Table 1 Simulation settings

Scenario 1

4

4

3

{50, 100, 200}

I ₄

I ₄

\(\left [\begin {array}{llll} \frac {9}{10} & 0 & 0 & 0 \\ 0 & \frac {1}{2} & 0 & 0 \\ 0 & 0 & \frac {1}{3} & 0 \\ 0 & 0 & 0 & 0 \end {array}\right ]\)

Scenario 2

4

6

2

{50, 100, 200}

I ₄

I ₆

\(\left [\begin {array}{llllllll} \frac {3}{5} & 0 & 0 & 0 & 0 & 0 \\ 0 & \frac {1}{2} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end {array}\right ]\)

Scenario 3

4

6

2

{50, 100, 200}

I ₄

I ₆

\(\left [\begin {array}{llllllllll} \frac {2}{5} & \frac {4}{25} & 0 & 0 & 0 & 0 \\ \frac {4}{25} & \frac {2}{5} & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \end {array}\right ] \)

Scenario 4

6

10

2

{50, 100, 200}

I ₆

\(\left [\begin {array}{lllllllll} \boldsymbol {M} & \boldsymbol {0} \\ \boldsymbol {0} & \boldsymbol {I}_{7} \end {array}\right ]\)

\(\frac {1}{2}\left [\begin {array}{llllll} \boldsymbol {I}_{2} & {\boldsymbol 0} \\ \boldsymbol {0} & \boldsymbol {0} \end {array}\right ]\)

with M(i,j)=0.3^|i−j|

Scenario 5

20

20

10

{50, 100, 200}

I ₂₀

I ₂₀

\(\frac {7}{10}\left [\begin {array}{llllll} \boldsymbol {I}_{10} & \boldsymbol {0} \\ \boldsymbol {0} & \boldsymbol {0} \end {array}\right ]\)

Scenario 6

20

20

10

{50, 100, 200}

I ₂₀

I ₂₀

\(\left [\begin {array}{lllllll} \boldsymbol {S}_{10} & \boldsymbol {0} \\ \boldsymbol {0} & \boldsymbol {0} \end {array}\right ]\)

with S ₁₀(i,j)=0.4^|i−j+1|