**2.3 Problem specification**

The formal specification of the described problem includes following elements:

resource requirements, the number of available resources must be larger than the resource

• **Criterion 4:** The data transmission task *eki* from sub-job *sk* to sub-job *si* must take place in dedicated time slots on the link between the RMS running sub-job *sk* to the RMS running

<sup>9</sup> w-TG: A Combined Algorithm to Optimize the Runtime

The goal is to minimize the makespan of the workflow. The makespan is defined as the period from the desired starting time until the finished time of the last sub-job in the workflow. In addition to the aspect that the workflow in our model includes both parallel and sequential

To check for the feasibility of a configuration, the mapping algorithm must go through the resource reservation profiles and bandwidth reservation profile. This step needs a significant amount of time. Suppose, for example, that the Grid system has *m* RMS, which can satisfy the requirement of *n* sub-jobs in a workflow. As an RMS can run several sub-jobs at a time, finding out the optimal solution needs (*mn*) loops for checking the feasibility. It can be easily shown that the optimizing of the execution time of the workflow on the Grid as described above is an NP hard problem Black et al. (1999). Previous experiment results have shown that with the number of sub-jobs equaling 6 and number of RMSs equaling 20, the runtime to find

The mapping algorithm for Grid workflow has received a lot of attentions from the scientific community. In the literature, there are many methods to mapping a Grid workflow to Grid resource within different contexts. Among those, the old but well-known algorithm Condor-DAGMan from the work of Condor (2004) is still used in some present Grid systems. This algorithm makes local decisions about which job to send to which resource and considers only jobs, which are ready to run at any given instance. Also, using a dynamic scheduling approach, Duan et al. (2006) and Ayyub et al. (2007) apply many techniques to frequently rearrange the workflow and reschedule it in order to reduce the runtime of the workflow. Those methods are not suitable for the context of resource reservation because whenever a reservation is canceled, a fee is charged. Thus, frequent rescheduling may lead to a higher

Deelman et al. (2004) presented an algorithm which maps Grid workflows onto Grid resources based on existing planning technology. This work focuses on coding the problem to be compatible with the input format of specific planning systems and thus transferring the mapping problem to a planning problem. Although this is a flexible way of gaining different destinations, which includes some SLA criteria, significant disadvantages regarding the time-intensive computation, long response times and the missing consideration of

In Mello et al. (2007), Mello et. al. describe a load balancing algorithm addressed to Grid computing environment called RouteGA. The algorithm uses GA techniques to provide an

sub-jobs, the SLA context imposes the following distinguishing characteristics.

• An RMS can run several parallel or sequential sub-jobs at a time.

• The bandwidth of the links connecting RMSs is reserved.

out the optimal solution is exponential Quan et al. (2007).

• The resources in each RMS are reserved.

of the Grid-Based Workflow Within an SLA Context

requirement.

**3. Related works**

running workflow cost.

Grid-specific constraints appeared.

sub-job *si*. *eki* ∈ *E*.


Table 2. Sample RMS configurations


Based on the given input, the required solution includes two sets defined in Formula 1 and 2.

$$M = \{ (s\_{i\prime}r\_{j\prime}\text{start}, \text{stop}) | s\_i \in \mathcal{S}, r\_j \in \mathcal{K}\_i \}\tag{1}$$

$$N = \{ (e\_{ik} \iota start\_{\prime} stop) | e\_{ik} \in E \} \tag{2}$$

If the solution does not have a start, stop slot for each *si*, it becomes a configuration as defined in Formula 3.

$$a = \{ (s\_{i'}r\_{\bar{j}}) | s\_{i} \in \mathcal{S}, r\_{\bar{j}} \in \mathcal{K}\_{i} \}\tag{3}$$

A feasible solution must satisfy following conditions:


resource requirements, the number of available resources must be larger than the resource requirement.

• **Criterion 4:** The data transmission task *eki* from sub-job *sk* to sub-job *si* must take place in dedicated time slots on the link between the RMS running sub-job *sk* to the RMS running sub-job *si*. *eki* ∈ *E*.

The goal is to minimize the makespan of the workflow. The makespan is defined as the period from the desired starting time until the finished time of the last sub-job in the workflow. In addition to the aspect that the workflow in our model includes both parallel and sequential sub-jobs, the SLA context imposes the following distinguishing characteristics.


To check for the feasibility of a configuration, the mapping algorithm must go through the resource reservation profiles and bandwidth reservation profile. This step needs a significant amount of time. Suppose, for example, that the Grid system has *m* RMS, which can satisfy the requirement of *n* sub-jobs in a workflow. As an RMS can run several sub-jobs at a time, finding out the optimal solution needs (*mn*) loops for checking the feasibility. It can be easily shown that the optimizing of the execution time of the workflow on the Grid as described above is an NP hard problem Black et al. (1999). Previous experiment results have shown that with the number of sub-jobs equaling 6 and number of RMSs equaling 20, the runtime to find out the optimal solution is exponential Quan et al. (2007).
