${n}_{i}\left(0\right)$ 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 $\left(\sum _{i=1}^{n}{n}_{i}\left(t\right)\right)$ 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, $t=1,2,\cdots ,T$ .