### Working paper

## Local Virtual Times Analysis in PCS Model

We study synchronization aspects in parallel discrete event simulation (PDES) algorithms. Our analysis is based on the recently introduced model of virtual times evolution in an optimistic synchronization algorithm. This model connects synchronization aspects with the properties of the profile of the local virtual times. The main parameter of the model is a “growth rate” q = 1/(1 + b), where b is a mean rollback length. We measure the average utilization of events and the desynchronization between logical processes as functions of the parameter q. We found that there is a phase transition between an “active phase”, i.e. when the utilization of the average processing time is finite, and an “absorbing state” with zero utilization, vanishing at a critical point qc ≈ 0.136. The average desynchronization degree (i.e. the vari- ance of local virtual times) grows with the parameter q. We also investi- gate the influence of the sparse distant communications between logical processes and found that they do not change drastically the synchronization properties in the optimistic synchronization algorithm, which is the sharp contrast with the conservative algorithm [1]. Finally, we compare our results with the existing case-study simulations.

We address question of synchronisation in parallel discrete event simulation (PDES) algorithms. We study synchronisation in conservative PDES model adding long-range connections between processing elements. We investigate how fraction of the random long-range connections in the synchronisation scheme influences the simulation time profile of PDES. We found that small fraction of random distant connections enhance synchronisation, namely, the width of the local virtual times remains constant with increasing number of processing elements. At the same time the conservative algorithm of PDES on small-world networks remains free from deadlocks. We compare our results with the case-study simulations.

We extend concept of local simulation times in parallel discrete event simulation (PDES) in order to take into account architecture of the current hardware and software in high-performance computing. We shortly review previous research on the mapping of PDES on physical problems, and emphasise how physical results may help to predict parallel algorithms behaviour.

The paper deals with the problem of optimizing the stages during the simulation experiment. That is an optimization by time. The need to reduce the execution time of the simulation experiment is explained by the fact that very often the simulation method is used for the study of complex systems (computer networks, for example). The problems of optimization of synchronization algorithm, load balancing algorithm and analysis of simulation results are discussed.

We investigate synchronisation aspects of an optimistic algorithm for parallel discrete event simulations (PDES). We present a model for the time evolution in optimistic PDES. This model evaluates the local virtual time profile of the processing elements. We argue that the evolution of the time profile is reminiscent of the surface profile in the directed percolation problem and in unrestricted surface growth. We present results of the simulation of the model and emphasise predictive features of our approach.

Nowadays simulation modeling is applied for solving a wide range of problems. There are simulations which require significant performance and time resources. To decrease overall simulation time a model can be converted to a distributed system and executed on a computer network. The goal of this project is to create a library enabling clear and rapid development parallel discrete event models in AnyLogic. The library is aimed for professionals in computer simulation and helps to reduce code amount. The project includes a research on different synchronization algorithms. In this paper we present techniques which can be used in creating distributed models. We present comparison of a single threaded model with a distributed model implementing optimistic algorithm. The comparison shows a significant improvement in wallclock time achieved by separating the model into independent submodels with minimal communications.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.