### TABLE 5. Coefficients of conventional centered midpoint interpolation.

2001

### Table 3: Pi2 Ni for increasing number of interpolation nodes; the evaluation point located at the center of the smallest square formed by the interpolating nodes at the lower left corner of the domain.

1994

Cited by 2

### Table 2: Performance of the fast evaluation method (d = 2). The N centers coincide with the M evaluation points and are uniformly distributed in the unit square. The table shows times in seconds for the approximate and direct evaluation of the Inverse Multiquadric interpolants.

2004

"... In PAGE 14: ... Test Problem 2. The second test case is two-dimensional Inverse Multiquadric interpolation ( Table2 ). The evaluation points coincide with the centers and are uniformly distributed on the unit square.... In PAGE 15: ...Figure 1: Graphic representation of Table2 , comparing the performance of the direct and the fast method. Dotted line is the fast method.... ..."

### Table 1: Timings (in seconds) for tesselating several implicit surface models. The marching cubes approach invokes either the tri-linear interpolation disambiguation method (left) or a tetrahedral decomposition of cells (center) to produce a topologically consistent mesh

2001

"... In PAGE 9: ... Our experiments demonstrate that it is difficult to compare the marching triangles and the marching cubes algorithms as the marching triangles adapt to the curvature of the surface, whereas the marching cubes relies on fixed size cells to poly- gonize an implicit surface. Table1 reports several statistics for meshing the bird model and other shapes displayed in Figure 7. The march- ing cubes rely on a voxel decomposition of space, and the size of the seed cube was defined as 1a6 50th of the size of the bounding box of the implicit model.... ..."

Cited by 16

### Table 2: Mean Residual Service Time Estimates (two-center networks, N=5, p=0.99, =50) (a) \Other quot; Center is a Delay Center

2000

"... In PAGE 5: ... 3.2 Mean Residual Service Time Accuracy Table2 provides results that illustrate the typical accuracy of each of three AMVA techniques for estimating the mean residual service time at a FCFS center with high service time CV: (1) the standard AMVA approximation, (2) the simple interpolation given in equation 3, and (3) the new interpolation given in equation 4 (\New Interp. quot;).... In PAGE 5: ... Actual values of the mean residual service time are derived from numerical solutions of the correspond- ing Markov chains. For Table2 (a), in which the second center is a delay center, the new interpolation is exact as es- tablished in Section 3.1.... In PAGE 5: ...1. In Table2 (b), the exact value of the mean residence time at the other queueing center (Rother), as obtained from the Markov chain analysis, is used in the interpolation formulas. Section 4 develops an accurate new AMVA technique for estimating this mean residence time.... In PAGE 5: ... Section 4 develops an accurate new AMVA technique for estimating this mean residence time. In all cases shown in Table2 , the new interpolation is more accurate than the simple interpolation de ned in Section 2.2, which is in turn more accurate than the \standard quot; AMVA Table 2: Mean Residual Service Time Estimates (two-center networks, N=5, p=0.... In PAGE 5: ... Each contour line corresponds to a particular ab- solute value of percent relative error for the mean residual service time estimated using the new interpolation. As in Table2 (b), the exact value of the mean residence time at the other queueing center is used in the interpolation formula.... In PAGE 6: ... quot;) [31]. The techniques are compared for the same two-queue net- work parameter sets that were used in Table2 . The exact values for the mean residence time at the FCFS center with high CV service times are derived from numerical solutions of the corresponding Markov chains.... ..."

Cited by 3

### Table 2: Mean Residual Service Time Estimates (two-center networks, N=5, p=0.99, =50) (a) \Other quot; Center is a Delay Center

2000

"... In PAGE 5: ... 3.2 Mean Residual Service Time Accuracy Table2 provides results that illustrate the typical accuracy of each of three AMVA techniques for estimating the mean residual service time at a FCFS center with high service time CV: (1) the standard AMVA approximation, (2) the simple interpolation given in equation 3, and (3) the new interpolation given in equation 4 (\New Interp. quot;).... In PAGE 5: ... Actual values of the mean residual service time are derived from numerical solutions of the correspond- ing Markov chains. For Table2 (a), in which the second center is a delay center, the new interpolation is exact as es- tablished in Section 3.1.... In PAGE 5: ...1. In Table2 (b), the exact value of the mean residence time at the other queueing center (Rother), as obtained from the Markov chain analysis, is used in the interpolation formulas. Section 4 develops an accurate new AMVA technique for estimating this mean residence time.... In PAGE 5: ... Section 4 develops an accurate new AMVA technique for estimating this mean residence time. In all cases shown in Table2 , the new interpolation is more accurate than the simple interpolation de ned in Section 2.2, which is in turn more accurate than the \standard quot; AMVA Table 2: Mean Residual Service Time Estimates (two-center networks, N=5, p=0.... In PAGE 5: ... Each contour line corresponds to a particular ab- solute value of percent relative error for the mean residual service time estimated using the new interpolation. As in Table2 (b), the exact value of the mean residence time at the... In PAGE 6: ... quot;) [31]. The techniques are compared for the same two-queue net- work parameter sets that were used in Table2 . The exact values for the mean residence time at the FCFS center with high CV service times are derived from numerical solutions of the corresponding Markov chains.... ..."

Cited by 3

### Table 1: Performance of the fast evaluation method (d = 1). The N centers and the M evaluation points are uniformly distributed in the unit interval. The table shows times in seconds for the approximate and direct evaluation of the Hardy Multiquadric interpolants at observed relative accuracy of O(10 14).

2004

"... In PAGE 14: ... The N centers and the M evaluation points are chosen from the uniform distribution on the unit interval. The method scales linearly with respect to N and M ( Table1 ). Although of little practical signi cance, this test problem is included here to show the scaling of the method with respect to the number of dimensions.... ..."

### Table 2. Confidence Interval Coverage for Wholly Interpolative Test Set (0).

1999

"... In PAGE 17: ... In general, these were the networks trained on Y , rather than on replications of Y. Table2 shows the coverage of the 100 replications averaged over the 144 testing pairs of the wholly interpolative test set (Test Set 0) for 90%, 95% and 99% confidence levels for both neural network confidence intervals and for confidence intervals obtained directly from the simulation. TABLE 2 HERE Two further observations from Table 2 can be made.... In PAGE 17: ... Table 2 shows the coverage of the 100 replications averaged over the 144 testing pairs of the wholly interpolative test set (Test Set 0) for 90%, 95% and 99% confidence levels for both neural network confidence intervals and for confidence intervals obtained directly from the simulation. TABLE 2 HERE Two further observations from Table2 can be made. First, the neural network intervals are not likely to be correctly centered, that is, they are biased upwards or downwards.... ..."

Cited by 1

### Table 3: Mean Residence Time Estimates for FCFS Queue with High Service Time CV (two-center networks, N = 5, p=0.99, =50) (a) \Other quot; Center is a Delay Center

2000

"... In PAGE 6: ... 3.4 Mean Queue Residence Time Accuracy Table3 provides typical results for the accuracy of ve tech- niques for estimating the mean residence time at a FCFS center with high service time variability. Those techniques are: (1) the standard AMVA technique, (2) use of the sim- ple interpolation to estimate mean residual service time in equation 2, (3) use of the new interpolation to estimate mean residual service time in equation 2, (4) the new technique proposed in Section 3.... In PAGE 6: ... The exact values for the mean residence time at the FCFS center with high CV service times are derived from numerical solutions of the corresponding Markov chains. For Table3 (b), the exact value of Rother is used in the calculations for all of the techniques except for the decomposition approach, in which this quantity is not used. Rother could instead be computed using the accurate approximation developed in Section 4.... In PAGE 8: ...n the rest of the system (i.e., the mean residence time at the second queueing center) to be the same in each of the de- composed submodels. However, for the cases considered in Table3 , the AMVA-Decomp technique appears to be quite accurate in spite of this possibility for error. The accuracy of the AMVA-Decomp approach is evaluated over a wide range of the parameter space of the two-center networks in the contour plots of Figures 4 and 5.... In PAGE 8: ... The accuracy of the AMVA-Decomp approach is evaluated over a wide range of the parameter space of the two-center networks in the contour plots of Figures 4 and 5. In Figure 5, as in Table3 (b), the exact value of the mean residence time at the other queueing center is used where needed. The key conclusions from Table 3 and Figures 4 and 5 are: The standard AMVA estimate of mean queue residence time is not very robust.... In PAGE 8: ... In Figure 5, as in Table 3(b), the exact value of the mean residence time at the other queueing center is used where needed. The key conclusions from Table3 and Figures 4 and 5 are: The standard AMVA estimate of mean queue residence time is not very robust. The interpolation techniques can also yield inaccurate estimates of the mean queue residence time, since the standard AMVA estimates of the mean arrival queue length and the probability that the server is busy at an arrival instant are inaccurate.... In PAGE 8: ... However, since the simple interpolation is less accurate than the new interpolation in estimating the mean residual service time, the cases where it leads to higher accuracy in predicting mean queue residence time are due to fortuitously compensating errors in the standard approx- imation of mean arrival queue length and/or the probability that the server is busy at an arrival instant for the center. Furthermore, the results for the simple interpolation in Fig- ure 1 are perhaps more accurate than one would expect from the results in Table3 (b). This is due to the fact that, in cases where the simple interpolation overpredicts mean residence time, the error is partially compensated in the throughput k k B I I I I Figure 6: Model of a Bursty Arrival Process estimate because, as noted in Section 1, the bursty arrivals at the downstream queues were not modeled.... ..."

Cited by 3

### Table 3: Mean Residence Time Estimates for FCFS Queue with High Service Time CV (two-center networks, N = 5, p=0.99, =50) (a) \Other quot; Center is a Delay Center

2000

"... In PAGE 6: ... 3.4 Mean Queue Residence Time Accuracy Table3 provides typical results for the accuracy of ve tech- niques for estimating the mean residence time at a FCFS center with high service time variability. Those techniques are: (1) the standard AMVA technique, (2) use of the sim- ple interpolation to estimate mean residual service time in equation 2, (3) use of the new interpolation to estimate mean residual service time in equation 2, (4) the new technique proposed in Section 3.... In PAGE 6: ... The exact values for the mean residence time at the FCFS center with high CV service times are derived from numerical solutions of the corresponding Markov chains. For Table3 (b), the exact value of Rother is used in the calculations for all of the techniques except for the decomposition approach, in which this quantity is not used. Rother could instead be computed using the accurate approximation developed in Section 4.... In PAGE 8: ...n the rest of the system (i.e., the mean residence time at the second queueing center) to be the same in each of the de- composed submodels. However, for the cases considered in Table3 , the AMVA-Decomp technique appears to be quite accurate in spite of this possibility for error. The accuracy of the AMVA-Decomp approach is evaluated over a wide range of the parameter space of the two-center networks in the contour plots of Figures 4 and 5.... In PAGE 8: ... The accuracy of the AMVA-Decomp approach is evaluated over a wide range of the parameter space of the two-center networks in the contour plots of Figures 4 and 5. In Figure 5, as in Table3 (b), the exact value of the mean residence time at the other queueing center is used where needed. The key conclusions from Table 3 and Figures 4 and 5 are: The standard AMVA estimate of mean queue residence time is not very robust.... In PAGE 8: ... In Figure 5, as in Table 3(b), the exact value of the mean residence time at the other queueing center is used where needed. The key conclusions from Table3 and Figures 4 and 5 are: The standard AMVA estimate of mean queue residence time is not very robust. The interpolation techniques can also yield inaccurate estimates of the mean queue residence time, since the standard AMVA estimates of the mean arrival queue length and the probability that the server is busy at an arrival instant are inaccurate.... In PAGE 8: ... However, since the simple interpolation is less accurate than the new interpolation in estimating the mean residual service time, the cases where it leads to higher accuracy in predicting mean queue residence time are due to fortuitously compensating errors in the standard approx- imation of mean arrival queue length and/or the probability that the server is busy at an arrival instant for the center. Furthermore, the results for the simple interpolation in Fig- ure 1 are perhaps more accurate than one would expect from the results in Table3 (b). This is due to the fact that, in cases where the simple interpolation overpredicts mean residence time, the error is partially compensated in the throughput k k B I I I I Figure 6: Model of a Bursty Arrival Process estimate because, as noted in Section 1, the bursty arrivals at the downstream queues were not modeled.... ..."

Cited by 3