### Article

## Simulation of Virtual Time Profile in Conservative Parallel Discrete Event Simulation Algorithm for Small-World Network

We simulate model for evolution of local virtual time profile in conservative parallel discrete event the simulation (PDES) algorithm with long-range communication links. The main findings of simulation are that i) growth exponent depends logarithmically on the concentration *p* of long-range links; ii) utilisation of processing elements time decreases slowly with *p*. Thismeans that the conservative PDES with long-range communication links is fully scalable.

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.

In this paper, we present an approach to scalable co-scheduling in distributed computing for complex sets of interrelated tasks(jobs). The scalability means that schedules are formed for job models with various levels of task granularity, data replication policies, and processor resource and memory can be upgraded. The necessary of guaranteed job execution at the required quality of service causes taking into account the distributed environment dynamics, namely, changes in the number of jobs for servicing, volumes of computations, possible failures of processor nodes, etc. At a consequence, in the general case, a set of versions of scheduling, or a strategy, is required instead of a single version. We propose a callable model of scheduling based on multicriteria strategies. The choice of the specific schedule depends on the load level of the resource dynamics and is formed as a resource query which is sent to a local batch-job management system.

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.

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

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.