RIA

laboria

<figure><img src="image_1.png" /></figure>

laboratoire de recherche
en informatique
et automatique

Accuracy of an approximate
computer system model

Marc
M. Badel, Annie V.Y. Shum

Institut de Recherche
d'Informatique
et d'Automatique

Domaine de Voluceau
Rocquencourt
78150 - Le Chesnay
Tél. 954.90.20

Rapport de Recherche n° 130

Juillet 1975
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ACCURACY OF AN APPROXIMATE COMPUTER SYSTEM MODEL

M. Badel, Annie V.Y. Shum*

IRIA - LABORIA

(présenté par E. Gelenbe)

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ABSTRACT

The purpose of this note is to evaluate by simulation the predictions of a theoretical multiprogramming system model [2] and to propose a simple method for establishing a correspondance between the continuous state model [2] and the discrete state results obtained by simulation. We observe that over a wide range of parameter values, maximum relative error in the theoretically predicted CPU utilization does not exceed 15 % . Good agreement is also obtained for queue length distributions.

RESUME

L'objet de cet article est l'évaluation par simulation
de la qualité des résultats d'un modèle théorique de système multi-
programmé [2] et la proposition d'une méthode simple de correspondance
entre les résultats d'un modèle continu [2] et des résultats discrets
obtenus par simulation. Nous observons que dans un large domaine de
valeurs des paramètres, l'erreur relative maximum sur les taux d'utili-
sation UC calculés théoriquement n'excède pas 15 %. Un bon accord
est également obtenu pour les distributions de la longueur des files
d'attente.

<footnote>*) Presently with the Center of Research in Computing Technology, Harvard University, Cambridge, Mass.</footnote>
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# INTRODUCTION

Diffusion processes as approximation of queueing systems have been studied and proved to be by a promising method [1,2,3,4]. One interesting application is the computation of the steady state CPU utilization in a model of a multiprogrammed computer systems. The earlier diffusion models of GAVER and SHEDLER [1] and KOBAYASHI [4] assumed reflecting boundaries. GELENBE [2] prepared an elementary return (IR) process model which proved to be a more accurate approximation. In [3] the model has been generalized to assume holding times at the boundaries distributed according to the Cox or almost general distribution. The resulting diffusion process is used to solve approximately for various queueing systems including the steady state solutions of the closed two-server system with general service time distributions. The results in [3] demonstrated that the stationary solution so obtained depends only on the expected values and not on higher moments of the holding times at the boundaries.

The purpose of this note is to evaluate, via simulation experiments, the accuracy of this approximation method for the computation of stationary (equilibrium) server utilization and queue length probabilities.

In the next section we review briefly the results from [2], [3] concerning the approximate stationary probability distributions for the multiprogram-
<figure><img src="image_5.png" /></figure>
ming system model shown in Figure 1, which consists of a CPU and an
input-output device (I/O) interconnected so that a fixed number M of
jobs circulate in the system.

In section III we briefly describe the simulations used for computing the
stationary CPU utilization in the model. The results obtained are compared
with those predicted by the formula of [2],[3].

Section IV is devoted to simulations used to evaluate the accuracy of
the diffusion approximation for predicting stationary queue length distri-
butions. For this purpose, histograms of queue lengths are obtained by
simulation for different parameter values. An integration method is
proposed for computing the discrete probability distribution of queue
length from the continuous results obtained via the diffusion approximation
and comparisons with simulation results are provided.

## II - SUMMARY OF THE STEADY STATE SOLUTIONS OF THE CLOSED TWO-SERVER MODEL OBTAINED BY IR DIFFUSION MODEL

On order to facilitate readers not familiar with [3] here in this section,
a brief summary of the results derived by Gelenbe will be presented. In
further details, interested readers should refer to [3]. Consider the
closed two server model of Figure 1 with one CPU and one I/O device. Let
the service times at the CPU be independent and identically distributed
(i.i.d) random variables with mean $\mu^{-1}$ and variance $V_S$; they are indepen-
dent of the I/O service times. Similarly let the service time at I/O the
i.i.d. random variables with mean $\lambda^{-1}$ and variances $V_a$. Let M be the degree
of multiprogramming, that is the number of programs being executed simul-
taneously in the system. The stationary probability density function for
$\{X(t), t \ge 0\}$ which is the stochastic diffusion process approximating the
number of programs in the CPU queue exists and is given by

$$f = \begin{cases} K [1 - e^{\gamma^X}] & , 0 < X \le 1 \\ K [e^{-\gamma} - 1]e^{\gamma^X} & , 1 \le X \le M-1 \\ K [e^{\gamma(X-M)} - 1]e^{\gamma(M-1)} & , M-1 \le X < M \end{cases}$$

where $\gamma = 2 \frac{(\lambda - \mu)}{\alpha}$, and $\alpha = \lambda^3 V_a + \mu^3 V_s$. If $\rho = \lambda/\mu$, then

$$K = \rho (1 - \rho^2 e^{\gamma(M-1)})^{-1}$$

and P, Q which are the stationary probabilities that the CPU queue, and the I/O queue, respectively are empty, are given by

$$P = K(\frac{1-\rho}{\rho}), \quad Q = K(1-\rho)e^{\gamma(M-1)}$$

The long-run (or stationary) CPU utilization is then $n = 1-P$.

### III - ESTIMATION VIA SIMULATION OF STATIONARY CPU UTILIZATION

In this section the steady state CPU utilization is the measure for the comparison of the simulation results and diffusion results. We choose a hyperexponential of order $2(H-2)$ distribution for CPU service times. Various reports have demonstrated that in some installations, H-2 is a realistic representation for this quantity. Besides, there is another point of interest which prompted the choice of the H-2 distribution. Experience has demonstrated that the accuracy of the diffusion approximation decreases with the value of the squared coefficient of variation $K (= \text{variance}/(\text{mean})^2)$ of the service time distribution. H-2 is a standard example for having $K > 1$ and could assume arbitrarily large K depending on the parameter values of the density. Let $f(t)$ be the H-2 density

$$f(t) = a\lambda_1 e^{-\lambda_1 t} + (1-a)\lambda_2 e^{-\lambda_2 t} \quad \begin{cases} \lambda_1, & \lambda_2 \ge 0 \\ a, & a \ge 0 \end{cases}$$
The 3 parameters being a ; $λ_1$ and $λ_2$.

Two sets of experiments have been run :

In the first we have an H-2 CPU with an exponential I/O. M, the degree of multiprogramming or the total number of customers in the closed model is varied from 1 to 10 while the value of the load factor ρ is varied from 0.25 to 0.90 for each value of M. In order to observe the effect of increasing K on the magnitude of the relative error we vary K of the CPU service time from 1 to 10. By relative error we refer to the relative difference in magnitude between the corresponding results obtained from the two approaches separately. The data obtained are tabulated on Tables 1 to 10. The second set of experiments is completely analogous to the first except for the I/O service time which is assumed constant. The results are tabulated on Tables 11 to 20.

On figure 2 we summarize these results by plotting the maximum relative error E as a function of K for both sets of experiments. E, for a given value of K, is obtained over all values of ρ and M.

Let us now turn our attention to the first set of experiments summarized on Tables 1 to 10.

The first table with K=1 gives us a reduced case with both CPU and I/O being exponential. Here we can observe that the results from the two models agree almost everywhere. The relative errors are computed and the maximum relative error occurs at ρ = 0.9 is only 0.8%. Of course an exact treatment of this case is available [5].
**K = 2 to 4** : The results indicate that the two approaches agree very well especially for small ρ. The maximum relative error again occurs at ρ = 0.9 for all three cases ; the magnitude is increased from 5 °/° for K=2 to 7.5 °/° for K=4.

**K = 5 to 10** : For ρ < 0.75, the two approaches still demonstrate the good correspondence. However for ρ ≥ 0.75, particularly ρ = 0.90, the two begin to diverge. The maximum relative error increases from 8 °/° for K=5 to about 10 °/° for K=10.

It is interesting to note that in most cases the simulation results are higher than the corresponding values from the diffusion model.

For the second set with constant service time at the I/O device, Tables 11-20, on the whole the accuracy is not a good as the first set for K=1 and K=2, the two agree very well even though the maximum relative error for K=1 is increased to 2.6 °/°.

In the first set, we may consider that with K ≤ 5 we have good accuracy. In the second set, comparable accuracy is obtained for K ≤ 3. The maximum relative error for K=3 is 9.6 °/° while for K=4 it is increased to 12 °/°. The highest of these maximum relative errors among tables 13-20 is found to be 13.5 °/°. As before all these maximum relative errors occur at ρ = 0.9. On the whole for ρ < 0.75, the simulation model agrees very well with the diffusion approximation.

95 °/° confidence intervals are computed for each CPU utilization value from the simulation (see Appendix 1 for the method used). In the first
set of Tables -the exp. I/0- it is noted that all the values of the diffusion model are well within the corresponding confidence intervals. For the second set, except for some cases with p = 0.9 and K=7 that the confidence interval fails to cover the corresponding value from the diffusion model, all values are adequately covered.

On figure 2 we have plotted the maximum relative percentage error for exponential I/0 and constant I/0. In addition the corresponding relative confidence interval is plotted. It is observed that the latter almost always covers the former for the exponential I/0 and for the constant I/0; this term is defined as the confidence interval value divided by the CPU utilization predicted by the diffusion model.

Note that if the confidence interval covers the corresponding value from the diffusion model then this maximum relative confidence interval error will always be larger than the corresponding maximum relative error. To see this, let $X_M$, $X_S$ be the values of CPU utilization obtained from the diffusion model and simulator respectively; if C is the confidence interval and if $X_M \in (X_S^{+} - C)$, then

$$ \left| \frac{X_S - X_M}{X_M} \right| \le \left| \frac{C}{X_M} \right| $$

The overall comparison for stationary CPU utilization between the simulation and diffusion formula approach is satisfactory; this serves as a preliminary step for establishing the accuracy of the diffusion approximation.

## IV - EVALUATION OF ACCURACY OF QUEUE LENGTH DISTRIBUTIONS

The results of the previous sections show that for a range of parameter values of interest, the diffusion approximation results yield predictions
of stationary CPU utilization of accuracy comparable with that of
simulation experiments at a computational cost which is negligible by
comparison with simulation.

In this section we shall examine the accuracy of predictions for queue
length distributions. Since simulation experiments will yield a discrete
probability distribution {$p_i$} of CPU queue length $i = 0, \dots, M$, we must
integrate the mixed distribution predicted by the diffusion model to
obtain the corresponding distribution {$\Pi_i$}. In general, it will be obtained
by taking

$$
\begin{align*}
\Pi_0 &= P + \int_0^{B_0} fdx \\
\Pi_i &= \int_{B_{i-1}}^{B_i} fdx \qquad , \quad 1 \le i \le M-1 \\
\Pi_M &= \int_{B_{M-1}}^{M} fdx + Q
\end{align*}
$$

It is clear that the distribution {$\Pi_i$} will be dependent on the choice
of the $B_i$, $1 \le i \le M-1$, which need not be $B_i = i$.

Notice that in the previous section we have chosen $\mu_i = 1-P$ or $\Pi_0 = P$.
In fact the choice $\Pi_0 = P$, $\Pi_M = Q$ (or $B_0 = 0$, $B_{M-1} = M$) yields a very satisfac-
tory degree of accuracy as will be seen via simulation results.

Let us first consider the simplest approach which would be to take
$\Pi_0 = P$, $\Pi_M = Q$ and $B_i = iM/(M-1)$; that is, the interval $(0,M)$ is divided
into $M-1$ equal subintervals over which $f$ is integrated to obtain $\Pi_i$,
$1 \le i \le M-1$. Comparisons of the results obtained by the approach with
the {$p_i$} obtained by simulation are shown on Figures 3, 4. This method
appears to be unsatisfactory except for $\Pi_0$ and $\Pi_M$. The general tendency seems to be to underestimate the true values of the probability distribution for $0 < i < j$, and to overestimate them for $M > i > j$ where j is some small integer.

From these remarks we see that the values $B_i - B_{i-1}$ must be larger for smaller values of i in order to obtain better agreement between $\Pi_i$ and $p_i$. Therefore we propose and evaluate the following simple approach.

Take $\Pi_0 = P$ and

$$ \Pi_1 = \int_0^{B_1} fdx $$

and choose $B_1$ such that

$$ \int_0^{B_1} xfdx = \int_0^{B_1} fdx $$

These relationships state that the first term $\Pi_1$ of the sum yielding the expected queue length

$$ \sum_{i=1}^{M} i\Pi_{i} $$

obtained from the discrete distribution, is identical to the part

$$ \int_{0}^{B_{1}} xfdx $$

for the corresponding quantity in the expected value computed from the continuous distribution. This yields (numerically) the value of $B_1$. The remaining $B_i$, $2 \le i \le M-1$, are chosen by dividing the interval $(B_1, M)$
into M-2 equal subintervals : $B_i = B_1 + (i-1) (M-B_1)/(M-2)$. The comparisons are given on Figures 5, 6 for constant service time at the I/O device and exponential service time distribution at the CPU. On Figures 7, 8 we present similar comparisons for hyperexponential service time at the CPU.

The accuracy of the predictions using the integration method we propose is particularly satisfactory for small values of $\kappa_s^2$ (2, 3, 4) but is degraded for larger values.
BIBLIOGRAPHIE

1 - GAVER, D., SHEDLER, G.S. - "Processor utilization in multiprogramming systems via diffusion approximations" - *Operations Research* 21, 569-576 - 1973).

2 - GELENBE, E. - "On approximate computer system models" - *Journal ACM* 22 261-269 (April 1975).

3 - GELENBE, E. - "A non-Markovian diffusion process and its application to the approximation of queueing and computer system behaviour" - Res. Report 74-1 - Chaire de Systèmes Informatiques - Université de Liège.

4 - KOBAYASHI, H. - "Application of the diffusion approximation to queueing networks, Part I - Equilibrium probability distributions" - *Journal ACM* 21, 316-328 (April 1974).

5 - REISER, M., KOBAYASHI, H. - "The effects of service time distributions on system performance" - *Proc. IFIP Congress 1974 - Part 2 - 230-234* (August 1974).
$$K_s^2 = 1$$

<table><caption>TABLE 1</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td rowspan="2">1</td><td></td><td>0.200</td><td>0.200</td><td>0.331</td><td>0.333</td><td>0.428</td><td>0.429</td><td>0.443</td><td>0.494</td><td>0.472</td><td>0.474</td></tr><tr><td></td><td>0.239</td><td>0.236</td><td>0.430</td><td>0.426</td><td>0.569</td><td>0.567</td><td>0.591</td><td>0.590</td><td>0.626</td><td>0.631</td></tr><tr><td rowspan="2">2</td><td></td><td>0.246</td><td>0.246</td><td>0.464</td><td>0.465</td><td>0.631</td><td>0.634</td><td>0.662</td><td>0.661</td><td>0.707</td><td>0.709</td></tr><tr><td></td><td>0.249</td><td>0.249</td><td>0.480</td><td>0.482</td><td>0.672</td><td>0.672</td><td>0.696</td><td>0.702</td><td>0.753</td><td>0.756</td></tr><tr><td rowspan="2">3</td><td></td><td>0.252</td><td>0.250</td><td>0.496</td><td>0.491</td><td>0.697</td><td>0.695</td><td>0.733</td><td>0.729</td><td>0.791</td><td>0.786</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.493</td><td>0.496</td><td>0.708</td><td>0.711</td><td>0.748</td><td>0.747</td><td>0.803</td><td>0.808</td></tr><tr><td rowspan="2">4</td><td></td><td>0.250</td><td>0.250</td><td>0.501</td><td>0.498</td><td>0.712</td><td>0.722</td><td>0.760</td><td>0.759</td><td>0.818</td><td>0.824</td></tr><tr><td></td><td>0.249</td><td>0.249</td><td>0.494</td><td>0.499</td><td>0.717</td><td>0.729</td><td>0.778</td><td>0.769</td><td>0.823</td><td>0.839</td></tr><tr><td rowspan="2">5</td><td></td><td>0.250</td><td>0.250</td><td>0.496</td><td>0.491</td><td>0.697</td><td>0.695</td><td>0.733</td><td>0.729</td><td>0.791</td><td>0.786</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.493</td><td>0.496</td><td>0.708</td><td>0.711</td><td>0.748</td><td>0.747</td><td>0.803</td><td>0.808</td></tr><tr><td rowspan="2">6</td><td></td><td>0.250</td><td>0.250</td><td>0.501</td><td>0.498</td><td>0.712</td><td>0.722</td><td>0.760</td><td>0.759</td><td>0.818</td><td>0.824</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.493</td><td>0.496</td><td>0.708</td><td>0.711</td><td>0.748</td><td>0.747</td><td>0.803</td><td>0.808</td></tr><tr><td rowspan="2">7</td><td></td><td>0.250</td><td>0.250</td><td>0.501</td><td>0.498</td><td>0.712</td><td>0.722</td><td>0.760</td><td>0.759</td><td>0.818</td><td>0.824</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.493</td><td>0.496</td><td>0.708</td><td>0.711</td><td>0.748</td><td>0.747</td><td>0.803</td><td>0.808</td></tr><tr><td rowspan="2">8</td><td></td><td>0.248</td><td>0.250</td><td>0.494</td><td>0.499</td><td>0.717</td><td>0.729</td><td>0.778</td><td>0.769</td><td>0.823</td><td>0.839</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.497</td><td>0.499</td><td>0.727</td><td>0.735</td><td>0.771</td><td>0.776</td><td>0.845</td><td>0.846</td></tr><tr><td rowspan="2">9</td><td></td><td>0.249</td><td>0.250</td><td>0.494</td><td>0.499</td><td>0.717</td><td>0.729</td><td>0.778</td><td>0.769</td><td>0.823</td><td>0.839</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.497</td><td>0.499</td><td>0.727</td><td>0.735</td><td>0.771</td><td>0.776</td><td>0.845</td><td>0.846</td></tr><tr><td rowspan="2">10</td><td></td><td>0.247</td><td>0.250</td><td>0.503</td><td>0.500</td><td>0.743</td><td>0.739</td><td>0.776</td><td>0.781</td><td>0.851</td><td>0.854</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.493</td><td>0.496</td><td>0.708</td><td>0.711</td><td>0.748</td><td>0.747</td><td>0.803</td><td>0.808</td></tr></tbody></table>
$$K_s^2 = 2$$

<table><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.200</td><td>0.200</td><td>0.334</td><td>0.333</td><td>0.425</td><td>0.429</td><td>0.443</td><td>0.444</td><td>0.473</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.237</td><td>0.232</td><td>0.426</td><td>0.411</td><td>0.552</td><td>0.537</td><td>0.579</td><td>0.557</td><td>0.623</td><td>0.593</td></tr><tr><td>3</td><td></td><td>0.243</td><td>0.244</td><td>0.450</td><td>0.449</td><td>0.617</td><td>0.599</td><td>0.630</td><td>0.622</td><td>0.688</td><td>0.664</td></tr><tr><td>4</td><td></td><td>0.251</td><td>0.248</td><td>0.473</td><td>0.470</td><td>0.652</td><td>0.638</td><td>0.686</td><td>0.665</td><td>0.728</td><td>0.711</td></tr><tr><td>5</td><td></td><td>0.249</td><td>0.249</td><td>0.493</td><td>0.482</td><td>0.665</td><td>0.665</td><td>0.701</td><td>0.694</td><td>0.751</td><td>0.744</td></tr><tr><td>6</td><td></td><td>0.252</td><td>0.250</td><td>0.485</td><td>0.490</td><td>0.684</td><td>0.685</td><td>0.714</td><td>0.716</td><td>0.771</td><td>0.769</td></tr><tr><td>7</td><td></td><td>0.249</td><td>0.250</td><td>0.499</td><td>0.494</td><td>0.701</td><td>0.699</td><td>0.734</td><td>0.732</td><td>0.792</td><td>0.788</td></tr><tr><td>8</td><td></td><td>0.250</td><td>0.250</td><td>0.492</td><td>0.496</td><td>0.690</td><td>0.710</td><td>0.752</td><td>0.944</td><td>0.796</td><td>0.803</td></tr><tr><td>9</td><td></td><td>0.250</td><td>0.250</td><td>0.503</td><td>0.498</td><td>0.721</td><td>0.718</td><td>0.754</td><td>0.754</td><td>0.831</td><td>0.816</td></tr><tr><td>10</td><td></td><td>0.253</td><td>0.250</td><td>0.491</td><td>0.499</td><td>0.726</td><td>0.724</td><td>0.765</td><td>0.762</td><td>0.834</td><td>0.826</td></tr></tbody></table>
$K_s^2 = 3$

<table><caption>TABLE 3</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">P</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td rowspan="2">1</td><td></td><td>0.199</td><td>0.200</td><td>0.329</td><td>0.333</td><td>0.428</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.477</td><td>0.474</td></tr><tr><td></td><td>0.232</td><td>0.230</td><td>0.411</td><td>0.399</td><td>0.546</td><td>0.517</td><td>0.566</td><td>0.536</td><td>0.601</td><td>0.570</td></tr><tr><td rowspan="2">3</td><td></td><td>0.241</td><td>0.241</td><td>0.448</td><td>0.437</td><td>0.893</td><td>0.574</td><td>0.626</td><td>0.595</td><td>0.675</td><td>0.634</td></tr><tr><td></td><td>0.245</td><td>0.426</td><td>0.455</td><td>0.459</td><td>0.630</td><td>0.613</td><td>0.668</td><td>0.637</td><td>0.710</td><td>0.679</td></tr><tr><td rowspan="2">5</td><td></td><td>0.249</td><td>0.248</td><td>0.486</td><td>0.473</td><td>0.641</td><td>0.641</td><td>0.685</td><td>0.667</td><td>0.745</td><td>0.712</td></tr><tr><td></td><td>0.251</td><td>0.249</td><td>0.488</td><td>0.482</td><td>0.673</td><td>0.662</td><td>0.700</td><td>0.690</td><td>0.746</td><td>0.738</td></tr><tr><td rowspan="2">7</td><td></td><td>0.255</td><td>0.250</td><td>0.477</td><td>0.488</td><td>0.676</td><td>0.678</td><td>0.716</td><td>0.708</td><td>0.774</td><td>0.759</td></tr><tr><td></td><td>0.249</td><td>0.250</td><td>0.485</td><td>0.492</td><td>0.696</td><td>0.691</td><td>0.723</td><td>0.722</td><td>0.783</td><td>0.775</td></tr><tr><td rowspan="2">9</td><td></td><td>0.249</td><td>0.250</td><td>0.489</td><td>0.495</td><td>0.697</td><td>0.701</td><td>0.726</td><td>0.733</td><td>0.783</td><td>0.789</td></tr><tr><td></td><td>0.250</td><td>0.250</td><td>0.497</td><td>0.497</td><td>0.703</td><td>0.709</td><td>0.780</td><td>0.743</td><td>0.805</td><td>0.801</td></tr></tbody></table>
$$K_S^2 = 4$$

<table><caption>TABLE 4</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.200</td><td>0.200</td><td>0.329</td><td>0.333</td><td>0.425</td><td>0.429</td><td>0.445</td><td>0.444</td><td>0.475</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.233</td><td>0.227</td><td>0.414</td><td>0.391</td><td>0.539</td><td>0.504</td><td>0.555</td><td>0.522</td><td>0.596</td><td>0.554</td></tr><tr><td>3</td><td></td><td>0.236</td><td>0.239</td><td>0.440</td><td>0.426</td><td>0.887</td><td>0.555</td><td>0.604</td><td>0.575</td><td>0.659</td><td>0.612</td></tr><tr><td>4</td><td></td><td>0.246</td><td>0.245</td><td>0.459</td><td>0.449</td><td>0.613</td><td>0.592</td><td>0.651</td><td>0.615</td><td>0.698</td><td>0.654</td></tr><tr><td>5</td><td></td><td>0.245</td><td>0.248</td><td>0.476</td><td>0.465</td><td>0.628</td><td>0.621</td><td>0.654</td><td>0.645</td><td>0.716</td><td>0.687</td></tr><tr><td>6</td><td></td><td>0.245</td><td>0.249</td><td>0.476</td><td>0.475</td><td>0.661</td><td>0.642</td><td>0.682</td><td>0.668</td><td>0.720</td><td>0.713</td></tr><tr><td>7</td><td></td><td>0.249</td><td>0.249</td><td>0.481</td><td>0.482</td><td>0.678</td><td>0.660</td><td>0.709</td><td>0.687</td><td>0.755</td><td>0.734</td></tr><tr><td>8</td><td></td><td>0.248</td><td>0.250</td><td>0.487</td><td>0.488</td><td>0.682</td><td>0.673</td><td>0.707</td><td>0.702</td><td>0.776</td><td>0.752</td></tr><tr><td>9</td><td></td><td>0.250</td><td>0.250</td><td>0.498</td><td>0.491</td><td>0.694</td><td>0.685</td><td>0.725</td><td>0.715</td><td>0.771</td><td>0.766</td></tr><tr><td>10</td><td></td><td>0.249</td><td>0.250</td><td>0.493</td><td>0.494</td><td>0.699</td><td>0.694</td><td>0.726</td><td>0.725</td><td>0.797</td><td>0.779</td></tr></tbody></table>
<table><caption>TABLE 5
$K_s^2 = 5$</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">P</th><th colspan="3">1/μ = 0.25</th><th colspan="3">0.5</th><th colspan="3">0.75</th><th colspan="3">0.8</th><th colspan="3">0.9</th></tr><tr><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th></tr></thead><tbody><tr><td>1</td><td></td><td>0.198</td><td>0.200</td><td></td><td>0.334</td><td>0.333</td><td></td><td>0.425</td><td>0.429</td><td></td><td>0.443</td><td>0.444</td><td></td><td>0.474</td><td>0.474</td><td></td></tr><tr><td>2</td><td></td><td>0.233</td><td>0.225</td><td></td><td>0.404</td><td>0.384</td><td></td><td>0.537</td><td>0.494</td><td></td><td>0.553</td><td>0.511</td><td></td><td>0.589</td><td>0.589</td><td></td></tr><tr><td>3</td><td></td><td>0.240</td><td>0.237</td><td></td><td>0.431</td><td>0.418</td><td></td><td>0.574</td><td>0.541</td><td></td><td>0.601</td><td>0.560</td><td></td><td>0.645</td><td>0.645</td><td></td></tr><tr><td>4</td><td></td><td>0.243</td><td>0.244</td><td></td><td>0.442</td><td>0.441</td><td></td><td>0.607</td><td>0.576</td><td></td><td>0.635</td><td>0.587</td><td></td><td>0.682</td><td>0.682</td><td></td></tr><tr><td>5</td><td></td><td>0.248</td><td>0.247</td><td></td><td>0.453</td><td>0.457</td><td></td><td>0.627</td><td>0.604</td><td></td><td>0.643</td><td>0.626</td><td></td><td>0.700</td><td>0.700</td><td></td></tr><tr><td>6</td><td></td><td>0.249</td><td>0.248</td><td></td><td>0.468</td><td>0.468</td><td></td><td>0.647</td><td>0.626</td><td></td><td>0.662</td><td>0.650</td><td></td><td>0.712</td><td>0.712</td><td></td></tr><tr><td>7</td><td></td><td>0.248</td><td>0.249</td><td></td><td>0.477</td><td>0.476</td><td></td><td>0.663</td><td>0.643</td><td></td><td>0.680</td><td>0.669</td><td></td><td>0.748</td><td>0.748</td><td></td></tr><tr><td>8</td><td></td><td>0.249</td><td>0.250</td><td></td><td>0.478</td><td>0.482</td><td></td><td>0.656</td><td>0.658</td><td></td><td>0.694</td><td>0.685</td><td></td><td>0.760</td><td>0.760</td><td></td></tr><tr><td>9</td><td></td><td>0.245</td><td>0.250</td><td></td><td>0.488</td><td>0.487</td><td></td><td>0.673</td><td>0.670</td><td></td><td>0.705</td><td>0.698</td><td></td><td>0.767</td><td>0.767</td><td></td></tr><tr><td>10</td><td></td><td>0.255</td><td>0.250</td><td></td><td>0.482</td><td>0.490</td><td></td><td>0.671</td><td>0.680</td><td></td><td>0.709</td><td>0.710</td><td></td><td>0.771</td><td>0.771</td><td></td></tr></tbody></table>
$K_s^2 = 6$

<table><caption>TABLE 6</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.197</td><td>0.200</td><td>0.329</td><td>0.333</td><td>0.429</td><td>0.429</td><td>0.445</td><td>0.444</td><td>0.468</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.228</td><td>0.223</td><td>0.396</td><td>0.379</td><td>0.527</td><td>0.486</td><td>0.539</td><td>0.503</td><td>0.585</td><td>0.535</td></tr><tr><td>3</td><td></td><td>0.235</td><td>0.236</td><td>0.421</td><td>0.411</td><td>0.560</td><td>0.529</td><td>0.583</td><td>0.548</td><td>0.634</td><td>0.582</td></tr><tr><td>4</td><td></td><td>0.237</td><td>0.242</td><td>0.436</td><td>0.433</td><td>0.595</td><td>0.563</td><td>0.620</td><td>0.583</td><td>0.659</td><td>0.619</td></tr><tr><td>5</td><td></td><td>0.241</td><td>0.246</td><td>0.455</td><td>0.449</td><td>0.609</td><td>0.589</td><td>0.641</td><td>0.611</td><td>0.679</td><td>0.649</td></tr><tr><td>6</td><td></td><td>0.241</td><td>0.248</td><td>0.459</td><td>0.461</td><td>0.619</td><td>0.611</td><td>0.654</td><td>0.634</td><td>0.702</td><td>0.654</td></tr><tr><td>7</td><td></td><td>0.255</td><td>0.249</td><td>0.463</td><td>0.470</td><td>0.640</td><td>0.629</td><td>0.678</td><td>0.653</td><td>0.701</td><td>0.676</td></tr><tr><td>8</td><td></td><td>0.249</td><td>0.249</td><td>0.484</td><td>0.477</td><td>0.654</td><td>0.644</td><td>0.684</td><td>0.669</td><td>0.767</td><td>0.714</td></tr><tr><td>9</td><td></td><td>0.257</td><td>0.250</td><td>0.473</td><td>0.482</td><td>0.669</td><td>0.657</td><td>0.685</td><td>0.683</td><td>0.746</td><td>0.729</td></tr><tr><td>10</td><td></td><td>0.252</td><td>0.250</td><td>0.493</td><td>0.486</td><td>0.669</td><td>0.667</td><td>0.713</td><td>0.695</td><td>0.770</td><td>0.743</td></tr></tbody></table>
<caption>$K_s^2 = 7$</caption>

TABLE 7

<table><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.198</td><td>0.200</td><td>0.334</td><td>0.333</td><td>0.424</td><td>0.429</td><td>0.451</td><td>0.444</td><td>0.474</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.225</td><td>0.222</td><td>0.394</td><td>0.375</td><td>0.520</td><td>0.480</td><td>0.535</td><td>0.497</td><td>0.874</td><td>0.528</td></tr><tr><td>3</td><td></td><td>0.231</td><td>0.234</td><td>0.419</td><td>0.405</td><td>0.557</td><td>0.520</td><td>0.578</td><td>0.538</td><td>0.618</td><td>0.571</td></tr><tr><td>4</td><td></td><td>0.240</td><td>0.241</td><td>0.433</td><td>0.426</td><td>0.591</td><td>0.552</td><td>0.600</td><td>0.571</td><td>0.663</td><td>0.606</td></tr><tr><td>5</td><td></td><td>0.249</td><td>0.245</td><td>0.448</td><td>0.443</td><td>0.601</td><td>0.577</td><td>0.612</td><td>0.598</td><td>0.683</td><td>0.635</td></tr><tr><td>6</td><td></td><td>0.246</td><td>0.247</td><td>0.454</td><td>0.455</td><td>0.629</td><td>0.599</td><td>0.641</td><td>0.621</td><td>0.706</td><td>0.660</td></tr><tr><td>7</td><td></td><td>0.256</td><td>0.248</td><td>0.467</td><td>0.465</td><td>0.633</td><td>0.617</td><td>0.646</td><td>0.640</td><td>0.712</td><td>0.680</td></tr><tr><td>8</td><td></td><td>0.247</td><td>0.249</td><td>0.474</td><td>0.472</td><td>0.646</td><td>0.632</td><td>0.668</td><td>0.656</td><td>0.717</td><td>0.698</td></tr><tr><td>9</td><td></td><td>0.249</td><td>0.250</td><td>0.466</td><td>0.478</td><td>0.649</td><td>0.645</td><td>0.676</td><td>0.670</td><td>0.753</td><td>0.714</td></tr><tr><td>10</td><td></td><td>0.245</td><td>0.250</td><td>0.503</td><td>0.482</td><td>0.652</td><td>0.656</td><td>0.688</td><td>0.682</td><td>0.741</td><td>0.728</td></tr></tbody></table>
$$K_s^2 = 8$$

<table><caption>TABLE 8</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="3">1/μ = 0.25</th><th colspan="3">0.5</th><th colspan="3">0.75</th><th colspan="3">0.8</th><th colspan="3">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.201</td><td>0.200</td><td>0.331</td><td>0.333</td><td>0.423</td><td>0.429</td><td>0.451</td><td>0.444</td><td>0.479</td><td>0.474</td><td>0.523</td><td>0.562</td><td>0.595</td><td>0.623</td><td>0.647</td></tr><tr><td>2</td><td></td><td>0.222</td><td>0.220</td><td>0.386</td><td>0.371</td><td>0.519</td><td>0.475</td><td>0.536</td><td>0.492</td><td>0.575</td><td>0.523</td><td>0.606</td><td>0.562</td><td>0.692</td><td>0.660</td><td>0.683</td></tr><tr><td>3</td><td></td><td>0.234</td><td>0.232</td><td>0.420</td><td>0.399</td><td>0.543</td><td>0.512</td><td>0.572</td><td>0.530</td><td>0.606</td><td>0.562</td><td>0.692</td><td>0.595</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>4</td><td></td><td>0.241</td><td>0.239</td><td>0.416</td><td>0.420</td><td>0.569</td><td>0.542</td><td>0.597</td><td>0.561</td><td>0.692</td><td>0.595</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>5</td><td></td><td>0.247</td><td>0.244</td><td>0.444</td><td>0.437</td><td>0.599</td><td>0.567</td><td>0.612</td><td>0.587</td><td>0.660</td><td>0.595</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>6</td><td></td><td>0.245</td><td>0.246</td><td>0.457</td><td>0.449</td><td>0.604</td><td>0.588</td><td>0.643</td><td>0.609</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.647</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>7</td><td></td><td>0.246</td><td>0.248</td><td>0.465</td><td>0.459</td><td>0.629</td><td>0.605</td><td>0.647</td><td>0.628</td><td>0.709</td><td>0.667</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>8</td><td></td><td>0.253</td><td>0.249</td><td>0.454</td><td>0.467</td><td>0.626</td><td>0.621</td><td>0.660</td><td>0.614</td><td>0.696</td><td>0.685</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>9</td><td></td><td>0.244</td><td>0.249</td><td>0.481</td><td>0.473</td><td>0.649</td><td>0.634</td><td>0.662</td><td>0.658</td><td>0.736</td><td>0.700</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.623</td><td>0.647</td></tr><tr><td>10</td><td></td><td>0.244</td><td>0.269</td><td>0.476</td><td>0.478</td><td>0.637</td><td>0.645</td><td>0.693</td><td>0.670</td><td>0.724</td><td>0.714</td><td>0.660</td><td>0.623</td><td>0.660</td><td>0.623</td><td>0.647</td></tr></tbody></table>
<caption>$K_s^2 = 9$</caption>

TABLE 9

<table><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.200</td><td>0.200</td><td>0.338</td><td>0.333</td><td>0.429</td><td>0.429</td><td>0.445</td><td>0.444</td><td>0.475</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.224</td><td>0.219</td><td>0.381</td><td>0.368</td><td>0.503</td><td>0.471</td><td>0.523</td><td>0.488</td><td>0.565</td><td>0.518</td></tr><tr><td>3</td><td></td><td>0.237</td><td>0.231</td><td>0.405</td><td>0.395</td><td>0.538</td><td>0.506</td><td>0.554</td><td>0.523</td><td>0.602</td><td>0.555</td></tr><tr><td>4</td><td></td><td>0.237</td><td>0.238</td><td>0.420</td><td>0.415</td><td>0.557</td><td>0.534</td><td>0.580</td><td>0.533</td><td>0.636</td><td>0.586</td></tr><tr><td>5</td><td></td><td>0.238</td><td>0.243</td><td>0.442</td><td>0.431</td><td>0.590</td><td>0.558</td><td>0.612</td><td>0.578</td><td>0.650</td><td>0.613</td></tr><tr><td>6</td><td></td><td>0.235</td><td>0.245</td><td>0.460</td><td>0.444</td><td>0.595</td><td>0.578</td><td>0.621</td><td>0.599</td><td>0.666</td><td>0.635</td></tr><tr><td>7</td><td></td><td>0.253</td><td>0.247</td><td>0.458</td><td>0.454</td><td>0.614</td><td>0.596</td><td>0.623</td><td>0.617</td><td>0.686</td><td>0.655</td></tr><tr><td>8</td><td></td><td>0.250</td><td>0.248</td><td>0.458</td><td>0.462</td><td>0.630</td><td>0.611</td><td>0.649</td><td>0.633</td><td>0.699</td><td>0.673</td></tr><tr><td>9</td><td></td><td>0.244</td><td>0.249</td><td>0.471</td><td>0.469</td><td>0.631</td><td>0.624</td><td>0.664</td><td>0.647</td><td>0.690</td><td>0.688</td></tr><tr><td>10</td><td></td><td>0.244</td><td>0.249</td><td>0.469</td><td>0.474</td><td>0.628</td><td>0.635</td><td>0.651</td><td>0.660</td><td>0.710</td><td>0.702</td></tr></tbody></table>
$$K_s^2 = 10$$

<table><caption>TABLE 10</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">P</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>10.203</td><td>0.200</td><td>0.337</td><td>0.333</td><td>0.428</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.475</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.222</td><td>0.218</td><td>0.381</td><td>0.366</td><td>0.511</td><td>0.468</td><td>0.529</td><td>0.484</td><td>0.558</td><td>0.515</td></tr><tr><td>3</td><td></td><td>0.229</td><td>0.230</td><td>0.400</td><td>0.391</td><td>0.529</td><td>0.500</td><td>0.549</td><td>0.517</td><td>0.586</td><td>0.549</td></tr><tr><td>4</td><td></td><td>0.235</td><td>0.237</td><td>0.413</td><td>0.411</td><td>0.549</td><td>0.527</td><td>0.576</td><td>0.545</td><td>0.608</td><td>0.578</td></tr><tr><td>5</td><td></td><td>0.239</td><td>0.241</td><td>0.429</td><td>0.426</td><td>0.571</td><td>0.550</td><td>0.599</td><td>0.569</td><td>0.642</td><td>0.604</td></tr><tr><td>6</td><td></td><td>0.242</td><td>0.244</td><td>0.436</td><td>0.439</td><td>0.610</td><td>0.570</td><td>0.616</td><td>0.590</td><td>0.645</td><td>0.626</td></tr><tr><td>7</td><td></td><td>0.243</td><td>0.246</td><td>0.460</td><td>0.449</td><td>0.602</td><td>0.587</td><td>0.613</td><td>0.608</td><td>0.676</td><td>0.645</td></tr><tr><td>8</td><td></td><td>0.246</td><td>0.248</td><td>0.453</td><td>0.458</td><td>0.614</td><td>0.602</td><td>0.634</td><td>0.623</td><td>0.691</td><td>0.662</td></tr><tr><td>9</td><td></td><td>0.248</td><td>0.248</td><td>0.465</td><td>0.465</td><td>0.625</td><td>0.615</td><td>0.647</td><td>0.637</td><td>0.695</td><td>0.677</td></tr><tr><td>10</td><td></td><td>0.249</td><td>0.249</td><td>0.469</td><td>0.470</td><td>0.637</td><td>0.626</td><td>0.662</td><td>0.650</td><td>0.714</td><td>0.691</td></tr></tbody></table>
$$K_s^2 = 1$$

<table><caption>TABLE 11</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">ρ</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.201</td><td>0.200</td><td>0.333</td><td>0.333</td><td>0.429</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.474</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.249</td><td>0.250</td><td>0.470</td><td>0.482</td><td>0.625</td><td>0.648</td><td>0.645</td><td>0.673</td><td>0.696</td><td>0.715</td></tr><tr><td>3</td><td></td><td>0.252</td><td>0.250</td><td>0.493</td><td>0.498</td><td>0.699</td><td>0.706</td><td>0.729</td><td>0.738</td><td>0.782</td><td>0.792</td></tr><tr><td>4</td><td></td><td>0.249</td><td>0.250</td><td>0.502</td><td>0.500</td><td>0.724</td><td>0.729</td><td>0.762</td><td>0.767</td><td>0.817</td><td>0.829</td></tr><tr><td>5</td><td></td><td>0.250</td><td>0.250</td><td>0.498</td><td>0.500</td><td>0.736</td><td>0.740</td><td>0.776</td><td>0.781</td><td>0.840</td><td>0.850</td></tr><tr><td>6</td><td></td><td>0.250</td><td>0.250</td><td>0.418</td><td>0.500</td><td>0.743</td><td>0.745</td><td>0.789</td><td>0.789</td><td>0.864</td><td>0.864</td></tr><tr><td>7</td><td></td><td>0.250</td><td>0.250</td><td>0.500</td><td>0.500</td><td>0.750</td><td>0.747</td><td>0.794</td><td>0.793</td><td>0.872</td><td>0.873</td></tr><tr><td>8</td><td></td><td>0.252</td><td>0.250</td><td>0.502</td><td>0.500</td><td>0.760</td><td>0.749</td><td>0.794</td><td>0.796</td><td>0.876</td><td>0.879</td></tr><tr><td>9</td><td></td><td>0.253</td><td>0.250</td><td>0.501</td><td>0.500</td><td>0.746</td><td>0.749</td><td>0.795</td><td>0.798</td><td>0.879</td><td>0.884</td></tr><tr><td>10</td><td></td><td>0.250</td><td>0.250</td><td>0.500</td><td>0.500</td><td>0.763</td><td>0.750</td><td>0.805</td><td>0.789</td><td>0.885</td><td>0.888</td></tr></tbody></table>
<caption>$K_s^2 = 2$</caption>

<table><caption>TABLE 12</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.199</td><td>0.200</td><td>0.333</td><td>0.333</td><td>0.429</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.473</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.246</td><td>0.248</td><td>0.449</td><td>0.449</td><td>0.602</td><td>0.581</td><td>0.629</td><td>0.601</td><td>0.672</td><td>0.637</td></tr><tr><td>3</td><td></td><td>0.249</td><td>0.250</td><td>0.471</td><td>0.482</td><td>0.663</td><td>0.648</td><td>0.689</td><td>0.673</td><td></td><td></td></tr><tr><td>4</td><td></td><td>0.249</td><td>0.250</td><td>0.492</td><td>0.494</td><td>0.683</td><td>0.685</td><td>0.720</td><td>0.713</td><td>0.779</td><td>0.762</td></tr><tr><td>5</td><td></td><td>0.249</td><td>0.250</td><td>0.485</td><td>0.498</td><td>0.702</td><td>0.706</td><td>0.736</td><td>0.738</td><td>0.808</td><td>0.792</td></tr><tr><td>6</td><td></td><td>0.257</td><td>0.250</td><td>0.491</td><td>0.499</td><td>0.704</td><td>0.720</td><td>0.762</td><td>0.755</td><td>0.820</td><td>0.813</td></tr><tr><td>7</td><td></td><td>0.252</td><td>0.250</td><td>0.492</td><td>0.500</td><td>0.726</td><td>0.729</td><td>0.764</td><td>0.767</td><td>0.827</td><td>0.829</td></tr><tr><td>8</td><td></td><td>0.250</td><td>0.250</td><td>0.496</td><td>0.500</td><td>0.734</td><td>0.736</td><td>0.777</td><td>0.775</td><td>0.841</td><td>0.841</td></tr><tr><td>9</td><td></td><td>0.249</td><td>0.250</td><td>0.494</td><td>0.500</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>10</td><td></td><td>0.251</td><td>0.250</td><td>0.497</td><td>0.500</td><td>0.723</td><td>0.743</td><td>0.776</td><td>0.786</td><td>0.849</td><td>0.858</td></tr></tbody></table>
<caption>$K_s^2 = 3$</caption>

TABLE 13

<table><thead><tr><th rowspan="2">M</th><th rowspan="2">P</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.199</td><td>0.200</td><td>0.334</td><td>0.333</td><td>0.429</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.471</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.241</td><td>0.244</td><td>0.436</td><td>0.426</td><td>0.592</td><td>0.545</td><td>0.606</td><td>0.564</td><td>0.653</td><td>0.597</td></tr><tr><td>3</td><td></td><td>0.248</td><td>0.244</td><td>0.465</td><td>0.465</td><td>0.635</td><td>0.609</td><td>0.656</td><td>0.631</td><td>0.718</td><td>0.668</td></tr><tr><td>4</td><td></td><td>0.247</td><td>0.250</td><td>0.473</td><td>0.482</td><td>0.665</td><td>0.648</td><td>0.701</td><td>0.673</td><td>0.748</td><td>0.715</td></tr><tr><td>5</td><td></td><td>0.247</td><td>0.250</td><td>0.480</td><td>0.491</td><td>0.676</td><td>0.675</td><td>0.707</td><td>0.702</td><td>0.770</td><td>0.749</td></tr><tr><td>6</td><td></td><td>0.253</td><td>0.250</td><td>0.487</td><td>0.496</td><td>0.698</td><td>0.693</td><td>0.738</td><td>0.723</td><td>0.801</td><td>0.773</td></tr><tr><td>7</td><td></td><td>0.244</td><td>0.250</td><td>0.485</td><td>0.498</td><td>0.710</td><td>0.706</td><td>0.738</td><td>0.738</td><td>0.798</td><td>0.792</td></tr><tr><td>8</td><td></td><td>0.248</td><td>0.250</td><td>0.505</td><td>0.499</td><td>0.712</td><td>0.716</td><td>0.753</td><td>0.750</td><td>0.814</td><td>0.807</td></tr><tr><td>9</td><td></td><td>0.249</td><td>0.250</td><td>0.494</td><td>0.499</td><td>0.723</td><td>0.724</td><td>0.759</td><td>0.759</td><td>0.820</td><td>0.819</td></tr><tr><td>10</td><td></td><td>0.251</td><td>0.250</td><td>0.509</td><td>0.500</td><td>0.712</td><td>0.729</td><td>0.757</td><td>0.767</td><td>0.829</td><td>0.829</td></tr></tbody></table>
$$K_s^2 = 4$$

<table><caption>TABLE 14</caption><thead><tr><th rowspan="2">p</th><th colspan="3">1/μ = 0.25</th><th colspan="3">0.5</th><th colspan="3">0.75</th><th colspan="3">0.8</th><th colspan="3">0.9</th></tr><tr><th>S</th><th>I</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td>0.199</td><td>0.200</td><td>0.328</td><td>0.333</td><td>0.430</td><td>0.429</td><td>0.442</td><td>0.444</td><td>0.476</td><td>0.474</td><td>0.572</td><td>0.637</td><td>0.715</td><td>0.741</td><td>0.762</td></tr><tr><td>2</td><td>0.238</td><td>0.239</td><td>0.434</td><td>0.411</td><td>0.573</td><td>0.523</td><td>0.599</td><td>0.540</td><td>0.643</td><td>0.572</td><td>0.637</td><td>0.715</td><td>0.741</td><td>0.762</td><td>0.778</td></tr><tr><td>3</td><td>0.248</td><td>0.248</td><td>0.457</td><td>0.449</td><td>0.617</td><td>0.581</td><td>0.636</td><td>0.601</td><td>0.695</td><td>0.637</td><td>0.715</td><td>0.741</td><td>0.762</td><td>0.778</td><td>0.790</td></tr><tr><td>4</td><td>0.243</td><td>0.249</td><td>0.473</td><td>0.470</td><td>0.647</td><td>0.621</td><td>0.667</td><td>0.643</td><td>0.723</td><td>0.682</td><td>0.715</td><td>0.741</td><td>0.762</td><td>0.778</td><td>0.790</td></tr><tr><td>5</td><td>0.249</td><td>0.250</td><td>0.476</td><td>0.482</td><td>0.662</td><td>0.648</td><td>0.689</td><td>0.673</td><td>0.741</td><td>0.715</td><td>0.741</td><td>0.762</td><td>0.778</td><td>0.790</td><td>0.803</td></tr><tr><td>6</td><td>0.250</td><td>0.250</td><td>0.482</td><td>0.490</td><td>0.679</td><td>0.669</td><td>0.702</td><td>0.696</td><td>0.768</td><td>0.741</td><td>0.762</td><td>0.778</td><td>0.790</td><td>0.803</td><td>0.803</td></tr><tr><td>7</td><td>0.252</td><td>0.250</td><td>0.485</td><td>0.494</td><td>0.688</td><td>0.685</td><td>0.733</td><td>0.713</td><td>0.781</td><td>0.762</td><td>0.778</td><td>0.790</td><td>0.803</td><td>0.810</td><td>0.803</td></tr><tr><td>8</td><td>0.251</td><td>0.250</td><td>0.498</td><td>0.496</td><td>0.704</td><td>0.697</td><td>0.730</td><td>0.727</td><td>0.794</td><td>0.778</td><td>0.790</td><td>0.803</td><td>0.810</td><td>0.803</td><td>0.803</td></tr><tr><td>9</td><td>0.245</td><td>0.250</td><td>0.492</td><td>0.498</td><td>0.711</td><td>0.706</td><td>0.731</td><td>0.738</td><td>0.808</td><td>0.778</td><td>0.790</td><td>0.803</td><td>0.810</td><td>0.803</td><td>0.803</td></tr><tr><td>10</td><td>0.247</td><td>0.250</td><td>0.492</td><td>0.499</td><td>0.714</td><td>0.714</td><td>0.745</td><td>0.748</td><td>0.810</td><td>0.778</td><td>0.790</td><td>0.803</td><td>0.810</td><td>0.803</td><td>0.803</td></tr></tbody></table>
$$K_s^2 = 5$$

<table><caption>TABLE 15</caption><thead><tr><th rowspan="2">H/ρ</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td>0.200</td><td>0.200</td><td>0.337</td><td>0.333</td><td>0.428</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.470</td><td></td></tr><tr><td>2</td><td>0.221</td><td>0.236</td><td>0.412</td><td>0.399</td><td>0.554</td><td>0.508</td><td>0.591</td><td>0.525</td><td>0.628</td><td>0.556</td></tr><tr><td>3</td><td>0.240</td><td>0.246</td><td>0.443</td><td>0.437</td><td>0.597</td><td>0.561</td><td>0.619</td><td>0.580</td><td>0.681</td><td>0.614</td></tr><tr><td>4</td><td>0.252</td><td>0.249</td><td>0.454</td><td>0.459</td><td>0.623</td><td>0.599</td><td>0.650</td><td>0.620</td><td>0.696</td><td>0.656</td></tr><tr><td>5</td><td>0.242</td><td>0.250</td><td>0.475</td><td>0.473</td><td>0.646</td><td>0.627</td><td>0.667</td><td>0.650</td><td>0.724</td><td>0.689</td></tr><tr><td>6</td><td>0.245</td><td>0.250</td><td>0.477</td><td>0.482</td><td>0.652</td><td>0.648</td><td>0.692</td><td>0.673</td><td>0.748</td><td>0.715</td></tr><tr><td>7</td><td>0.250</td><td>0.250</td><td>0.488</td><td>0.488</td><td>0.665</td><td>0.665</td><td>0.709</td><td>0.692</td><td>0.741</td><td>0.737</td></tr><tr><td>8</td><td>0.247</td><td>0.250</td><td>0.499</td><td>0.492</td><td>0.671</td><td>0.679</td><td>0.717</td><td>0.707</td><td>0.769</td><td>0.754</td></tr><tr><td>9</td><td>0.250</td><td>0.250</td><td>0.495</td><td>0.495</td><td>0.681</td><td>0.690</td><td>0.719</td><td>0.719</td><td>0.771</td><td>0.769</td></tr><tr><td>10</td><td>0.244</td><td>0.250</td><td>0.490</td><td>0.491</td><td>0.691</td><td>0.699</td><td>0.717</td><td>0.730</td><td>0.808</td><td>0.781</td></tr></tbody></table>
$K_s^2 = 6$

<table><caption>TABLE 16</caption><thead><tr><th rowspan="2">M</th><th rowspan="2">p</th><th colspan="2">1/μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.199</td><td>0.200</td><td>0.335</td><td>0.335</td><td>0.424</td><td>0.429</td><td>0.446</td><td>0.444</td><td>0.472</td><td>0.474</td></tr><tr><td>2</td><td></td><td>0.233</td><td>0.232</td><td>0.407</td><td>0.391</td><td>0.550</td><td>0.497</td><td>0.575</td><td>0.514</td><td>0.612</td><td>0.544</td></tr><tr><td>3</td><td></td><td>0.241</td><td>0.244</td><td>0.435</td><td>0.426</td><td>0.588</td><td>0.545</td><td>0.608</td><td>0.564</td><td>0.653</td><td>0.597</td></tr><tr><td>4</td><td></td><td>0.652</td><td>0.248</td><td>0.453</td><td>0.449</td><td>0.594</td><td>0.581</td><td>0.636</td><td>0.601</td><td>0.685</td><td>0.637</td></tr><tr><td>5</td><td></td><td>0.249</td><td>0.249</td><td>0.466</td><td>0.465</td><td>0.625</td><td>0.609</td><td>0.640</td><td>0.631</td><td>0.695</td><td>0.668</td></tr><tr><td>6</td><td></td><td>0.250</td><td>0.250</td><td>0.479</td><td>0.475</td><td>0.637</td><td>0.631</td><td>0.668</td><td>0.654</td><td>0.724</td><td>0.694</td></tr><tr><td>7</td><td></td><td>0.250</td><td>0.250</td><td>0.473</td><td>0.482</td><td>0.647</td><td>0.648</td><td>0.673</td><td>0.673</td><td>0.753</td><td>0.715</td></tr><tr><td>8</td><td></td><td>0.250</td><td>0.250</td><td>0.482</td><td>0.488</td><td>0.674</td><td>0.663</td><td>0.701</td><td>0.689</td><td>0.762</td><td>0.733</td></tr><tr><td>9</td><td></td><td>0.255</td><td>0.250</td><td>0.472</td><td>0.491</td><td>0.684</td><td>0.675</td><td>0.724</td><td>0.702</td><td>0.769</td><td>0.749</td></tr><tr><td>10</td><td></td><td>0.255</td><td>0.250</td><td>0.791</td><td>0.494</td><td>0.674</td><td>0.685</td><td>0.712</td><td>0.713</td><td>0.777</td><td>0.762</td></tr></tbody></table>
$$K_s^2 = 7$$

<table><caption>TABLE 17</caption><thead><tr><th rowspan="2">N</th><th rowspan="2">p</th><th colspan="3">1/μ = 0.25</th><th colspan="3">0.5</th><th colspan="3">0.75</th><th colspan="3">0.8</th><th colspan="3">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.200</td><td>0.200</td><td>0.328</td><td>0.333</td><td>0.424</td><td>0.429</td><td>0.443</td><td>0.444</td><td>0.443</td><td>0.444</td><td>0.443</td><td>0.444</td><td>0.443</td><td>0.444</td></tr><tr><td>2</td><td></td><td>0.230</td><td>0.230</td><td>0.706</td><td>0.384</td><td>0.549</td><td>0.488</td><td>0.560</td><td>0.505</td><td>0.560</td><td>0.505</td><td>0.560</td><td>0.505</td><td>0.560</td><td>0.505</td></tr><tr><td>3</td><td></td><td>0.246</td><td>0.241</td><td>0.438</td><td>0.418</td><td>0.582</td><td>0.533</td><td>0.593</td><td>0.551</td><td>0.593</td><td>0.551</td><td>0.593</td><td>0.551</td><td>0.593</td><td>0.551</td></tr><tr><td>4</td><td></td><td>0.243</td><td>0.246</td><td>0.433</td><td>0.441</td><td>0.602</td><td>0.567</td><td>0.615</td><td>0.586</td><td>0.615</td><td>0.586</td><td>0.615</td><td>0.586</td><td>0.615</td><td>0.586</td></tr><tr><td>5</td><td></td><td>0.248</td><td>0.248</td><td>0.455</td><td>0.451</td><td>0.605</td><td>0.594</td><td>0.637</td><td>0.615</td><td>0.637</td><td>0.615</td><td>0.637</td><td>0.615</td><td>0.637</td><td>0.615</td></tr><tr><td>6</td><td></td><td>0.248</td><td>0.249</td><td>0.475</td><td>0.468</td><td>0.633</td><td>0.616</td><td>0.664</td><td>0.638</td><td>0.664</td><td>0.638</td><td>0.664</td><td>0.638</td><td>0.664</td><td>0.638</td></tr><tr><td>7</td><td></td><td>0.247</td><td>0.250</td><td>0.477</td><td>0.476</td><td>0.631</td><td>0.634</td><td>0.671</td><td>0.657</td><td>0.671</td><td>0.657</td><td>0.671</td><td>0.657</td><td>0.671</td><td>0.657</td></tr><tr><td>8</td><td></td><td>0.252</td><td>0.250</td><td>0.473</td><td>0.482</td><td>0.648</td><td>0.648</td><td>0.682</td><td>0.673</td><td>0.682</td><td>0.673</td><td>0.682</td><td>0.673</td><td>0.682</td><td>0.673</td></tr><tr><td>9</td><td></td><td>0.248</td><td>0.250</td><td>0.485</td><td>0.487</td><td>0.659</td><td>0.661</td><td>0.695</td><td>0.687</td><td>0.695</td><td>0.687</td><td>0.695</td><td>0.687</td><td>0.695</td><td>0.687</td></tr><tr><td>10</td><td></td><td>0.256</td><td>0.250</td><td>0.486</td><td>0.490</td><td>0.678</td><td>0.672</td><td>0.708</td><td>0.699</td><td>0.708</td><td>0.699</td><td>0.708</td><td>0.699</td><td>0.708</td><td>0.699</td></tr></tbody></table>
$$K_s^2 = 8$$

<table><caption>TABLE 18</caption><thead><tr><th rowspan="2">N</th><th rowspan="2">p</th><th colspan="3">1/μ = 0.25</th><th colspan="3">0.5</th><th colspan="3">0.75</th><th colspan="3">0.8</th><th colspan="3">0.9</th></tr><tr><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>1</td><td></td><td>0.199</td><td>0.200</td><td>0.331</td><td>0.333</td><td>0.430</td><td>0.429</td><td>0.444</td><td>0.444</td><td>0.444</td><td>0.444</td><td>0.444</td><td>0.444</td><td>0.444</td><td>0.444</td></tr><tr><td>2</td><td></td><td>0.225</td><td>0.227</td><td>0.392</td><td>0.379</td><td>0.542</td><td>0.482</td><td>0.550</td><td>0.498</td><td>0.593</td><td>0.593</td><td>0.593</td><td>0.593</td><td>0.593</td><td>0.593</td></tr><tr><td>3</td><td></td><td>0.239</td><td>0.239</td><td>0.416</td><td>0.411</td><td>0.553</td><td>0.523</td><td>0.586</td><td>0.540</td><td>0.631</td><td>0.572</td><td>0.631</td><td>0.572</td><td>0.631</td><td>0.572</td></tr><tr><td>4</td><td></td><td>0.241</td><td>0.245</td><td>0.413</td><td>0.433</td><td>0.590</td><td>0.555</td><td>0.611</td><td>0.574</td><td>0.650</td><td>0.607</td><td>0.650</td><td>0.650</td><td>0.650</td><td>0.650</td></tr><tr><td>5</td><td></td><td>0.219</td><td>0.248</td><td>0.454</td><td>0.449</td><td>0.606</td><td>0.581</td><td>0.625</td><td>0.601</td><td>0.678</td><td>0.637</td><td>0.678</td><td>0.637</td><td>0.678</td><td>0.637</td></tr><tr><td>6</td><td></td><td>0.247</td><td>0.249</td><td>0.452</td><td>0.461</td><td>0.619</td><td>0.603</td><td>0.643</td><td>0.624</td><td>0.680</td><td>0.661</td><td>0.680</td><td>0.680</td><td>0.680</td><td>0.661</td></tr><tr><td>7</td><td></td><td>0.252</td><td>0.249</td><td>0.468</td><td>0.470</td><td>0.628</td><td>0.621</td><td>0.652</td><td>0.643</td><td>0.710</td><td>0.682</td><td>0.710</td><td>0.682</td><td>0.710</td><td>0.682</td></tr><tr><td>8</td><td></td><td>0.249</td><td>0.250</td><td>0.471</td><td>0.477</td><td>0.637</td><td>0.636</td><td>0.683</td><td>0.659</td><td>0.725</td><td>0.700</td><td>0.725</td><td>0.725</td><td>0.725</td><td>0.700</td></tr><tr><td>9</td><td></td><td>0.247</td><td>0.250</td><td>0.472</td><td>0.482</td><td>0.643</td><td>0.648</td><td>0.680</td><td>0.673</td><td>0.733</td><td>0.715</td><td>0.733</td><td>0.733</td><td>0.733</td><td>0.715</td></tr><tr><td>10</td><td></td><td>0.259</td><td>0.250</td><td>0.467</td><td>0.486</td><td>0.662</td><td>0.660</td><td>0.682</td><td>0.685</td><td>0.743</td><td>0.709</td><td>0.743</td><td>0.743</td><td>0.743</td><td>0.709</td></tr></tbody></table>
$$K_s^2 = 9$$

<table><caption>TABLE 19</caption><thead><tr><th rowspan="2">N</th><th rowspan="2">p</th><th colspan="3">1/μ = 0.25</th><th colspan="3">0.5</th><th colspan="3">0.75</th><th colspan="3">0.8</th><th colspan="3">0.9</th></tr><tr><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th><th>S</th><th>F</th><th></th></tr></thead><tbody><tr><td>1</td><td></td><td>0.198</td><td>0.200</td><td></td><td>0.333</td><td>0.333</td><td></td><td>0.428</td><td>0.429</td><td></td><td>0.450</td><td>0.444</td><td></td><td>0.474</td><td>0.474</td><td></td></tr><tr><td>2</td><td></td><td>0.231</td><td>0.225</td><td></td><td>0.383</td><td>0.375</td><td></td><td>0.429</td><td>0.477</td><td></td><td>0.546</td><td>0.493</td><td></td><td>0.584</td><td>0.584</td><td></td></tr><tr><td>3</td><td></td><td>0.240</td><td>0.237</td><td></td><td>0.412</td><td>0.405</td><td></td><td>0.543</td><td>0.515</td><td></td><td>0.558</td><td>0.532</td><td></td><td>0.621</td><td>0.621</td><td></td></tr><tr><td>4</td><td></td><td>0.235</td><td>0.244</td><td></td><td>0.432</td><td>0.426</td><td></td><td>0.574</td><td>0.545</td><td></td><td>0.607</td><td>0.564</td><td></td><td>0.625</td><td>0.625</td><td></td></tr><tr><td>5</td><td></td><td>0.248</td><td>0.247</td><td></td><td>0.450</td><td>0.443</td><td></td><td>0.682</td><td>0.570</td><td></td><td>0.599</td><td>0.590</td><td></td><td>0.658</td><td>0.658</td><td></td></tr><tr><td>6</td><td></td><td>0.244</td><td>0.248</td><td></td><td>0.457</td><td>0.55</td><td></td><td>0.620</td><td>0.591</td><td></td><td>0.624</td><td>0.612</td><td></td><td>0.677</td><td>0.677</td><td></td></tr><tr><td>7</td><td></td><td>0.251</td><td>0.249</td><td></td><td>0.466</td><td>0.465</td><td></td><td>0.622</td><td>0.609</td><td></td><td>0.654</td><td>0.631</td><td></td><td>0.682</td><td>0.682</td><td></td></tr><tr><td>8</td><td></td><td>0.249</td><td>0.250</td><td></td><td>0.481</td><td>0.472</td><td></td><td>0.642</td><td>0.624</td><td></td><td>0.657</td><td>0.647</td><td></td><td>0.706</td><td>0.706</td><td></td></tr><tr><td>9</td><td></td><td>0.249</td><td>0.250</td><td></td><td>0.482</td><td>0.478</td><td></td><td>0.638</td><td>0.637</td><td></td><td>0.657</td><td>0.661</td><td></td><td>0.725</td><td>0.725</td><td></td></tr><tr><td>10</td><td></td><td>0.251</td><td>0.250</td><td></td><td>0.483</td><td>0.482</td><td></td><td>0.658</td><td>0.648</td><td></td><td>0.689</td><td>0.673</td><td></td><td>0.738</td><td>0.738</td><td></td></tr></tbody></table>
<table><caption>TABLE 20</caption><thead><tr><th rowspan="2">μ = 0.25</th><th colspan="2">0.5</th><th colspan="2">0.75</th><th colspan="2">0.8</th><th colspan="2">0.9</th></tr><tr><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th><th>S</th><th>F</th></tr></thead><tbody><tr><td>97</td><td>0.200</td><td>0.333</td><td>0.333</td><td>0.438</td><td>0.429</td><td>0.446</td><td>0.444</td><td>0.473</td><td>0.474</td></tr><tr><td>926</td><td>0.223</td><td>0.387</td><td>0.371</td><td>0.507</td><td>0.472</td><td>0.528</td><td>0.489</td><td>0.577</td><td>0.519</td></tr><tr><td>938</td><td>0.236</td><td>0.413</td><td>0.399</td><td>0.547</td><td>0.508</td><td>0.555</td><td>0.525</td><td>0.586</td><td>0.556</td></tr><tr><td>945</td><td>0.242</td><td>0.422</td><td>0.490</td><td>0.574</td><td>0.539</td><td>0.583</td><td>0.555</td><td>0.616</td><td>0.587</td></tr><tr><td>942</td><td>0.246</td><td>0.440</td><td>0.437</td><td>0.585</td><td>0.561</td><td>0.600</td><td>0.580</td><td>0.645</td><td>0.614</td></tr><tr><td>945</td><td>0.248</td><td>0.437</td><td>0.449</td><td>0.593</td><td>0.581</td><td>0.628</td><td>0.601</td><td>0.691</td><td>0.637</td></tr><tr><td>937</td><td>0.249</td><td>0.448</td><td>0.459</td><td>0.610</td><td>0.599</td><td>0.638</td><td>0.620</td><td>0.698</td><td>0.656</td></tr><tr><td>952</td><td>0.250</td><td>0.467</td><td>0.469</td><td>0.615</td><td>0.614</td><td>0.639</td><td>0.636</td><td>0.699</td><td>0.674</td></tr><tr><td>943</td><td>0.250</td><td>0.478</td><td>0.473</td><td>0.640</td><td>0.627</td><td>0.662</td><td>0.650</td><td>0.694</td><td>0.689</td></tr><tr><td>950</td><td>0.250</td><td>0.470</td><td>0.478</td><td>0.640</td><td>0.638</td><td>0.680</td><td>0.662</td><td>0.707</td><td>0.703</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>Figure 1</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>Figure 2</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 3</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 4</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 5</figcaption></figure>
Probabilities

<figure><img src="image_11.png" /><figcaption>Figure 6</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 7a)</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 7b)</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 8a)</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure 8b)</figcaption></figure>
Probabilities

<figure><img src="image_16.png" /></figure>

$$
\begin{array}{l}
M = 5 \\
1/\mu = 0.50 \\
K_s^2 = 5
\end{array}
$$

$K_s^2 = 5$

Number of customers

<caption>Figure 8c)</caption>