Byung S. Yoo

FORECASTING AND TESTING IN CO-INTEGRATED SYSTEMS*

Abstract This paper examines the behavior of forecasts made from a co-integrated system as introduced by Granger (1981), Granger and Weiss (1983) and Engle and Granger (1987). It is established that a multi-step forecast will satisfy the co-integrating relation exactly and that this particular linear combination of forecasts will have a finite limiting forecast error variance. A simulation study compares the multi-step forecast accuracy of unrestricted vector autoregression with the two-step estimation of the vector autoregression imposing the co-integration restriction. To test whether a system exhibits co-integration, the procedures introduced in Engle and Granger (1987) are extended to allow different sample sizes and numbers of variables.

A fast and efficient processor allocation scheme for mesh-connected multicomputers

Efficient processor allocation is crucial for obtaining high performance in space-shared parallel computers. A good processor allocation algorithm should find available processors for incoming jobs, if they exist, with minimum overhead. In this paper, we propose such a fast and efficient processor allocation scheme for mesh-connected multicomputers. By using simple coordinate calculation and spatial subtraction, the proposed scheme reduces the search space drastically and, hence, can locate a free submesh very quickly. The algorithm is implemented efficiently using a stack and therefore is called the stack-based allocation (SBA) algorithm. Extensive simulation reveals that our scheme incurs much less allocation overhead than all of the existing allocation algorithms, while delivering competitive performance.

A Fast and Efficient Processor Management Scheme fork-aryn-cubes

Job scheduling and processor allocation are two key components of processor management technique in a multiprocessor operating system. We propose a fast and efficient processor management technique, called virtual cube (VC), fork-aryn-cubes in this paper. The proposed scheme supports spatial allocation of jobs to the virtual cubes of the system and multiprograms the virtual cubes in a round-robin fashion. The objective here is to reduce job waiting time and fragmentation. The VC scheme uses a fast subcube allocation algorithm called enhancedk-ary buddy. A novel approach, called paging, is proposed for fast submesh allocation. When used with the first fit algorithm, the paging scheme is shown to be extremely fast and efficient compared to other contemporary submesh allocation algorithms fork-aryn-cubes. We also study the impact of page size on performance and illustrate a methodology to compute optimal page size. Simulation results show that the VC scheme with its multiprogramming capability can boost system performance considerably and outperforms all existing policies while incurring minimal run-time overhead.

Good processor management=fast allocation+efficient scheduling

Fast and efficient processor allocation and job scheduling algorithms are essential components of a multi-user multicomputer operating system. In this paper we propose two novel processor management schemes which meet such demands for mesh-connected multicomputers. A stack-based allocation algorithm that can locate a free sub-mesh for a job very quickly using simple coordinate calculation and spatial subtraction is proposed. Simulation results show that the stack-based allocation algorithm outperforms all the existing allocation policies in terms of allocation overhead while delivering competitive performance. Another technique, called group scheduling, schedules jobs in such a way that the jobs belonging to the same group do not block each other. The groups are scheduled in an FCFS order to prevent starvation. This simple but efficient scheduling policy reduces the response rime significantly by minimizing the queueing delay for the jobs in the same group. These two schemes, when used together can provide faster service to users with very little overhead.

Efficient processor management schemes for mesh-connected multicomputers

Abstract This paper investigates various processor management techniques for improving the performance of mesh-connected multicomputers. Unlike almost all prior work where the focus was on improving the submesh recognition ability of the processor allocation algorithms, this research examines other alternatives to improve system performance beyond what is achievable with usually assumed first come first served (FCFS) scheduling and any allocation. First, we use the smallest job first (SJF) policy to improve the spatial parallelism in a mesh. Next, we introduce a generic processor management scheme called multitasking and multiprogramming (M 2 ). Then, an M 2 policy for mesh-connected multicomputers called virtual mesh (VM) is proposed and analyzed. The proposed VM scheme allows multiprogramming of jobs on several VMs. Finally, a novel approach called limit allocation is used for job allocation. With this scheme, a job (submesh) size is reduced if the job cannot be allocated. The objective here is to reduce the job waiting time and hence improve the overall performance. While all of the three approaches are viable alternatives to reduce the average job response time under various workloads, the VM and the limit allocation techniques are especially attractive for providing some additional features. The VM scheme brings in the concept of time-sharing execution for better efficiency and limit allocation shows how job size restriction can be beneficial for performance and fault-tolerance in a mesh topology. Moreover, the limit allocation scheme using even the simplest allocation policy can outperform any other approach.

Seasonal integration and cointegration

This paper develops tests for roots in linear time series which have a modulus of one but which correspond to seasonal frequencies. Critical values for the tests are generated by Monte Carlo methods or are shown to be available from Dickey-Fuller or Dickey-Hasza-Fuller critical values. Representations for multivariate processes with combinations of seasonal and zero-frequency unit roots are developed leading to a variety of autoregressive and error-correction representations. The techniques are used to examine cointegration at different frequencies between consumption and income in the U.K.

A performance modeling technique for mesh-connected multicomputers

Modeling the perfomance of space-shared multicomputers is a non-trivial task mainly due to difficulty in modeling the effect of external fragmentation on system performance. Mesh-connected multicomputers are hard to model in particular because of great variance in job sizes. Therefore, researchers have relied on simulation method to evaluate the mesh performance. We propose a novel modeling technique called hybrid method in this paper. The proposed technique utilizes simulation method to estimate the capacity of a system. Then, a queueing model with multiple servers is constructed using the system capacity as the number of servers in the queueing system. The technique is validated through simulation experiments. The results reveal that the hybrid method provides very close estimation of the mesh performance with very little overhead. The proposed technique can also be used for performance modeling of other multicomputers with different topologies.

A task-based dependability model for k-ary n-cubes

Dependability (reliability and availability) modeling of k-ary n-cube architectures is addressed in this paper. The dependability model considered here is known as task-based dependability because the system working condition is specified by the task requirement. For the k-ary n-cube, we therefore compute the probability of finding a working k-ary m-cube. Due to the complexity of the problem, a structural decomposition technique is used to develop the analytical model. Two probability terms care required for computing either reliability or availability. The first term finds the probability that there are x working nodes in the system. Computation of this term for the availability analysis needs the solution of a simple Markov chain. The second term finds the probability that the x working nodes form the required subcube, called the task connection probability. A recursive expression, is developed for this. Analytical results are provided for various system configurations and task requirements. It is shown through simulation that the analytical model is quite accurate.