Модели массового обслуживания для описания работы узлов беспроводных сенсорных сетей с самогенерацией энергии

Wireless sensor networks have a lot of important applications in various real-world systems. Nodes of sensor networks, which collect and transmit information about some objects, have small batteries with limited power and storage space. When the battery of a node is discharged, it should be charged again or replaced. Otherwise and the node terminates its operation and, eventually, the network may not be able to perform its designated task. Recent advances in developing various energy harvesting technologies have resulted in the design of new types of sensor nodes which are able to extract energy from the surrounding environment. The major sources of energy harvesting include solar, wind, sound, vibration, thermal, and electromagnetic power. The energy harvested from existing environmental sources is accumulated in energy storage devices. Design of such nodes requires, in particular, making decisions about the required equipment for energy harvesting and accumulation. The useful tool for decision support regarding the design of such nodes is provided by queueing theory. In this presentation, short survey of queueing literature devoted to optimization of operation of energy harvesting sensor nodes and its relation to the previously studied in the literature queueing models are presented.Беспроводные сенсорные сети имеют множество важных приложений в различных реальных системах. Узлы сенсорных сетей, которые собирают и передают информацию о некоторых объектах, имеют небольшие батареи с ограниченными мощностью и пространством для хранения энергии. Когда аккумулятор узла разряжается, его необходимо снова зарядить или заменить. В противном случае, узел прекращает свою работу, и, в конечном итоге, сеть может не выполнить поставленные перед ней задачи. Недавние достижения в разработке различных технологий сбора энергии привели к созданию новых типов узлов сетей, которые способны извлекать энергию из окружающей среды. Основными источниками сбора энергии являются солнечная энергия, ветер, звуковая, вибрационная, тепловая и энергия электромагнитных волн. Энергия, собранная из существующих источников окружающей среды, накапливается в аккумуляторах энергии. Проектирование таких узлов требует, в частности, принятия решений относительно необходимого оборудования для сбора и накопления энергии. Полезный инструмент для поддержки принятия решений в отношении проектирования таких узлов обеспечивается теорией массового обслуживания. В этой презентации приведено краткое описание литературы о очередях, посвященной оптимизации работы узлов узлов сбора энергии и их связи с ранее изученными в литературе моделями массового обслуживания

OPTIMAL CONTROL BY A NODE OF WIRELESS SENSOR NETWORK WITH QUALITY OF TRANSMISSION DEPENDING ON THE AMOUNT OFHARVESTED ENERGY

In this paper, we briefly consider a queueing model with energy harvesting and multi-threshold control by the service modes. The available service modes distinguish by the service rate, the number of required for a customer service energy units and the probability of error occurrence during service. The account of the possibility of error occurrence is very important in modelling wireless sensor networks. The use of a larger number of energy units corresponds in real-life wireless communication systems to the ability to send a stronger signal what implies the faster service (transmission) rate and a lower probability of incorrect transmission (due to the noise in the wireless transmission channel). Incorrect transmission implies the necessity of repeated transmission and additional consumption of energy. Under the fixed thresholds defining the control strategy, behavior of the system is described by multi-dimensional Markov chain what allows to formulate and solve optimization problems

OPTIMIZATION OF A SIGNAL PROCESSING STRATEGY IN SENSOR NODES WITH ENERGY HARVESTING AND CONSUMPTION FOR ADMISSION AND TRANSMISSION

Operation of a sensor node of a wireless sensor network with energy har- vesting is described by the single-server queue. Customers and energy units arrive according to the marked Markov arrival process. Service of a customer is possible only in presence of an energy unit. We assume that, besides the use of one energy unit for service of any customer, one more unit is expended at the moment of a customer arrival if the customer is accepted to the system. To optimize operation of the system, a parametric strategy of admission control is used. Under the fixed value of control parameter, the behavior of the sys- tem is described by the five-dimensional Markov chain. The generator of this Markov chain is obtained. Expressions for computation of the key performance indicators of the system are presented

Модели массового обслуживания для описания работы узлов беспроводных сенсорных сетей с самогенерацией энергии

Wireless sensor networks have a lot of important applications in various real-world systems. Nodes of sensor networks, which collect and transmit information about some objects, have small batteries with limited power and storage space. When the battery of a node is discharged, it should be charged again or replaced. Otherwise and the node terminates its operation and, eventually, the network may not be able to perform its designated task. Recent advances in developing various energy harvesting technologies have resulted in the design of new types of sensor nodes which are able to extract energy from the surrounding environment. The major sources of energy harvesting include solar, wind, sound, vibration, thermal, and electromagnetic power. The energy harvested from existing environmental sources is accumulated in energy storage devices. Design of such nodes requires, in particular, making decisions about the required equipment for energy harvesting and accumulation. The useful tool for decision support regarding the design of such nodes is provided by queueing theory. In this presentation, short survey of queueing literature devoted to optimization of operation of energy harvesting sensor nodes and its relation to the previously studied in the literature queueing models are presented.Беспроводные сенсорные сети имеют множество важных приложений в различных реальных системах. Узлы сенсорных сетей, которые собирают и передают информацию о некоторых объектах, имеют небольшие батареи с ограниченными мощностью и пространством для хранения энергии. Когда аккумулятор узла разряжается, его необходимо снова зарядить или заменить. В противном случае, узел прекращает свою работу, и, в конечном итоге, сеть может не выполнить поставленные перед ней задачи. Недавние достижения в разработке различных технологий сбора энергии привели к созданию новых типов узлов сетей, которые способны извлекать энергию из окружающей среды. Основными источниками сбора энергии являются солнечная энергия, ветер, звуковая, вибрационная, тепловая и энергия электромагнитных волн. Энергия, собранная из существующих источников окружающей среды, накапливается в аккумуляторах энергии. Проектирование таких узлов требует, в частности, принятия решений относительно необходимого оборудования для сбора и накопления энергии. Полезный инструмент для поддержки принятия решений в отношении проектирования таких узлов обеспечивается теорией массового обслуживания. В этой презентации приведено краткое описание литературы о очередях, посвященной оптимизации работы узлов узлов сбора энергии и их связи с ранее изученными в литературе моделями массового обслуживания

Analysis of queueing model with processor sharing discipline and customers impatience

Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. © 201

Analysis of queueing model with processor sharing discipline and customers impatience

Queueing systems with processor sharing represent the adequate models for sharing the resources, e.g., components of a computer or a bandwidth of communication systems. In this paper, we consider a queueing system with processor sharing discipline under quite general assumptions about the arrival and service processes. Arrivals are defined by the Markovian arrival process. The service time has a phase type distribution. Possible impatience of customers is taken into account. The number of customers, which can simultaneously obtain service, is limited. We compare two approaches for monitoring service of customers, namely, the approach counting the number of customers at each phase of service and the approach counting the phase of service of each customer and show the significant advantage of the former approach. We obtain the joint distribution of the number of customers in the system and the states of the underlying arrival and service processes as well as the loss probabilities. It is shown that the sojourn time in the system of an arbitrary customer has phase type distribution and an irreducible representation of this distribution is obtained. Numerical examples are presented. A possibility of optimal choice of the server capacity (e.g., multi-programming level) is numerically illustrated. An opportunity of increasing the speed of computations via the use of the graphics processing unit is discussed. © 201

Mathematical Models for the Operation of a Cell with Bandwidth Sharing and Moving Users

A mathematical model is proposed for the operation of a cell in a mobile communication network with moving users. The cell is divided into several zones distinguished by the strength of the signal and, consequently, by the transmission rate. The process of users activation in various zones is defined by the marked Markovian arrival process. After activation, a user can move and transit to other zones or to another cell. The service rate of an arbitrary user depends on the zone where the user is currently located and the total number of active users in the cell. When the total bandwidth required by all active users exceeds the bandwidth of the base station, a proportional reduction of the bitrate provided to each user (bandwidth sharing) is applied. The key performance indicators of the system are computed, and illustrative numerical examples are presented. © 2002-2012 IEEE

Competitive queueing systems with comparative rating dependent arrivals

We consider the joint operation of two multi-server queueing systems. Both systems provide the same type of service and compete for customers. It is assumed that the first system is controlled by ourselves while the second one is controlled by our competitor. The arriving customers are shared between the systems depending on the comparative rating of our system. The stationary behavior of the considered model under the fixed parameters of both systems and the fixed mechanism of calculation of the rating is described by a continuous-time multi-dimensional Markov chain. The stationary distribution of this Markov chain is computed. Expressions for the key performance measures of the systems are derived. Obtained results provide an opportunity to analyse possible consequences of various managerial actions aiming to maximize the profit of our system. A numerical experiment illustrates the application of the results for making a decision about the rationality of establishing and maintaining a service system while an alternative system providing the same type of service already exists. © 2020 The Author