Computer implementation of Mason\u27s rule and software development of stochastic petri nets

A symbolic performance analysis approach for discrete event systems can be formulated based on the integration of Petri nets and Moment Generating Function concepts [1-3]. The key steps in the method include modeling a system with arbitrary stochastic Petri nets (ASPN), generation of state machine Petri nets with transfer functions, derivation of equivalent transfer functions, and symbolic derivation of transfer functions to obtain the performance measures. Since Mason\u27s rule can be used to effectively derive the closed-form transfer function, its computer implementation plays a very important role in automating the above procedure. This thesis develops the computer implementation of Mason\u27s rule (CIMR). The algorithms and their complexity analysis are also given. Examples are used to illustrate CIMR method\u27s application for performance evaluation of ASPN and linear control systems. Finally, suggestions for future software development of ASPN are made

An Efficient Built-in Temporal Support in MVCC-based Graph Databases

Real-world graphs are often dynamic and evolve over time. To trace the evolving properties of graphs, it is necessary to maintain every change of both vertices and edges in graph databases with the support of temporal features. Existing works either maintain all changes in a single graph or periodically materialize snapshots to maintain the historical states of each vertex and edge and process queries over proper snapshots. The former approach presents poor query performance due to the ever-growing graph size as time goes by, while the latter one suffers from prohibitively high storage overheads due to large redundant copies of graph data across different snapshots. In this paper, we propose a hybrid data storage engine, which is based on the MVCC mechanism, to separately manage current and historical data, which keeps the current graph as small as possible. In our design, changes in each vertex or edge are stored once. To further reduce the storage overhead, we simply store the changes as opposed to storing the complete snapshot. To boost the query performance, we place a few anchors as snapshots to avoid deep historical version traversals. Based on the storage engine, a temporal query engine is proposed to reconstruct subgraphs as needed on the fly. Therefore, our alternative approach can provide fast querying capabilities over subgraphs at a past time point or range with small storage overheads. To provide native support of temporal features, we integrate our approach into Memgraph, and call the extended database system TGDB(Temporal Graph Database). Extensive experiments are conducted on four real and synthetic datasets. The results show TGDB performs better in terms of both storage and performance against state-of-the-art methods and has almost no performance overheads by introducing the temporal features