An adaptive job scheduling scheme for mesh-connected multicomputers

Allocating submeshes to jobs in mesh-connected multicomputers in an FCFS fashion leads to poor system performance because a large job at the head of the waiting queue can prevent the allocation of free submeshes to other smaller waiting jobs. However, serving jobs aggressively out-of-order can lead to excessive waiting delays for large jobs located at the head of the waiting queue. In this paper, we show that the ability of the job scheduling algorithm to bypass the head of the waiting queue should increase with the load, and we propose a scheduling scheme that can bypass the waiting queue head in a load-dependent adaptive fashion. Also, giving priority to large jobs because they are more difficult to accommodate is investigated. The performance of the proposed scheme has been compared to that of FCFS, aggressive out-of-order scheduling, and other previous job scheduling schemes. Extensive simulation results based on synthetic workloads and real workload traces indicate that our scheduling strategy is a good strategy when both average and maximum job waiting delays are considered. In particular, it is substantially superior to FCFS in terms of mean turnaround times, and to aggressive out-of-order scheduling in terms of maximum waiting delays.     

Analytical modelling of networks in multicomputer systems under bursty and batch arrival traffic

The hypercube and torus are two important message-passing network architectures of high-performance multicomputers. Analytical models of multicomputer networks under the non-bursty Poisson traffic have been widely reported. Motivated by the convincing evidence of bursty and batch arrival nature of traffic generated by many real-world parallel applications in high-performance computing environments, we develop a new and concise analytical model in this paper for hypercube and torus networks in the presence of batch message arrivals modelled by the compound Poisson process with geometrically distributed batch sizes. The average degree of virtual channel multiplexing is derived by employing a Markov chain which can capture the batch arrival nature. An attractive advantage of the model is its constant computation complexity independent of the network size. The accuracy of the analytical performance results is validated against those obtained from simulation experiments of an actual system.     

Comparative evaluation of contiguous allocation strategies on 3D mesh multicomputers

The performance of contiguous allocation strategies can be significantly affected by the type of the distribution adopted for job execution times. In this paper, the performance of the existing contiguous allocation strategies for 3D mesh multicomputers is re-visited in the context of heavy-tailed distributions (e.g., a Bounded Pareto distribution). The strategies are evaluated and compared using simulation experiments for both First-Come-First-Served (FCFS) and Shortest-Service-Demand (SSD) scheduling strategies under a variety of system loads and system sizes. The results show that the performance of the allocation strategies degrades considerably when job execution times follow a heavy-tailed distribution. Moreover, SSD copes much better than FCFS scheduling strategy in the presence of heavy-tailed job execution times. The results also reveal that allocation strategies that employ a list of allocated sub-meshes for both allocation and de-allocation exhibit low allocation overhead, and maintain good system performance in terms of average turnaround time and mean system utilization.     

Message latency in hypercubic computer networks with the bursty traffic pattern

An interconnection network is a crucial component of parallel computers because the overall system performance is very sensitive to the latency of messages delivered by the network to communicate among collaborating processors. This paper presents an analytical performance model to calculate message latency in circuit-switched hypercubic networks in the presence of bursty traffic pattern, which is a typical scenario for multimedia applications. A message in circuit switching may need a number of connection attempts before successfully setting up a path from source to destination. The proposed model uses the approach of superposing infinite bursty traffic streams to capture the effective traffic entering the network from a source node, which includes the traffic generated by the source and those due to many connection attempts. Results obtained from simulation experiments confirm that the proposed model exhibits a good degree of accuracy for various network sizes and under different operating conditions.     

An analytical model for torus networks in the presence of batch message arrivals with hot-spot destinations

Interconnection networks are hardware fabrics supporting communications between individual processors in multi- computers. The low-dimensional k-ary n-cubes （or torus） with adaptive wormhole switching have attracted significant research efforts to construct high-performance interconnection networks in contemporary multi-computers. The arrival process and destination distribution of messages have great effects on network performance. With the aim of capturing the characteristics of the realistic traffic pattern and obtaining a deep understanding of the performance behaviour of interconneetion networks, this paper presents an analytical model to investigate the message latency in adaptive-routed wormhole-switched torus networks where there exists hot-spot nodes and the message arrivals follow a batch arrival process. Each generated message has a given probability to be directed to the hot-spot node. The average degree of virtual channel multiplexing is computed by the GE/G/1/V queueing system with finite buffer capacity. We compare analytical results of message latency with those obtained through the simulation experiments in order to validate the accuracy of the derived model.     

Performance modelling of pipelined circuit switching in hypercubes with hot spot traffic

Pipelined Circuit Switching (PCS) has been suggested as an efficient switching method for supporting interprocessor communication in multicomputer networks due to its ability to preserve both communication performance and fault-tolerant demands in these networks. A number of studies have demonstrated that PCS can exhibit superior performance characteristics over Wormhole Switching (WS) under uniform traffic. However, the performance properties of PCS have not yet been thoroughly investigated in the presence of non-uniform traffic. Analytical model of PCS for common networks (e.g., hypercube) under the uniform traffic pattern has been reported in the literature. A non-uniform traffic model that has attracted much attention is the hot spot model which leads to extreme network congestion resulting in serious performance degradation due to the tree saturation phenomenon in the network. An analytical model for WS with hot spot traffic has been reported in the literature. However, to the best of our knowledge, there has not been reported any analytical model for PCS augmented with virtual channels in the presence of hot spot traffic. This paper proposes a model for this switching mechanism using new methods to calculate the probability of message header blocking and hot spot rates on channels. The model makes latency predictions that are in good agreement with those obtained through simulation experiments. An extensive performance comparison using the new analytical model reveals that PCS performs the same or in some occasions worse than WS in the presence of hot spot traffic.     

On the Performance of Parallel Matrix Factorisation on the Hypermesh

Most common multicomputer networks, e.g. d-ary h-cubes, are graph topologies where an edge (channel) interconnects exactly two vertices (nodes). Hypergraphs are a generalisation of the graph model, where a channel interconnects an arbitrary number of nodes. Previous studies have used synthetic workloads (e.g. statistical distributions) to stress the superior performance characteristics of regular multi-dimensional hypergraphs, also known as hypermeshes, over d-ary h-cubes. There has been, however, hardly any study that has considered real-world parallel applications. This paper contributes towards filling this gap by providing a comparative study of the performance of one of the most common numerical problems, namely matrix factorisation, on the hypermesh, hypercube, and d-ary h-cube. To this end, the paper first introduces orthogonal networks as a unified model for describing both the graph and hypergraph topologies. It then develops a generalised parallel algorithm for matrix factorisation and evaluates its performance on the hypermesh, hypercube and d-ary h-cube. The results reveal that the hypermesh supports matrix computation more efficiently, and therefore provides more evidence of the hypermesh as a viable network for future large-scale multicomputers.