Pi,P2,P3,..,P,where 0<Pi<1.We also assume that standalone at initial step for calculating,so we can calculate there are m IT resources in the infrastructure,denoted by Ci, the current availability for each workflow as formula I shows: C2,...,Cm.Each resource consists of a "stack"of hardware and software components:for instance.an X86 server.a Linux m OS,and a Websphere Application Server. P(W (P(Cj)R) (1) C C W(P1 R1.1 1,21,3 Ri.m W2P2)2.1 2.22,3 R2.m P(Wi)is the current availability capability for workflow Wn(Pn)Rn.1 Rn.2 Rn.3.. Rn.m Wi.We compare it with the workflow's availability require- ment P:if P(W:)>P,the requirement is met:otherwise,the TABLE I availability requirement is unsatisfied,and some resources in THE WORKFLOW-RESOURCE RELATIONSHIP MATRIX the resource list of workflow W;need to have their availability enhanced through the deployment of an HA pattern to meet the availability requirement.This is an optimization problem: which resources should be enhanced for availability to meet Business Process Flow (Worknow 1] the availability requirement,while keeping HA enhancement SerAc 2 cost as low as possible? PIC PICa PICN A conventional method of addressing an optimization prob- onent 1 lem is by enumerating all possible solutions and comparing Resourse CI Resource C2 their cost;however,this approach is computationally expensive for all but the simplest problems,and is sometimes unsolvable when the number of resources is large.Literature [7]proposes Resourse C4 an approach to search for the optimal solution through multi- D4e*n4y山nm tier system design,based on exhaustive iteration.However, our weak-point analysis methodology calculates a near-optimal Fig.3.Example BPEL Workflow solution for HA enhancement using the method of Lagrange multipliers [8],which is a compute-effective approach. We construct a matrix to capture the workflow-resource Assume the number of workflows whose availability re- relationship.Table I shows the matrix;the relationship be- quirements have not yet been met is n;for workflow Wi tween workflow Wi and resource Cj is Ri.j,where Ri.j is an we define the enhancement parameter PWi as the amount integer value depicting the number of references to resource by which that workflow's current availability needs to be Ci from workflow Wi,and is set to 0 when resource C;is enhanced to meet the availability requirement Pi: not included in the resource list of Wi.For example,Fig. 3 shows a workflow with two services,which are mapped to three IT infrastructure resources,C1,C2 and C3,plus PWi=- P one resource Ca which is not included in the workflow. P(Wi) (2) Note that,at the application level,Component 1 depends on Component 2 to implement Service 1,Component 2 depends By definition.PW;1.We also define the enhancement on Component 3 to implement Service 2 as well.We denote parameter for each resource as PC1,PC2,..,PCm;thus,we the availability capability of resource Ci as P(Ci),therefore, form the following constraints: the availability for the two services are P(C1).P(C2).P(C3) and P(C2).P(C3);thus,the availability for the workflow is P(C1).P(C2)2.P(C3)2,and the matrix for Workflow I is set to [1,2.2.01.For standalone services which have no PW1≤PCB,1.PC1,2.…PCRm dependency relationships,we can simply set Ri.i to I for all PW2≤PCR.PCB22.…PCR2m the referenced resources,and 0 for unreferenced resources. PW≤PCR,1.PCB2.PCRm (3) B.Optimal Solution Calculation Given the workflow-resource relationship matrix,we can PWn≤PC1.PC2.…PCRm calculate the current availability capability for each workflow according to its resource list.Assume that the availability of In other words,the overall availability enhancement for the m resources are P(C1),P(C2),P(C3),.,P(Cm):these the IT resources within the workflow should be no less than availabilities can be derived from historical measurements the availability enhancement requirement for the workflow. or,perhaps,from data obtained from the manufacturer.For We take the logarithm of the inequalities 3 to simplify the this scenario,we assume that the relevant resources are all calculation,yielding:P1, P2, P3,..., Pn, where 0 < Pi < 1. We also assume that there are m IT resources in the infrastructure, denoted by C1, C2, ..., Cm. Each resource consists of a “stack” of hardware and software components; for instance, an X86 server, a Linux OS, and a Websphere Application Server. C1 C2 C3 ... Cm W1(P1) R1,1 R1,2 R1,3 ... R1,m W2(P2) R2,1 R2,2 R2,3 ... R2,m ... ... ... ... ... ... Wn(Pn) Rn,1 Rn,2 Rn,3 ... Rn,m TABLE I THE WORKFLOW-RESOURCE RELATIONSHIP MATRIX Fig. 3. Example BPEL Workflow We construct a matrix to capture the workflow-resource relationship. Table I shows the matrix; the relationship be￾tween workflow Wi and resource Cj is Ri,j , where Ri,j is an integer value depicting the number of references to resource Cj from workflow Wi , and is set to 0 when resource Cj is not included in the resource list of Wi . For example, Fig. 3 shows a workflow with two services, which are mapped to three IT infrastructure resources, C1, C2 and C3, plus one resource C4 which is not included in the workflow. Note that, at the application level, Component 1 depends on Component 2 to implement Service 1, Component 2 depends on Component 3 to implement Service 2 as well. We denote the availability capability of resource Ci as P(Ci), therefore, the availability for the two services are P(C1)·P(C2)·P(C3) and P(C2) · P(C3); thus, the availability for the workflow is P(C1) · P(C2) 2 · P(C3) 2 , and the matrix for Workflow 1 is set to [1,2,2,0]. For standalone services which have no dependency relationships, we can simply set Ri,j to 1 for all the referenced resources, and 0 for unreferenced resources. B. Optimal Solution Calculation Given the workflow-resource relationship matrix, we can calculate the current availability capability for each workflow according to its resource list. Assume that the availability of the m resources are P(C1), P(C2), P(C3), ..., P(Cm): these availabilities can be derived from historical measurements or, perhaps, from data obtained from the manufacturer. For this scenario, we assume that the relevant resources are all standalone at initial step for calculating, so we can calculate the current availability for each workflow as formula 1 shows: P(Wi) = Ym j=1 (P(Cj ) Ri,j ) (1) P(Wi) is the current availability capability for workflow Wi . We compare it with the workflow’s availability require￾ment Pi : if P(Wi) ≥ Pi , the requirement is met; otherwise, the availability requirement is unsatisfied, and some resources in the resource list of workflow Wi need to have their availability enhanced through the deployment of an HA pattern to meet the availability requirement. This is an optimization problem: which resources should be enhanced for availability to meet the availability requirement, while keeping HA enhancement cost as low as possible? A conventional method of addressing an optimization prob￾lem is by enumerating all possible solutions and comparing their cost; however, this approach is computationally expensive for all but the simplest problems, and is sometimes unsolvable when the number of resources is large. Literature [7] proposes an approach to search for the optimal solution through multi￾tier system design, based on exhaustive iteration. However, our weak-point analysis methodology calculates a near-optimal solution for HA enhancement using the method of Lagrange multipliers [8], which is a compute-effective approach. Assume the number of workflows whose availability re￾quirements have not yet been met is n; for workflow Wi we define the enhancement parameter PWi as the amount by which that workflow’s current availability needs to be enhanced to meet the availability requirement Pi : PWi = Pi P(Wi) (2) By definition, PWi ≥ 1. We also define the enhancement parameter for each resource as P C1, P C2, ..., P Cm; thus, we form the following constraints:    PW1 ≤ P CR1,1 1 · P CR1,2 2 · ... · P CR1,m m PW2 ≤ P CR2,1 1 · P CR2,2 2 · ... · P CR2,m m ... PWi ≤ P CRi,1 1 · P CRi,2 2 · ... · P CRi,m m ... PWn ≤ P CRn,1 1 · P CRn,2 2 · ... · P CRn,m m (3) In other words, the overall availability enhancement for the IT resources within the workflow should be no less than the availability enhancement requirement for the workflow. We take the logarithm of the inequalities 3 to simplify the calculation, yielding: