| Abstract: | 合成最大許可的一個活資源分發系統一直是個挑戰。 有3 種方法避免僵局︰ 避免，預防和恢復。 主要在文獻方面報告是僵局避免和預防。 在後者裡，控制器經常被靜止加入說導致更少的狀態達到，但是執行迅速⎯由於沒有線上的計算運轉。 前者不需要控制器，但是⎯由於線上的計算⎯執行較慢。 基於虹吸管的僵局預防控制FMS比最好方法達到更少的狀態。 我們報告著名的FMS 的另一控制模型到達與文獻內最好的Uzam等等(基於區域的理論和reachability 有分析受狀態爆炸問題之苦)相同的好狀態的數量。但是有更少的控制器和控制電弧借著以精煉一些控制器到幾個， 在綜合的更晚的階段，與更小的控制區。 因為控制地區被較少擾亂，所以更多的狀態可以被達到，借著只包括一個亞區裡一個地方⎯在任何可以達到的狀態一個亞區裡只有一個地方被標明的。 因此， 控制區比補充虹吸管小，這不過，可能引起這只虹吸管在綜合的起初時期變得未含標記。 我們提議發展一個正式的理論解決兩難並且把它延長到任意的S3PR，更錯綜複雜的資源分發系統(RAS)⎯如ES3PR， S2LSPR 和S3PMR那樣的系統。 但是，可以達到的狀態的數量， 比最佳的仍然更少，在最壞例子中要求的控制器的數量仍然可能是指數的， 新成問題的虹吸管可能被控制器產生並且引起更多的控制器被增加。 地區理論以Uzam 等等 能在所有方法中間達到最多狀態的數量。 我們更進一步提議運用僵局恢復透過增加控制器(並且控制電弧)到達與原先的未受控制的模型相同的狀態的數量⎯類似於預防方法。 因此，它是一種靜止的方法並且迅速地運轉。 當一只成問題的虹吸管到達臨界狀態時，一次事件將被起動返回一個以前的狀態； 如此從一個僵局中恢復。 與所有方法(包括Uzam 等的方法)相比較，因此它更許可。 更進一步，初步的研究表明沒有新成問題的虹吸管由於增加的控制器被產生。 因此,與其他方法( 也Uzam 等等) 比較,需要更少的控制器。 它已經適用於一個著名的例子。 我們提議進一步研究發展正式的理論並且把它延長到任意的S3PR 和更錯綜複雜的RAS(例如ES3PR，S2LSPR 和S3PMR)。
It has been challenging to synthesize a live resource allocation system that is maximal permissive. There are three approaches to avoid deadlocks: avoidance, prevention and recovery. Mostly reported in the literatures are deadlock avoidance and prevention. In the latter, monitors are often statically added resulting in fewer states reached, but runs faster due to no online computation. The former needs no monitors but runs slower due to online computation. Siphon-based deadlock prevention control of FMS suffers from reaching fewer states than best. We reported an alternative control model of a well-known FMS to reach the same number of good states as that by Uzam et al. (based on the theory of regions and reachability analysis suffering from the state explosion problem) ⎯ the best in the literature⎯ but with fewer monitors and control arcs by refining some monitors into several, in the later stages of the synthesis, with smaller controller regions. More states can be reached since the controller region is less disturbed by covering only a place in a subregion where only one place is marked at any reachable marking. As a result, the controller region is smaller than the complementary siphon, which, however, may cause the siphon to become unmarked in the initial stages of the synthesis. We propose to develop a formal theory to resolve the dilemma and extend it to arbitrary S3PR and more complicated resource allocated systems such as ES3PR, S2LSPR, and S3PMR. The number of reachable states, however, is still fewer than the optimal one and the number of monitors required in the worst case may still be exponential since new problematic siphons may be generated by the monitors and cause more monitors to be added. The region theory by Uzam et al. can reach the most number of states among all approaches. We further propose to employ deadlock recovery to reach the same number of states as the original uncontrolled model by adding monitors (and control arcs) similar to the prevention approach. Thus, it is a static approach and runs fast. When a problematic siphon reaches a critical state, an event will be initiated to return to a previous state; thus recovering from a deadlock. Hence it is more permissive than all current, including that by Uzam et al., approaches. Further, preliminary study indicates that no new problematic siphons are generated due to added monitors. Thus, fewer monitors are required than other (also Uzam et al.) approaches. It has applied to a well-known example. We propose further research to develop formal theory and extend it to arbitrary S3PR and more complicated RAS such as ES3PR, S2LSPR, and S3PMR. |
