On submesh allocation for 2D mesh multicomputers using the free-list approach: Global placement schemes

Abstract

Two global placement schemes for contiguous processor allocation in two-dimensional mesh-connected multicomputers are proposed in this paper. The first scheme gives preference to allocating a free peripheral submesh that has the largest number of mesh-boundary processors. This peripheral placement has for goal producing large leftover free submeshes, which can improve system performance. Another characteristic of this scheme is that it reduces the search space by halting the search process when a large-enough multicomputer corner submesh is found. The second proposed scheme considers allocation in the corners of all large-enough free submeshes and allocates a submesh that has the maximum number of allocated neighbors and multicomputer peripheral nodes. Using extensive simulations, we evaluated the proposed schemes and compared them with previous promising schemes. The simulation results show that the peripheral placement scheme produces the best average turnaround times, and its measured allocation and de-allocation times are smaller than those of the previous schemes. The second proposed scheme ranks overall second in terms of turnaround times, however it is last in terms of efficiency.

Introduction

Mesh-connected interconnection networks are widely used in current distributed memory parallel computers. This is mainly because they are regular, simple, easy to implement, and scalable. Both two-dimensional (2D) and three-dimensional (3D) meshes and tori have been used in recent commercial and experimental multicomputers, such as the Caltech Mosaic [4], the Intel Paragon [17], the IBM BlueGene/L [6], and the Cray XT3 [12].

In most processor allocation policies proposed in the literature for mesh-connected multicomputers, a parallel job is allocated a distinct submesh of processors of the size and shape it has requested. This can result in high external processor fragmentation, which occurs when free processors are not allocated to a parallel job because of the shape constraint. A recurring outcome in allocation studies is that contiguous allocation suffers from low overall system utilization [1], [10], [20]. It can reduce system utilization to levels unacceptable for government-audited systems in the USA [7]. Therefore, noncontiguous allocation policies have been proposed with the goal of increasing system utilization by allowing dispersed free processors to be allocated to a parallel job [2], [8], [20]. Another approach to improving system utilization is using job scheduling policies that are not strictly first-come-first-served. These policies consider allocation to recent jobs so as to decrease the number of idle processors [5], [14], [21].

Notwithstanding the ability of noncontiguous allocation to reduce, even eliminate, processor fragmentation, an advantage of contiguous allocation over noncontiguous allocation is that it isolates jobs from each other, which is useful for security and accounting reasons. For example, contiguous allocation is proposed for use in the IBM BlueGene/L for security reasons. Because of the sensitive nature of some of its applications a BlueGene/L job is allocated a partition of processors that is isolated from partitions allocated to other jobs [3].

Contiguous allocation for 2D meshes has received extensive interest in the literature. Several of the proposed policies use the first-fit approach to submesh selection [9], [11], [15], [24], [25]. In addition, a global compaction scheme was proposed [13]. This scheme considers allocation on the corners of all allocated submeshes along with the four corners of the mesh system, and attempts to compact allocated submeshes by selecting an allocation submesh that has the largest number of busy adjacent processors and mesh peripheral length. Also, a first-fit policy that supports compaction in a similar fashion was proposed [19]. It places the current request in a corner of the first large-enough free submesh that it finds. The corner chosen is one that also has the largest number of busy neighbors and mesh peripheral length. These two compacting policies have shown better queue waiting times than the previous strategies; they performed well in several studies [9], [13], [19]. By placing allocated submeshes together, compaction has for goal reducing processor fragmentation.

A transformation that can improve the performance of 2D submesh allocation schemes is switching the orientation of allocation requests [15]. This technique was adopted in many previous algorithms [9], [13], [19], [24], and it will be adopted in the algorithms proposed in this paper.

A common issue with the two previous compacting schemes is that they do not give strict priority to allocating peripheral submeshes. A submesh allocated inside the mesh can generate more free fragments than a peripheral allocated submesh. That is, peripheral placement is expected to produce larger leftover free submeshes, which should decrease processor fragmentation and increase system utilization, meaning a decrease in the average job waiting delays and turnaround times. In this paper, we propose an allocation policy that assigns a submesh with the largest number of multicomputer peripheral processors to the current request. An internal submesh is allocated only when no corner or boundary submesh can accommodate the current request, however the choice of the internal submesh is independent from the allocation states of adjacent processors. The allocation search space is reduced in this Maximal Peripheral Length (MPL) policy by halting the search process when a suitable mesh corner submesh is found. Another factor that contributes to the efficiency of MPL is that adjacency with busy processors is not an allocation factor. Such adjacency is considered fundamental in previous promising policies, where a busy-list is maintained and employed in computing the number of busy processors adjacent to candidate submeshes [1], [13], [19]. In addition to MPL, we propose a global compacting allocation policy that considers all possible request placements in the corners of the free submeshes, and allocates a candidate submesh that has the largest number of busy adjacent processors and multicomputer peripheral nodes. This is different from the previous global compacting scheme proposed in [13] in that the previous scheme considers allocation on the corners of all allocated submeshes, whereas the proposed scheme considers allocation in the corners of all free submeshes.

Using detailed simulations, we have compared the two proposed schemes to previous effective and efficient schemes. The simulation results show that the peripheral placement scheme produces the best average turnaround times, while being very efficient. The measured allocation and de-allocation times of MPL are smaller than those of the previous allocation schemes, including the simple first-fit scheme. The second proposed scheme ranks overall second in terms of turnaround times and last in terms of efficiency.

Because the relative performance of allocation algorithms can depend on the job scheduling scheme, we have considered First-Come-First-Served (FCFS) scheduling and non-FCFS scheduling schemes that allow bypassing the head of the FIFO job waiting queue. The simulation results show that job scheduling has substantial influence on the mean turnaround times and maximum waiting delays of jobs. That is, an effective job scheduling scheme should be used in conjunction with an effective submesh allocation scheme so as to obtain good system performance.

This paper is organized as follows. The following section contains relevant preliminaries. Section 3 contains a review of previous related allocation schemes. The proposed schemes are presented and analyzed in Section 4. Simulation results are presented in Section 5. Finally, conclusions are given in Section 6.