Анализ системы со складом и коррелированным марковским групповым потоком заявок с разнотипными катастрофическими сбоями

Рассмотрена система со складом, моделирующая ситуации, когда во время отсутствия требований обслуживающее устройство производит «заготовки», которые хранятся на «складе заготовок». Время обслуживания требования зависит от количества заготовок на складе на момент начала обслуживания. Катастрофа — это специальный вид заявки, уничтожающий все заявки в очереди или на складе. Описана система с мгновенным восстановлением после прихода катастрофы.Описано систему зі складом, яка моделює ситуації, коли під час відсутності вимог обслуговуючий пристрій виготовляє «заготовки», що зберігаються на «складі заготовок». Час обслуговування вимоги залежить від кількості заготовок на складі на момент початку обслуговування. Катастрофа — це спеціальний вид заявки, що знищує всі заявки в черзі чи на складі. Розглянуто систему з миттєвим відновленням після приходу катастрофи.A system with a storehouse that models real-life situations when in an idle state of the system so called «items» can be produced, in the storehouse. Service time depends on the quantity of items in the storehouse at the moment of the beginning of the service. Disaster is a special type of demand that clears up the queue or the storehouse. A system with instantaneous recovery after disaster arrival is considered

Multi-threshold Control of the BMAP/SM/1/K Queue with Group Services

We consider a finite capacity queue in which arrivals occur according to a batch Markovian arrival process (BMAP). The customers are served in groups of varying sizes. The services are governed by a controlled semi-Markovian process according to a multithreshold strategy. We perform the steady-state analysis of this model by computing (a) the queue length distributions at departure and arbitrary epochs, (b) the Laplace-Stieltjes transform of the sojourn time distribution of an admitted customer, and (c) some selected system performance measures. An optimization problem of interest is presented and some numerical examples are illustrated

Markovian arrivals in stochastic modelling: a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.Peer Reviewe

Оптимальное многопороговое управление потоком в системе массового обслуживания G/MSP/1 с MAP-потоком сбоев

Рассмотрена система массового обслуживания G/MSP/1 с марковским потоком катастрофических сбоев и управляемым потоком запросов. Найдено стационарное распределение вероятностей состояний вложенной цепи Маркова. Разработан алгоритм нахождения оптимальной многопороговой стратегии управления потоком запросов. Приведен численный пример.G/MSP/1 queuing system with a MAP-input of disasters, causing all customers to leave the system instantaneously, and controlled input of customers is considered. The stationary queue length distribution has been derived and the optimal multithreshold strategy for customers input control has been determined. Obtained results are illustrated by a numerical example.Розглянуто систему масового обслуговування G/MSP/1 з марковським потоком катастрофічних збоїв та керованим потоком заявок. Знайдено стаціонарний розподіл станів укладеного ланцюга Маркова. Розроблено алгоритм пошуку оптимальної багатопорогової стратегії керування потоком заявок. Наведено чисельний приклад

Markovian arrivals in stochastic modelling : a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension

Cross-layer performance control of wireless channels using active local profiles

To optimize performance of applications running over wireless channels state-of-the-art wireless access technologies incorporate a number of channel adaptation mechanisms. While these mechanisms are expected to operate jointly providing the best possible performance for current wireless channel and traffic conditions, their joint effect is often difficult to predict. To control functionality of various channel adaptation mechanisms a new cross-layer performance optimization system is sought. This system should be responsible for exchange of control information between different layers and further optimization of wireless channel performance. In this paper design of the cross-layer performance control system for wireless access technologies with dynamic adaptation of protocol parameters at different layers of the protocol stack is proposed. Functionalities of components of the system are isolated and described in detail. To determine the range of protocol parameters providing the best possible performance for a wide range of channel and arrival statistics the proposed system is analytically analyzed. Particularly, probability distribution functions of the number of lost frames and delay of a frame as functions of first- and second-order wireless channel and arrival statistics, automatic repeat request, forward error correction functionality, protocol data unit size at different layers are derived. Numerical examples illustrating performance of the whole system and its elements are provided. Obtained results demonstrate that the proposed system provide significant performance gains compared to static configuration of protocols

Two approaches to the construction of perturbation bounds for continuous-time Markov chains

The paper is largely of a review nature. It considers two main methods used to study stability and obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable state space. An approach is described to the construction of perturbation estimates for the main five classes of such chains associated with queuing models. Several specific models are considered for which the limit characteristics and perturbation bounds for admissible "perturbed" processes are calculated