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

Algorithm 2

if   𝑛=𝑁   then

 if   𝜃=𝛿_𝑁   then

  𝜁^(𝑙)_𝑁,𝜃𝐴=−^∗(𝑙+1)(𝜃)(𝜓_𝑁−1+𝜓_𝑁)𝑙+1

 else

  𝜁^(𝑙)_𝑁,𝜃=𝐴^∗(𝑙)(𝜃)(𝜓_𝑁−1+𝜓_𝑁)+𝑙𝜁^(𝑙−1)_𝑁,𝜃𝛿_𝑁−𝜃

 end  if

else  if   1≤𝑛≤𝑁−1   then

 if   𝜃=𝛿_𝑛   then

  𝜁^(𝑙)_𝑛,𝜃𝜂=−^𝑛+1𝜁^(𝑙+1)_𝑛+1,𝜃+𝐴^∗(𝑙+1)(𝜃)𝜓_𝑁−1𝑙+1

 else

  𝜁^(𝑙)_𝑛,𝜃=𝜂_𝑛+1𝜁^(𝑙)_𝑛+1,𝜃+𝐴^∗(𝑙)(𝜃)𝜓_𝑛−1+𝑙𝜁^(𝑙−1)_𝑛,𝜃(𝜃)(𝛿_𝑛−𝜃)

 end  if

end  if