$n_i\left(0\right)$

Represent the initial grade size of grade i.

$n_i\left(t\right)$

Represent the number of students in grade i at time t.

$n\left(t\right)$

Represent the total size of the

System $\left({\displaystyle \sum _{i=1}^n{n}_i\left(t\right)}\right)$ at the end of the ${\left(t=1\right)}^{th}$ session.

$n_{ij}\left(t\right)$

Represent the number of students who move

from grade i to grade j at time t (representing

the promotion flow).

$n_{ik}\left(t\right)$

Represent the inflow to grade j at time $\left(t+1\right)$ ,

$m=7$ Represent the wastage flow for the grade within the session. That is the number of students who leave the entire system at time t and $k=7$ .

$n_{mj}\left(t+1\right)$

Represent the inflow to grade j at time $\left(t+1\right)$ , $m=7$ .

$p_{ij}\left(t\right)$

Represents the probability of a student in grade i moving to grade j at time t (if transition is stationary then $p_{ij}\left(t\right)=p_{ij}$ for all t, $j=1,2,\cdots ,6$ .

$w_{i=}{p}_{ij}\left(t\right)$

Represents the probability of a student dropping out from grade i or represents the probability of wastage from grade i within the $t_{th}$ session and

$k=7$ .

$p_{mi}\left(t+1\right)$

Represents the probability of inflow into grade j at time $\left(t+1\right)$ , $j=1,2,\cdots ,6$ , $m=7$ .

i

Represents number of rows, $i=1,2,\cdots ,m$ .

j

Represents number of rows, $j=1,2,\cdots ,k$ .

k

Represents number of rows, $t=1,2,\cdots ,T$ .