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

Algorithm 1

if   𝑛=𝑁  then

 if   𝜃=𝛿_𝑁   then

  𝜁_𝑁,𝜃=−𝐴^∗(1)(𝜃)(𝜓_𝑁−1+𝜓_𝑁)

 else

  𝜁_𝑁,𝜃=𝐴^∗(𝜃)(𝜓_𝑁+𝜓_𝑁)−𝜓_𝑁(𝛾_𝑁+𝜂_𝑁−𝜃)

 end  if

else  if  1≤𝑛≤𝑁−1  then

 if  𝜃=𝛿_𝑛  then

  𝜁_𝑛,𝜃=−(𝜂_𝑛+1𝜁⁽¹⁾_𝑛+1,𝜃+𝐴^∗(1)(𝜃)𝜓_𝑛−1)

 else

  𝜁_𝑛,𝜃=𝜂_𝑛+1𝜁_𝑛+1,𝜃+𝐴^∗(𝜃)𝜓_𝑁−1−𝜓_𝑁(𝛿_𝑛−𝜃)

 end  if

end  if