Chandy–Misra–Haas algorithm resource model

Consider the n processes P1, P2, P3, P4, P5,, ... ,Pn which are performed in a single system (controller). P1 is locally dependent on Pn, if P1 depends on P2, P2 on P3, so on and Pn−1 on Pn. That is, if P_1 \rightarrow P_2 \rightarrow P_3 \rightarrow \ldots \rightarrow P_n , then P_1 is locally dependent on P_n. If P1 is said to be locally dependent to itself if it is locally dependent on Pn and Pn depends on P1: i.e. if P_1 \rightarrow P_2 \rightarrow P_3 \rightarrow \ldots \rightarrow P_n \rightarrow P_1, then P_1 is locally dependent on itself. == Description ==

The algorithm uses a message called probe(i,j,k) to transfer a message from controller of process Pj to controller of process Pk. It specifies a message started by process Pi to find whether a deadlock has occurred or not. Every process Pj maintains a boolean array dependent which contains the information about the processes that depend on it. Initially the values of each array are all "false". Controller sending a probe Before sending, the probe checks whether Pj is locally dependent on itself. If so, a deadlock occurs. Otherwise it checks whether Pj, and Pk are in different controllers, are locally dependent and Pj is waiting for the resource that is locked by Pk. Once all the conditions are satisfied it sends the probe. Controller receiving a probe On the receiving side, the controller checks whether Pk is performing a task. If so, it neglects the probe. Otherwise, it checks the responses given Pk to Pj and dependentk(i) is false. Once it is verified, it assigns true to dependentk(i). Then it checks whether k is equal to i. If both are equal, a deadlock occurs, otherwise it sends the probe to next dependent process. == Algorithm ==

In pseudocode, the algorithm works as follows: Controller sending a probe if Pj is locally dependent on itself then declare deadlock else for all Pj,Pk such that (i) Pi is locally dependent on Pj, (ii) Pj is waiting for P'k'' and (iii) Pj, Pk are on different controllers. send probe(i, j, k). to home site of Pk Controller receiving a probe if (i)Pk is idle / blocked (ii) dependentk(i) = false, and (iii) Pk has not replied to all requests of to Pj then begin "dependents""k"(i) = true; if k == i then declare that Pi is deadlocked else for all Pa,Pb such that (i) Pk is locally dependent on Pa, (ii) Pa is waiting for P'b'' and (iii) Pa, Pb are on different controllers. send probe(i, a, b). to home site of Pb end == Example ==

P1 initiates deadlock detection. C1 sends the probe saying P2 depends on P3. Once the message is received by C2, it checks whether P3 is idle. P3 is idle because it is locally dependent on P4 and updates dependent3(2) to True. As above, C2 sends probe to C3 and C3 sends probe to C1. At C1, P1 is idle so it update dependent1(1) to True. Therefore, deadlock can be declared. == Complexity ==

Suppose there are n controllers and m processes, at most m(n-1)/2 messages need to be exchanged to detect a deadlock, with a delay of O(n) messages. ==References==