A New Approach to Determine the Critical Path in Stochastic Activity Network

Algorithm 1

Downward_Tracing (current_node)

i = current_node;

while (𝛾_𝑁 has not been calculated) do

 if (𝑓𝑖𝑛𝑖𝑠ℎ_𝑓𝑙𝑎𝑔_𝑖=1)

  𝑆ℎ𝑎𝑟𝑒𝑑_𝑓𝑙𝑎𝑔=1;

  𝑘=𝑐𝑢𝑟𝑟𝑒𝑛𝑡_𝑛𝑜𝑑𝑒;

  𝑖=𝑝𝑢𝑙𝑙_𝑠𝑡𝑎𝑐𝑘();

  perform Upward_Tracing( k,i );

 Else

  if (𝑖=1?)

   𝛾₁=0;

   𝑓𝑖𝑛𝑖𝑠ℎ_𝑓𝑙𝑎𝑔_𝑖=1;

   𝑘=𝑖;

   𝑖=𝑝𝑢𝑙𝑙_𝑠𝑡𝑎𝑐𝑘();

   perform Upward_Tracing( k, i );

  Else

   push_stack(i);

   𝑖=𝑘;

  End

 End

End

Upward_ Tracing ( last_node, current_node )

𝑘=𝑙𝑎𝑠𝑡_𝑛𝑜𝑑𝑒;

𝑖=𝑐𝑢𝑟𝑟𝑒𝑛𝑡_𝑛𝑜𝑑𝑒;

while (𝛾_𝑁 not been calculated) do

 if (Has node(k) been visited?)

  𝑌^𝑖_𝑘=𝜇(𝛾_𝑘)1⊕𝑋_𝑘𝑖; // an constant mean 𝜇(𝛾_𝑘)

  𝑆ℎ𝑎𝑟𝑒𝑑_𝑓𝑙𝑎𝑔=0;

   Else

   𝑌^𝑖_𝑘=𝛾_𝑘⊕𝑋_𝑘𝑖;

   𝑆ℎ𝑎𝑟𝑒𝑑_𝑓𝑙𝑎𝑔=0;

   End

 if (𝑓𝑖𝑛𝑖𝑠ℎ_𝑓𝑙𝑎𝑔_𝑖=1)

  𝑊^𝑖=𝑅𝑆𝐷𝑂(𝑖)={𝑌^𝑖_𝑘∣∀𝑘∈𝐵_𝑖};

  𝛾_𝑖=min(𝑌^𝑖_𝑘)  or 𝛾_𝑖=max(𝑌^𝑖_𝑘);

  𝑆ℎ𝑎𝑟𝑒𝑑_𝑓𝑙𝑎𝑔=0;

  𝑘=𝑖;

  𝑖=𝑝𝑢𝑙𝑙_𝑠𝑡𝑎𝑐𝑘();

 Else

  𝑝𝑢𝑠ℎ_𝑠𝑡𝑎𝑐𝑘(𝑖);

  perform Downward_Tracing( i );

 End

End