| A. Housni, M. Trhel, "Specification of the prioritized algorithm for N groups", internal paper, Laboratoire d'Informatique de l'Universit de Franche Comt, France, February (2001). |
....3.3.1. Performance of the path compression algorithm The average number of messages is H n 1 in the initial algorithm [10] The messages between the sites of a group and the router have to be added. The algorithm remains O(Log(n) 3.2.2. Performance of Raymond s algorithm It have been shown [4] that the cheapest tree is the star where the node of maximum probability is in the center. The average number of messages is less than 4. However, this structure corresponds more to a centralized than a distributed algorithm. On the set of possible trees, Raymond [12] checked by simulation that ....
A. Housni, M. Trhel, "Specification of the prioritized algorithm for N groups", internal paper, Laboratoire d'Informatique de l'Universit de Franche Comt, France, February (2001).
....rooted trees by the average numbers of messages: Lemma 3: The cost (average number of messages) of a tree is: 2 1 1 = n i n j j i j i d p p . Raymond[8] obtains an average number of messages of O(Log (N) by simulation, in the case of equiprobability. He has been proved in [4] that the cheapest tree is the star with the greatest probability at the center. The cost is less than 4 messages. 5.3.2 Messages between the root of a group and the router If the request in not in the privileged group, there are 4 messages (2 per group) 2 1 4 5 3 2 1 4 5 3 5.3.3 ....
A. Housni, M. Trhel, "Specification of the prioritized algorithm for N groups", internal paper, Laboratoire d'Informatique de l'Universit de Franche Comt, France, February (2001).
..... Then, this implies that the average number of messages of a tree will be the sum of the products of the probabilities of the rooted trees by the average numbers of messages: Lemma 3 The cost (average number of messages) of a tree is: n n j j i j i d p p 1 1 ) 2 . We have proved [3] that the cheapest tree is the star with the greatest probability at the center. The cost is less than 4 messages. However, star is not a good structure for fault tolerance, because the center is frequently impelled. Raymond obtains an average number of messages of O(Log (n) by simulation, in the ....
.... site in critical section releases it, the token is sent to the first site of the queue (this site has the maximum priority) If the token is not in the group, the request is sent to the router of the group, which sends it to the group owner of the token (figure 6) The detailed program is given in [3]. Fig. 6. Example for three structured groups. 8 Mutual exclusion is satisfied The proof of mutual exclusion is the same than in one group. Concerning deadlock, it is the same thing: deadlock is impossible. Nevertheless, there is absence of equity in prioritized mutual exclusion, because it is ....
A. Housni, M. Trhel, "Specification of the prioritized algorithm for N groups", intern paper, Laboratore d'Informatique de l'universit de Franche Comt, France, February (2001).
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