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

Algorithm 3

if   𝑛=𝑁  then

 if   𝜃=𝜇_𝑁   then

  𝑒_𝑁,𝜃=−𝛾_𝑁𝜁⁽¹⁾_𝑁,𝜃+𝐴^∗(1)(𝜃)𝑡_𝑁−1

  𝑓_𝑁,𝜃=−𝐴^∗(1)(𝜃)𝑑_𝑁−1+𝑑_𝑁

 else

  𝑒_𝑁,𝜃=𝛾_𝑁𝜁_𝑁,𝜃+𝐴^∗(𝜃)𝑡_𝑁−1𝜇_𝑁−𝜃

  𝑓_𝑁,𝜃=𝐴^∗(1)(𝜃)(𝑑_𝑁−1+𝑑_𝑁)−𝑑_𝑁𝜇_𝑁−𝜃

 end  if

else  if   1≤𝑛≤𝑁−1   then

 if   𝜃=𝜇_𝑛   then

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

  𝑓_𝑛,𝜃=−𝜇_𝑛+1𝑓⁽¹⁾_𝑛+1,𝜃+𝐴^∗(1)(𝜃)𝑑_𝑛−1

 else

  𝑒_𝑛,𝜃=𝛾_𝑛𝜁_𝑛,𝜃+𝜇_𝑛+1𝑒_𝑛+1,𝜃+𝐴^∗(𝜃)𝑡_𝑛−1−𝑡_𝑛𝜇_𝑛−𝜃

  𝑓_𝑛,𝜃=𝜇_𝑛+1𝑓_𝑛+1,𝜃+𝐴^∗(𝜃)𝑑_𝑛−1−𝑑_𝑛𝜇_𝑛−𝜃

 end  if

end  if