Multiprocessor scheduling with practical constraints

The problem of scheduling tasks onto multiprocessor systems has increasing practical importance as more applications are being addressed with multiprocessor systems. Actual applications and multiprocessor systems have many characteristics which become constraints to the general scheduling problem of minimizing the schedule length. These practical constraints include precedence relations and communication delays between tasks, yet few researchers have considered both these constraints when developing schedulers. This work examines a more general multiprocessor scheduling problem, which includes these practical scheduling constraints, and develops a new scheduling heuristic using a list scheduler with dynamically computed priorities. The dynamic priority heuristic is compared against an optimal scheduler and against other researchers’ approaches for thousands of randomly generated scheduling problems. The dynamic priority heuristic produces schedules with lengths which are 10% to 20% over optimal on the average. The dynamic priority heuristic performs better than other researchers’ approaches for scheduling problems with the practical constraints. We conclude that it is important to consider practical constraints in the design of a scheduler and that a simple heuristic can still achieve good performance in this area

Improved Mixed-Integer Programming Models for Multiprocessor Scheduling with Communication Delays

We revise existing and introduce new mixed-integer programming models for the Multiprocessor Scheduling Problem with Communication Delays. At first, we show how to provably reduce the number of product variables necessary to explicitly linearize the so-called packing formulation that contains bilinear terms. Then, we reveal that the feasible region of almost all existing formulations contains redundant solutions and formulate new constraints in order to exclude these. At the same time, by exploiting further structural properties, the models are improved concerning their size, strength, and modeling complexity. The discussion of these improvements leads to new much more compact formulations which are then experimentally compared with each other and with other formulations from the literature. We set up a realistic scenario with a preprocessing of the task graphs, delivering the gained information equally to all the tested models and evaluate not only running times but also the obtained lower and upper bounds on the makespan objective for unsolved instances of a large scale benchmark set

Schedulability analysis of timed CSP models using the PAT model checker

Timed CSP can be used to model and analyse real-time and concurrent behaviour of embedded control systems. Practical CSP implementations combine the CSP model of a real-time control system with prioritized scheduling to achieve efficient and orderly use of limited resources. Schedulability analysis of a timed CSP model of a system with respect to a scheduling scheme and a particular execution platform is important to ensure that the system design satisfies its timing requirements. In this paper, we propose a framework to analyse schedulability of CSP-based designs for non-preemptive fixed-priority multiprocessor scheduling. The framework is based on the PAT model checker and the analysis is done with dense-time model checking on timed CSP models. We also provide a schedulability analysis workflow to construct and analyse, using the proposed framework, a timed CSP model with scheduling from an initial untimed CSP model without scheduling. We demonstrate our schedulability analysis workflow on a case study of control software design for a mobile robot. The proposed approach provides non-pessimistic schedulability results

Malleable Scheduling Beyond Identical Machines

In malleable job scheduling, jobs can be executed simultaneously on multiple machines with the processing time depending on the number of allocated machines. Jobs are required to be executed non-preemptively and in unison, in the sense that they occupy, during their execution, the same time interval over all the machines of the allocated set. In this work, we study generalizations of malleable job scheduling inspired by standard scheduling on unrelated machines. Specifically, we introduce a general model of malleable job scheduling, where each machine has a (possibly different) speed for each job, and the processing time of a job j on a set of allocated machines S depends on the total speed of S for j. For machines with unrelated speeds, we show that the optimal makespan cannot be approximated within a factor less than e/(e-1), unless P = NP. On the positive side, we present polynomial-time algorithms with approximation ratios 2e/(e-1) for machines with unrelated speeds, 3 for machines with uniform speeds, and 7/3 for restricted assignments on identical machines. Our algorithms are based on deterministic LP rounding and result in sparse schedules, in the sense that each machine shares at most one job with other machines. We also prove lower bounds on the integrality gap of 1+phi for unrelated speeds (phi is the golden ratio) and 2 for uniform speeds and restricted assignments. To indicate the generality of our approach, we show that it also yields constant factor approximation algorithms (i) for minimizing the sum of weighted completion times; and (ii) a variant where we determine the effective speed of a set of allocated machines based on the L_p norm of their speeds

Scalable parallel communications

Coarse-grain parallelism in networking (that is, the use of multiple protocol processors running replicated software sending over several physical channels) can be used to provide gigabit communications for a single application. Since parallel network performance is highly dependent on real issues such as hardware properties (e.g., memory speeds and cache hit rates), operating system overhead (e.g., interrupt handling), and protocol performance (e.g., effect of timeouts), we have performed detailed simulations studies of both a bus-based multiprocessor workstation node (based on the Sun Galaxy MP multiprocessor) and a distributed-memory parallel computer node (based on the Touchstone DELTA) to evaluate the behavior of coarse-grain parallelism. Our results indicate: (1) coarse-grain parallelism can deliver multiple 100 Mbps with currently available hardware platforms and existing networking protocols (such as Transmission Control Protocol/Internet Protocol (TCP/IP) and parallel Fiber Distributed Data Interface (FDDI) rings); (2) scale-up is near linear in n, the number of protocol processors, and channels (for small n and up to a few hundred Mbps); and (3) since these results are based on existing hardware without specialized devices (except perhaps for some simple modifications of the FDDI boards), this is a low cost solution to providing multiple 100 Mbps on current machines. In addition, from both the performance analysis and the properties of these architectures, we conclude: (1) multiple processors providing identical services and the use of space division multiplexing for the physical channels can provide better reliability than monolithic approaches (it also provides graceful degradation and low-cost load balancing); (2) coarse-grain parallelism supports running several transport protocols in parallel to provide different types of service (for example, one TCP handles small messages for many users, other TCP's running in parallel provide high bandwidth service to a single application); and (3) coarse grain parallelism will be able to incorporate many future improvements from related work (e.g., reduced data movement, fast TCP, fine-grain parallelism) also with near linear speed-ups