Joint Computing and Network Resource Scheduling in a Lambda Grid Network

Data-intensive Grid applications require huge data transfers between grid computing nodes. These computing nodes, where computing jobs are executed, are usually geographically separated. A grid network that employs optical wavelength division multiplexing (WDM) technology and optical switches to interconnect computing resources with dynamically provisioned multi-gigabit rate bandwidth lightpath is called a Lambda Grid network. A computing task may be executed on any one of several computing nodes which possesses the necessary resources. In order to reflect the reality in job scheduling, allocation of network resources for data transfer should be taken into consideration. However, few scheduling methods consider the communication contention on Lambda Grids. In this paper, we investigate the joint scheduling problem while considering both optical network and computing resources in a Lambda Grid network. The objective of our work is to maximize the total number of jobs that can be scheduled in a Lambda Grid network. An adaptive routing algorithm is proposed and implemented for accomplishing the communication tasks for every job submitted in the network. Four heuristics (FIFO, ESTF, LJF, RS) are implemented for job scheduling of the computational tasks. Simulation results prove the feasibility and efficiency of the proposed solution.

Joint Computing and Network Resource Scheduling in a Lambda Grid Network

Data-intensive Grid applications require huge data transfers between grid computing nodes. These computing nodes, where computing jobs are executed, are usually geographically separated. A grid network that employs optical wavelength division multiplexing (WDM) technology and optical switches to interconnect computing resources with dynamically provisioned multi-gigabit rate bandwidth lightpath is called a Lambda Grid network. A computing task may be executed on any one of several computing nodes which possesses the necessary resources. In order to reflect the reality in job scheduling, allocation of network resources for data transfer should be taken into consideration. However, few scheduling methods consider the communication contention on Lambda Grids. In this paper, we investigate the joint scheduling problem while considering both optical network and computing resources in a Lambda Grid network. The objective of our work is to maximize the total number of jobs that can be scheduled in a Lambda Grid network. An adaptive routing algorithm is proposed and implemented for accomplishing the communication tasks for every job submitted in the network. Four heuristics (FIFO, ESTF, LJF, RS) are implemented for job scheduling of the computational tasks. Simulation results prove the feasibility and efficiency of the proposed solution.

Vanishing of Ext and Tor over complete intersections

Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of Serre's condition and complexity to study the vanishing of Tor_{i}(M, N). In particular, building on results of C. Huneke, D. Jorgensen and R. Wiegand [32], and H. Dao [21], we obtain new results showing that good depth properties on the R-modules M, N and MtensorN force the vanishing of Tor_{i}(M, N) for all i>0. We give examples showing that our results are sharp. We also show that if R is a one-dimensional domain and M and MtensorHom(M,R) are torsion-free, then M is free if and only if M has complexity at most one. If R is a hypersurface and Ext^{i}(M, N) has finite length for all i>>0, then the Herbrand difference [18] is defined as length(Ext^{2n}(M, N))-(Ext^{2n-1}(M, N)) for some (equivalently, every) sufficiently large integer n. In joint work with Hailong Dao, we generalize and study the Herbrand difference. Using the Grothendieck group of finitely generated R-modules, we also examined the number of consecutive vanishing of Ext^{i}(M, N) needed to ensure that Ext^{i}(M, N) = 0 for all i>>0. Our results recover and improve on most of the known bounds in the literature, especially when R has dimension two.