Analysis of General Input State Dependent Working Vacation Queue with Changeover Time

Algorithm 4

if   𝑖=𝑁   then

 if   𝜃=𝜇_𝑁   then

  𝑒^(𝑙)_𝑁,𝜃𝛾=−^𝑁𝜁^(𝑙+1)_𝑁,𝜃+𝐴^∗(𝑙+1)(𝜃)𝑡_𝑁−1𝑙+1

  𝑓^(𝑙)_𝑁,𝜃𝐴=−^∗(𝑙+1)(𝜃)(𝑑_𝑁−1+𝑑_𝑁)𝑙+1

 else

  𝑒^(𝑙)_𝑁,𝜃=𝛾_𝑁𝜁^(𝑙)_𝑁,𝜃+𝐴^∗(𝑙)(𝜃)𝑡_𝑁−1+𝑙𝑒^(𝑙−1)_𝑁,𝜃𝜇_𝑁−𝜃

  𝑓^(𝑙)_𝑁,𝜃=𝐴^∗(𝑙)(𝜃)(𝑑_𝑁−1+𝑑_𝑁)+𝑙𝑓^(𝑙−1)_𝑁,𝜃(𝜇_𝑁−𝜃)

 end  if

else  if   1≤𝑛≤𝑁−1   then

 if   𝜃=𝜇_𝑛   then

  𝑒^(𝑙)_𝑛,𝜃𝛾=−^𝑛𝜁^(𝑙+1)_𝑛,𝜃+𝜇_𝑛+1𝑒^(𝑙+1)_𝑛+1,𝜃+𝐴^∗(𝑙+1)(𝜃)𝑡_𝑛−1𝑙+1

  𝑓^(𝑙)_𝑛,𝜃𝜇=−^𝑛+1𝑓^(𝑙+1)_𝑛+1,𝜃+𝐴^∗(𝑙+1)(𝜃)𝑑_𝑛−1𝑙+1

 else

  𝑒^(𝑙)_𝑛,𝜃=𝛾_𝑛𝜁^(𝑙)_𝑛,𝜃+𝜇_𝑛+1𝑒^(𝑙)_𝑛+1,𝜃+𝐴^∗(𝑙)(𝜃)𝑡_𝑛−1+𝑙𝑒^(𝑙−1)_𝑛,𝜃𝜇_𝑛−𝜃

  𝑓^(𝑙)_𝑛,𝜃=𝜇_𝑛+1𝑓^(𝑙)_𝑛+1,𝜃+𝐴^∗(𝑙)(𝜃)𝑑_𝑛−1+𝑙𝑓^(𝑙−1)_𝑛,𝜃𝜇_𝑛−𝜃

 end  if

end  if