Scheduling Algorithm: Tasks Scheduling Algorithm for Multiple Processors with Dynamic Reassignment

Algorithm 1

To assign a distributed program consisting of a set $T=\{t_1,t_2,t_3,\dots ,t_M\}$ of M tasks which is divided into $K$ phases to a set of $n$ processors $P=\{p_1,p_2,p_3,\dots ,p_N\}$ in order to minimize the total cost.

Step-1: Input:$K$, $M$, $N$, ECM(,   ,), RCM( , , ), RECM( , ), ITCCM( , , )

Step-2: Start with phase $k=1$.

Step-3: Calculate NECM(,  ,) by adding the ECM(,  ,) with RCM(,  ,) for $k$th phase.

Step-4: Assign the executing task $t_s$ to processor $p_r$ for which cost is minimum say $TE{C}_k$

Step-5: Add the effect of communication cost of executing tasks $t_s$ with other residing

     tasks by adding $k$th column of ITCCM(,   ,) to all the column of NECM(,   ,)

     except the $r$th column at which this task is assigned.

Step-6: Assign the residing tasks $t_g(g=1,2,\dots ,M,g\ne s)$ to processors $p_h$ at which time is

     minimum say $TRC(g{)}_k$

    Calculate:

              $TR{C}_k=\sum _{\begin{array}{l}i=\text{1}\\ i\ne \text{s}\end{array}}^{M}TRC(i{)}_k$

Step-7: Store executing and residing tasks and their position on processors in a linear

     array $POSS(,{)}_k\mathrm{.}$

    Calculate:

              $(TCOST{)}_k=TE{C}_k+TR{C}_k$

Step-8:$k=k+1.$

Step-9: Repeat step-3.

Step-10: Modify the cost of NECM(,  ,) by adding the relocation cost $re{l}_{sk-1}$ to all $e_{ksj},$

      $j=1,2,\dots ,N,j\ne r\mathrm{.}$

Step-11: Modify the cost of NECM(,   ,) by adding the relocation cost $re{l}_{gk-1}$ to $e_{kgj},$

      $j=1,2,\dots ,N,j\ne h\mathrm{.}$

Step-12: Repeat step-4 to step-6.

Step-13: Store executing and residing tasks and their position on processors in linear array

      $POSS(,{)}_{k+1}\mathrm{.}$

      Calculate:

              $(TCOST{)}_{k+1}=TE{C}_{k+1}+TR{C}_{k+1}$

Step-14: If $k\ne K$

then

         repeat step-8 to step-14.

     else

Step-15: Calculate:

          $TCOST=\sum _{k=1}^K(TCOST{)}_k$

Step-16: End.