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