Architecture of a distributed computing system based on mobile devices

The article outlines the architecture of the mathematical and software of a distributed computing system based on many mobile devices integrated into a common network infrastructure. The distributed computing system is based on a problem-oriented task execution model (known in foreign literature as the Task-Based Execution Model). This model of distributed computing is most preferable when solving optimization and inverse problems, when the set of admissible sets of input parameters is sufficiently large. At the same time, the tasks themselves are performed independently, but require significant time expenditures to solve each specific task, comparable to the “lifetime” of a computing node. The Task-Based Execution Model approach allows you to reduce the amount of information transferred between the server and the node, which in turn improves overall performance. The DHCA system we offer has a client-server architecture and is tailored for the Android system. The mobile client is written using the latest Android approaches to background computing, which allows for increased performance as well as improved security for end users. The system takes into account all the features of the interaction of client-server architecture for distributed systems, and also solves the problem associated with the unavailability of computing nodes by automatically redistributing tasks. Open source code increases trust in the system from end users, which can have a beneficial effect on the number of active participants in computing. The web client is a web application written in PHP. User interaction with the web client interface is carried out using the jQuery JavaScript library, which allows you to send requests and receive data from the server asynchronously. Interaction with the server is carried out through HTTP requests to the REST API, written in PHP. The DHCA server is a web server with PHP support, with a connected MySQL database. Thanks to the modular architecture of the API used, any relational DBMS that supports the structured query language SQL can be connected to the system. The mobile client is an application installed on a smartphone running Android operating system version 6.0 (Marshmallow) and higher. The client is written in Kotlin using the MVVM design pattern. The mobile client carries out all interactions with the server API using the Retrofit library, designed for processing HTTP requests. All data is returned in JSON format. Information messages are sent to the mobile client by the Firebase Cloud Messaging (FCM) library. To derive a formula for assessing scalability for the presented architecture, we take into account the following parameters: t - time required to calculate one data block; N - number of blocks to be calculated (in the case of a ray tracing problem, number of pixels); P is the number of devices involved in the calculation, t0 is the time required for the initial breakdown of the source data into computational blocks; tw - time of writing one initial block to the database after splitting; ts - time required for the client to receive one block of data from the server (send); tr - time required for the server to receive the calculated data block from the client (receive); tv - time required to write the result of the calculated block to the database (saVe). We obtain the calculation time on p devices T(P). Through acceleration as the ratio of T(l) to T(P), we obtain P devices at which maximum acceleration is achieved. To demonstrate the robustness of the developed system, a solution to three problems is presented, in which each elementary task has a different load on the processor and on the network infrastructure. Let us highlight three such tasks: 1) The problem of inverse ray tracing, which is characterized by a significant amount of transmitted data to form a scene and the received data of a full image block. At the same time, the time for ray tracing is much longer relative to the data transmission time. 2) The white dwarf collision problem, which is formulated in a one-dimensional formulation and is characterized by the transmission of only six values to describe the state of the dwarfs before the collision and one output value describing the maximum temperature during the collision. In this case, the calculation time is comparable to the data transmission time. The problem has an analytical solution that requires the resolution of nonlinear equations and is described in detail in the work. 3) The problem of nuclear combustion of carbon in white dwarfs, which is formulated in the form of changes in the concentrations of the main isotopes during nuclear combustion of carbon during the solution of the ODE system.