Journal of Control Science and Engineering

Research Article

Process Completing Sequences for Resource Allocation Systems with Synchronization

Algorithm 2

Input: 𝑁 ∈ G - A M G A and critical resource, π‘Ÿ 𝑐
Output: Serialized bounds, sequence of place markings.
πœ‚ = 𝑁 , πœ— = βˆ… ( πœ— is a last-in-first-out list )
For 𝑝 ∈ 𝑃 𝑆 βˆͺ 𝑃 𝐼 βˆͺ 𝑃 𝐹
  Ξ¨ β„Ž ( 𝑝 ) = 𝑒 β„Ž ( 𝑝 ) for β„Ž = 1 , … , | 𝑃 𝑅 |
While πœ‚ β‰  β„΅
 For each Type-I structure ⟨ 𝑑 𝐼 , 𝑝 ( 1 ) , … , 𝑑 ( 𝑛 βˆ’ 1 ) , 𝑝 ( 𝑛 ) , 𝑑 ( 𝑛 ) ⟩ in πœ‚
   Ξ¨ β„Ž ( 𝑝 ( 𝑛 ) ) = m a x { Ξ¨ β„Ž ( 𝑝 ( 1 ) ) , … , Ξ¨ β„Ž ( 𝑝 ( 𝑛 ) ) } , β„Ž = 1 … | 𝑃 𝑅 |
End For
πœ‚ = 𝜌 1 ( πœ‚ )
For a Type-II structure { ⟨ 𝑑 𝐼 , 𝑝 ( 1 1 ) , 𝑑 ( 1 1 ) , 𝑝 ( 1 2 ) , 𝑑 𝑗 ⟩ , ⟨ 𝑑 𝐼 , 𝑝 ( 2 1 ) , 𝑑 ( 2 1 ) , 𝑝 ( 2 2 ) , 𝑑 𝑗 ⟩ β‹― ⟨ 𝑑 𝐼 , 𝑝 ( π‘š 1 ) , 𝑑 ( π‘š 1 ) , 𝑝 ( π‘š 2 ) , 𝑑 𝑗 ⟩ } in πœ‚
 Sort { 𝑝 ( 1 2 ) , 𝑝 ( 2 2 ) β‹― 𝑝 ( π‘š 2 ) } by decreasing 𝛿 𝑐 and let ⟨ 𝑝 1 , … , 𝑝 π‘š ⟩ be the sorted set
 Insert ⟨ 𝑝 1 , … , 𝑝 π‘š ⟩ into πœ—
 For β„Ž = 1 … | 𝑃 𝑅 |
 Set Ξ¨ β„Ž ( 𝑝 ( 1 2 ) ) to
  max { Ξ¨ β„Ž ( 𝑝 𝑑 βˆ‘ ) + 𝑑 βˆ’ 1 𝑗 = 1 𝑒 𝑗 ∢ 𝑑 = 1 , … , π‘š }
  End For
 End For
  πœ‚ = 𝜌 2 ( πœ‚ )
End While
Return { ⟨ Ξ¨ β„Ž ∢ β„Ž = 1 … | 𝑃 𝑅 | ⟩ , πœ— }