Vladimir Rykov

Multidimensional Alternative Processes Reliability Models

Multidimensional alternative processes are introduced, their stationary and quasi-stationary probabilities are investigated, and their applications in reliability models are considered.

Sensitivity Analysis of Reliability Characteristics to the Shape of the Life and Repair Time Distributions

The present paper deals with some simple finite population queueing systems which are used to describe the cold redundancy systems. The systems are assumed to be in a complete failure state as soon as all of the units are failed. For such models the time dependent state probabilities and reliability function are analyzed. It is shown that the reliability function have a weak sensitivity to the shape of the life and repair time distributions and this sensitivity vanishes upon the probability of the complete failure state decreases.

Heuristic Solution for the Optimal Thresholds in a Controllable Multi-server Heterogeneous Queueing System Without Preemption

As it known the optimal policy which minimizes the long-run average cost per unit of time in a multi-server queueing system with heterogeneous servers without preemption has a threshold structure. It means that the slower server must be activated whenever all faster servers are busy and the number of customers in the queue exceeds some specified for this server threshold level. The optimal thresholds can be evaluated using the Howard iteration algorithm or by minimizing the function of the average cost which can be obtained in closed form as a function of unknown threshold levels. The both cases have sufficient restrictions on dimensionality of the model. In present paper we provide a heuristic method to derive expressions for the optimal threshold levels in explicit form as functions of system parameters like service intensities, usage and holding costs for an arbitrary number of servers. The proposed method is based on the fitting of the boundary planes between the areas where the optimal threshold takes a certain value.

On a Slow Server Problem

The slow server problem is generalized for the case of additional cost structure. With the help of special partial ordering of the system state space it is shown that the optimal policy for the problem has a monotone property consisting in the following: an additional server should be switched on only in the case if the queue length exceeds some level depending on the system state, and in this case the server with minimal service cost should be used.

On Optimal Control of Systems on Their Life Time

Absorbing controllable Markov processes as models of some technical and/or biological objects behavior at their lifetime are proposed. A problem of optimal control of these objects during their lifetime for two-level control policies with respect to two objective functionals as control goals are considered; these goals are: the maximization of mean lifetime and the mean reward during it. The closed formulas for the main characteristic of the process and objective functional are given and some numerical examples of optimal policies calculation for both functionals are done.

Reliability-Centric Analysis of Offloaded Computation in Cooperative Wearable Applications

Motivated by the unprecedented penetration of mobile communications technology, this work carefully brings into perspective the challenges related to heterogeneous communications and offloaded computation operating in cases of fault-tolerant computation, computing, and caching. We specifically focus on the emerging augmented reality applications that require reliable delegation of the computing and caching functionality to proximate resource-rich devices. The corresponding mathematical model proposed in this work becomes of value to assess system-level reliability in cases where one or more nearby collaborating nodes become temporarily unavailable. Our produced analytical and simulation results corroborate the asymptotic insensitivity of the stationary reliability of the system in question (under the “fast” recovery of its elements) to the type of the “repair” time distribution, thus supporting the fault-tolerant system operation.

Degradation Models with Random Life Resources

Some degradation models with random life resources for technical and biological objects are introduced and studied. Conditional hazard rate function given fixed consumed resource is in the focus of consideration.

Mobility-Centric Analysis of Communication Offloading for Heterogeneous Internet of Things Devices

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.