### Table 1. The variables used in the IP model of MC-PERF. Variables in bold are the unknown decision variables. n and m are nodes, i is an interval and k is an object.

2004

Cited by 24

### Table 1. The variables used in the IP model of MC-PERF. Variables in bold are the unknown decision variables. n and m are nodes, i is an interval and k is an object.

2004

Cited by 24

### Table 1: The variables used in the IP model of MC-QOS. Variables in bold are the unknown decision variables. n and m are nodes, i is an interval and k is an object. Minimize:

2003

"... In PAGE 5: ... We do not consider replica removal cost, as it is negligible in most real systems. The notations are summarized in Table1 . For notational convenience, we write a0 n to mean a0 n a1 N, a0 i to mean a0 i a1 I and a0 k to signify a0 k a1 K.... ..."

Cited by 2

### Table 6: Elapsed time for performing various operations in each iteration of complex-symmetric QMR on a 64-node CM-5 with vector processors, and total iterative solution time at kd = . Mesh (Unknowns) Preconditioner

1995

"... In PAGE 27: ... In fact, very often data-parallel implementations only employ diagonal preconditioning [4] due to its potential for high parallel performance. A summary of parallel solution times, using diagonal and hierarchical basis precon- ditioners on a 64-node CM-5, is shown in Table6 . An examination of these solution times clearly demonstrates that savings of about 2.... In PAGE 27: ... For the coarse mesh size considered here (832 unknowns) this computational stage lacked data-parallelism, and therefore required special attention to implement in a synchronous data-parallel en- vironment. The results shown in Table6 are based on performing the coarse solution in serial mode on the control processor using a pro le solver. It is noteworthy that despite communication overheads inherent in such a procedure, the preconditioner MHBCS provides substantial reduction in overall iterative solution times.... ..."

Cited by 8

### Table 1: Number of unknowns on di erent meshes.

2004

"... In PAGE 10: ... In order to have a tetrahedral tessalation we divided the hexahedra in ve tetrahedras in the standard way without adding new nodes. Table1 shows the number of nodes and elements for the di erent mesh sizes. The reference con guration of the model problem is the axis-parallel brick [ 100; 100] [0; 100] [0; 100] (all length units are mm).... ..."

### Table 1: Three solutions were found by solving the circuit apos;s modi ed nodal equations using the xed-point homotopy. Unknown variables x1 through x6 are node voltages, and variable x7 is the current owing through the source Vcc.

"... In PAGE 12: ...q. (13). The elements of the diagonal matrix G were set to 10?3, and the starting vector a was chosen by a random number generator. The solutions for the circuit apos;s node voltages and the current owing through the independent source are listed in Table1 . The solution paths for voltages x1 through x4, and the current x7 versus the homotopy parameter are shown in Fig.... ..."

### Table 4: Node and edge attributes for some VCODE operations. l 0 is the size of the output vector. Each node shown here has exactly one output. A Out(n; 1) value of Unknown indicates that the output sizes cannot be computed in terms of the input sizes.

1993

"... In PAGE 13: ... The phrase is meant to be reminiscent of type signature , a phrase used with similar connotations in the context of languages with polymorphic type systems [48]. Thus, the constraint set and the transfer function of the SELECT operation in Table4 can be combined into the size signature #0B #02 #0B #02 #0B ! #0B, which means that SELECT takes as input three vectors of the same (unknown) size #0B and produces one output vector of this same size. Definition 6 (Node iteration space function) The iteration space function for a node n (denoted Loop(n)) is a function that computes the size of the iteration space of the operation performed by the node in terms of the sizes of its input and/or output vectors.... In PAGE 13: ... With the restrictions we have imposed, the loop structure of any operation is completely determined by a single number corresponding to the difference of the loop bounds. The node and edge attributes of some of the VCODE primitives are shown in Table4 . Note that the size of the output may be different from the size of the iteration space, as for the +_REDUCE operation.... ..."

Cited by 18

### Table 2: Failure cause by component and fault type. The component is described as node (node) or network (net), and fault type is described as operator error (op), hardware (hw), software (sw), unknown (unk), or environment. Operator and network failure are the leading causes of service failure.

2002

"... In PAGE 2: ... Analysis of problem causes Classifying the 62 problems we reviewed has allowed us to make a number of observations about the causes of user-visible service failures. The data from which we make these observations are summarized in Table 1, which breaks down problem causes by the part of the service containing the root cause, and in Table2 , which breaks down problem causes by the component that failed and the underlying cause of the failure. Table 1 shows that contrary to conventional wisdom, front-end machines can be a significant source of failure.... In PAGE 2: ... In the services we studied, this was largely due to the com- plexity of the service software running on those machines and the complexity of configuring and administering them. Table2 shows that operator error and networking problems are a significant cause of failure. In Online and Content, operator error caused more failures than did node hardware or software failures, while in ReadMostly net- working problems caused more failures than did node hardware or software problems.... ..."

Cited by 7

### Table 3: Service failure cause by component and type of cause. The component is described as node or network, and failure cause is described as operator error, hardware, software, unknown, or environment. We excluded the overload category because of the very small number of failures caused.

2003

"... In PAGE 4: ... Almost all of the prob- lems in ReadMostly were network-related; we attribute this to simpler and better-tested application software at that service, fewer changes made to the service on a day-to-day basis, and a higher degree of node redun- dancy than is used at Online and Content. Table3 shows that operator error is the leading cause of service failure in two of the three services. Figure 4: Number of component failures and resulting service failures for Content.... ..."

Cited by 125