Department of Applied Probability and Informatics

A redundant data transmission system with linear topology is studied using reliability modeling of a heterogeneous hot standby system with one repair unit and exponential repair time of its failed elements (data transmission channels). Two cases are considered-a special one, when the lifetime distribution of the elements is exponential, and a generalized one, when their lifetimes have general independent distribution. The goal of this paper is to calculate the reliability characteristics of the system and to investigate the effect of cross-redundancy on the system-level reliability.

The reliability function is considered for a hot double redundant repairable heterogeneous system with exponentially distributed lifetimes and generally distributed repair times of its components. The problem of its sensitivity to the repair time distribution is discussed.

Broadband wireless data transmission network for providing of automobile transport system safety is considered. The network operates under IEEE802.11n-2012 protocol that guarantees high-speed transmission of multimedia information between automatic stationary and mobile systems of traffic control. The model of stochastic network with dependent service time for the problem solution is used. Based on product form representation of the steady state probabilities of such system the formulas and algorithms for calculating the main system characteristics such as: mean marginal queue length and mean sojourn times in the nodes, as well as mean packages delivery time in the whole network are proposed. Results of some numerical experiments are presented.

Continuous development of computer networks and data transmission systems emphasizes the increasing need for adequate mathematical models and tools that allow for the study of their performance and reliability. We consider the problem of sensitivity analysis of reliability characteristics of a repairable cold standby data transmission system with exponential life time and general repair time distributions to shapes of the input distributions. The simulation model based on the discreteevent approach is introduced to obtain results in case of a general (non-exponential) distribution of repair time of the elements. There are several approaches to model the reliability of systems with general lifeand repair times distributions. Anyhow all of them are reduced to markovization of the process that describes the system behavior [1]. The proposed analytical methodology allows to assess system-level reliability in case of failures of system elements. Explicit analytical expressions were obtai...

Continuous development of computer networks and data transmission systems underlines the growing need for adequate mathematical models and methods for analyzing the performance and reliability metrics of these systems, taking into account the performance of their redundant components. We consider a mathematical model of a repairable data transmission system as a model of a closed homogeneous cold standby system with a single repair facility and with exponentially distributed lifetimes and generally distributed repair times of the system’s elements. We study the system-level reliability, defined as the stationary probability of failure-free operation of the considered system. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failures of its elements. Explicit analytical expressions were obtained for the stationary probability of the system’s failure-free operation and stationary system state probabilities, which allow ana...

The reliability function is considered for a hot double redundant repairable heterogeneous system with exponentially distributed lifetimes and generally distributed repair times of its components. The problem of its sensitivity to the repair time distribution is discussed.

A redundant data transmission system with linear topology is studied using reliability modeling of a heterogeneous hot standby system with one repair unit and exponential repair time of its failed elements (data transmission channels). Two cases are considered-a special one, when the lifetime distribution of the elements is exponential, and a generalized one, when their lifetimes have general independent distribution. The goal of this paper is to calculate the reliability characteristics of the system and to investigate the effect of cross-redundancy on the system-level reliability.

With the rapid development and proliferation of computer networks and information technologies, researchers are faced with new complex problems, both applied and theoretical, of studying the reliability and availability of networks and data transmission systems. One of them is the reliability study of redundant data transmission systems between devices. One of the main conditions for the stable functioning of the data transmission systems is the insensitivity of their quality and effectiveness to changes in the initial parameters of the model. The analysis of such sensitivity, which is supposed to be carried out as part of this work, is one of the new directions in the research of the next-generation data transmission networks. We consider the simulation model of the repairable data transmission system as a model of a closed homogeneous cold standby system with one repair unit with arbitrary distribution functions of uptime and repair time of its elements. In this paper, we study th...

Continuous development of computer networks and data transmission systems underlines the growing need for adequate mathematical models and methods for analyzing the performance and reliability metrics of these systems, taking into account the performance of their redundant components. We consider a mathematical model of a repairable data transmission system as a model of a closed homogeneous cold standby system with a single repair facility and with exponentially distributed lifetimes and generally distributed repair times of the system's elements. We study the system-level reliability, defined as the stationary probability of failure-free operation of the considered system. The proposed analytical methodology made it possible to evaluate the reliability of the entire system in case of failures of its elements. Explicit analytical expressions were obtained for the stationary probability of the system's failure-free operation and stationary system state probabilities, which a...

This paper aimed to demonstrate the capabilities of decomposable semi-regenerative processes for the investigation of the k-out-of-n system. Proposed in 1955 by W. Smith, the regeneration idea has come a long way in terms of development and has found widespread applications. First, we briefly recall the history of the development of the regeneration idea and the main results of the theory of regenerative, semi-regenerative, and decomposable semi-regenerative processes. Then, the methods of the theory of decomposable semi-regenerative processes are used for the study of a k-out-of-n renewable system with exponentially distributed life and generally distributed repair times of its components. This system is very important for practice and its special cases have previously been considered (including by the authors); however, only special cases and using other methods are considered herein. In the current paper, two scenarios of system repair after its failure are considered for the fir...

We consider a queueing inventory with one essential and m optional items for sale. The system evolves in environments that change randomly. There are n environments that appear in a random fashion governed by a Marked Markovian Environment change process. Customers demand the main item plus none, one, or more of the optional items, but were restricted to at most one unit of each optional item. Service time of the main item is phase type distributed and that of optional items have exponential distributions with parameters that depend on the type of the item, as well as the environment under consideration. If the essential item is not available, service will not be provided. The lead times of optional and main items have exponential distributions having parameters that depend on the type of the item. The condition for stability of the system is analyzed by considering a multi-dimensional continuous time Markov chain that represent the evolution of the system. Under this condition, var...

A single-server queuing-inventory system in which arrivals are governed by a batch Markovian arrival process and successive arrival batch sizes form a finite first-order Markov chain is considered in this paper. Service is provided in batches according to a batch Markovian service process, with consecutive service batch sizes forming a finite first-order Markov chain. A service starts for the next batch on completion of the current service, provided that inventory is available at that epoch; otherwise, there will be a delay in starting the next service. When the service of a batch is completed, the inventory decreases by 1 unit, irrespective of batch size. A control policy in which the server goes on vacation when a service process is frozen until a quorum can initiate the next batch service is proposed to ensure idle-time utilization. During the vacation, the server produces inventory (items) for future services until it hits a specified level L or until the number of customers in ...

The model discussed in this paper provides an efficient mechanism for the selection and allocation of available limited spectra for transmission of heterogeneous data in a network. The data packets (customers), belonging to different classes, arrive according to a batch marked the Markovian arrival process (BMMAP). The inventory considered is of multi-type (different types of channels becoming available) and are generated according to a marked Markovian arrival process (MMAP). The number of distinct types of inventory and that of the customers are the same. Arriving customers are allowed to wait in finite buffers of each category which are reserved for distinct classes of customers except for the most general class, which is provided with an infinite waiting space. The number of servers also equals the number of distinct types of inventory. When items of a particular type arrive in the inventory, the service starts, providing the buffer of customers of the corresponding class is non...

In this paper, we consider two queuing models. Model 1 considers a single-server working vacation queuing system with interdependent arrival and service processes. The arrival and service processes evolve by transitions on the product space of two Markovian chains. The transitions in the two Markov chains in the product space are governed by a semi-Markov rule, with sojourn times in states governed by the exponential distribution. In contrast, in the second model, we consider independent arrival and service processes following phase-type distributions with representation (α,T) of order m and (β,S) of order n, respectively. The service time during normal working is the above indicated phase-type distribution whereas that during working vacation is a phase-type distribution with representation (β,θS), 0<θ<1. The duration of the latter is exponentially distributed. The latter model is already present in the literature and will be briefly described. The main objective is to make a...

Today, the number of interconnected Internet of Things (IoT) devices is growing tremendously followed by an increase in the density of cellular base stations. This trend has an adverse effect on the power efficiency of communication, since each new infrastructure node requires a significant amount of energy. Numerous enablers are already in place to offload the scarce cellular spectrum, thus allowing utilization of more energy-efficient short-range radio technologies for user content dissemination, such as moving relay stations and network-assisted direct connectivity. In this work, we contribute a new mathematical framework aimed at analyzing the impact of network offloading on the probabilistic characteristics related to the quality of service and thus helping relieve the energy burden on infrastructure network deployments.