A Graph Transformation-Based Approach for the Validation of Checkpointing Algorithms in Distributed Systems

Abstract

Abstract-Autonomic Computing Systems are oriented to prevente the human intervention and to enable distributed systems to manage themselves. One of their challenges is the efficient monitoring at runtime oriented to collect information from which the system can automatically repair itself in case of failure. QuasiSynchronous Checkpointing is a well-known technique, which allows processes to recover in spite of failures. Based on this technique, several checkpointing algorithms have been developed. According to the checkpoint properties detected and ensured, they are classified into: Strictly Z-Path Free (SZPF), Z-Path Free (ZPF) and Z-Cycle Free (ZCF). In the literature, the simulation has been the method adopted for the performance evaluation of checkpointing algorithms. However, few works have been designed to validate their correctness. In this paper, we propose a validation approach based on graph transformation oriented to automatically detect the previous mentioned checkpointing properties. To achieve this, we take the vector clocks resulting from the algorithm execution, and we model it into a causal graph. Then, we design and use transformation rules oriented to verify if in such a causal graph, the algorithm is exempt from non desirable patterns, such as Z-paths or Z-cycles, according to the case.

An efficient validation approach for quasi-synchronous checkpointing oriented to distributed diagnosability

“…In this section, we present a set of validation rules designed over the HBR graph. These rules were initially introduced in a previous work [8]. Figure 4 contains the HBR graph which corresponds to the scenario depicted in Figure 2.…”

A Mechanism for the Causal Ordered Set Representation in Large-Scale Distributed Systems

“…Consequently, based on the graph output, we can decide if the algorithm is exempt of noncausal Z-paths. The validation of checkpointing algorithms may be based on graph transformation approaches as in [3]. if ((id 1 , id 2 ).label="d") then 6 test((id 1 , id 2 )) ; 7 Return G out = (N ode, Edge) 8 test(id 1 , id 2 ) 9 begin 10 if (∃(id 3 , id 2 ) ∈ Edge) and ∃(id 3 , id 4 ) ∈ Edge) and (id 3 , id 2 ).label="c" and (id 3 , id 4 ).label="d") then 11 (id 1 , id 4 ).label = "z" ; 12 Edge ← Edge ∪ {(id 1 , id 4 )} ;…”