

This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.

Solving the Task Assignment Problem with a Variable Neighborhood Search

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches all optimal solutions in a quite short amount of computational time.

Practical aspects of slot-based task- splitting dispatching in its schedulability analysis

Consider the problem of scheduling a set of sporadic tasks on a multiprocessor system to meet deadlines using a tasksplitting scheduling algorithm. Task-splitting (also called semipartitioning) scheduling algorithms assign most tasks to just one processor but a few tasks are assigned to two or more processors, and they are dispatched in a way that ensures that a task never executes on two or more processors simultaneously. A certain type of task-splitting algorithms, called slot-based task-splitting, is of particular interest because of its ability to schedule tasks at high processor utilizations. We present a new schedulability analysis for slot-based task-splitting scheduling algorithms that takes the overhead into account and also a new task assignment algorithm.

Unified overhead-aware schedulability analysis for slot-based task-splitting

Hard real- time multiprocessor scheduling has seen, in recent years, the flourishing of semi-partitioned scheduling algorithms. This category of scheduling schemes combines elements of partitioned and global scheduling for the purposes of achieving efficient utilization of the system’s processing resources with strong schedulability guarantees and with low dispatching overheads. The sub-class of slot-based “task-splitting” scheduling algorithms, in particular, offers very good trade-offs between schedulability guarantees (in the form of high utilization bounds) and the number of preemptions/migrations involved. However, so far there did not exist unified scheduling theory for such algorithms; each one was formulated in its own accompanying analysis. This article changes this fragmented landscape by formulating a more unified schedulability theory covering the two state-of-the-art slot-based semi-partitioned algorithms, S-EKG and NPS-F (both fixed job-priority based). This new theory is based on exact schedulability tests, thus also overcoming many sources of pessimism in existing analysis. In turn, since schedulability testing guides the task assignment under the schemes in consideration, we also formulate an improved task assignment procedure. As the other main contribution of this article, and as a response to the fact that many unrealistic assumptions, present in the original theory, tend to undermine the theoretical potential of such scheduling schemes, we identified and modelled into the new analysis all overheads incurred by the algorithms in consideration. The outcome is a new overhead-aware schedulability analysis that permits increased efficiency and reliability. The merits of this new theory are evaluated by an extensive set of experiments.

Assigning real-time tasks on heterogeneous multiprocessors with two unrelated types of processors

A preliminary version of this paper appeared in Proceedings of the 31st IEEE Real-Time Systems Symposium, 2010, pp. 239–248.

Real-time scheduling with resource sharing on uniform multiprocessors

Consider the problem of scheduling a set of implicit-deadline sporadic tasks to meet all deadlines on a uniform multiprocessor platform where each task may access at most one of |R| shared resources and at most once by each job of that task. The resources have to be accessed in a mutually exclusive manner. We propose an algorithm, GIS-vpr, which offers the guarantee that if a task set is schedulable to meet deadlines by an optimal task assignment scheme that allows a task to migrate only when it accesses or releases a resource, then our algorithm also meets the deadlines with the same restriction on the task migration, if given processors 4 + 6|R| times as fast. The proposed algorithm, by design, limits the number of migrations per job to at most two. To the best of our knowledge, this is the first result for resource sharing on uniform multiprocessors with proven performance guarantee.