Robustness analysis of Bitcoin confirmation times

Bitcoin payments require a random amount of time to get confirmed (i.e. to be grouped by the miners into a block and to be added to the Bitcoin blockchain). In [8, 11], the authors propose the modelling of the Bitcoin confirmation time by the so-called time to ruin of the Cramer-Lundberg (CL) model. This provides off-the-shelf results directly aimed at predicting the confirmation time. However, analyses suggest that the data may not fully conform with the CL model assumptions. In this manuscript, we show by means of a robustness analysis that the time to ruin of a CL model is near insensitive to small changes in the model assumptions and illustrate that the proposed heuristic model can be used to accurately predict the confirmation times even when the data deviate (to a small degree) from the model assumptions.

The Poisson process of machinery degradation: Application to valuation

The machinery degradation process is described by a random process in which failures occur with constant intensity, and with each failure the rate of benefits generated by the machinery item reduces by a random amount. If the machinery item begins to generate negative benefits, it is subject to decommissioning. We get explicit expressions for the average life of the machinery items and the coefficient of variation of the service life. Machine’s value is determined by discounting the flow of benefits from its future use. This allows to link this value with the rate of benefits that the machinery item brings. In cases where there is no information on the amount of such benefits, appraisers rely on the machine’s age. However, different machinery items of the same age may be found in a different condition and therefore are characterized by different values. We offer formulas for calculating the percent good factors reflecting the average decrease in the equipment’s value with age. To take into account the effects of income tax, property tax and inflation, it suffices to adjust the discount rate in the constructed model. It has been verified that the proposed dependencies are in a fairly good agreement with market price data for two different types of construction equipment.

Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

Reliability Analysis of DKNCP Systems with a Mixture of Degrading Components Subjected to Different Types of Shocks

This paper attempts to model the reliability of dynamic k-out-of-n systems with component partnership (DKNCP) in which a mixture of deteriorating components and multiple types of shocks are inflicted on the system. Previous studies were merely focused on the DKNCP systems affected by one type of shock that influenced all its components. In practice, however, shocks do not necessarily affect all the components. Hence, shocks may be classified based on their magnitude, specifications, and the components they affect. In this paper, random shocks are classified into distinct sets based on the components affected. DKNCP or adaptive KNCP is a new redundancy system that can be applied when a specific number of high-performance components is required which cannot be replaced by lower-performance components even if the number of these components is high. In a DKNCP system, the components contribute to the system operation in different ways and can make partnership groups for the system to survive when a component failure occurs. Also, we consider two failure mechanisms: accumulating degradation and random shocks. Two types of random shocks are also considered in the model: critical shocks, that cause instantaneous component failure, and non-critical ones, that increase natural degradation by a random amount.

Stress-Strain State of a Flat Tractive-Bearing Element of a Lifting and Transporting Machine at Operational Changes of its Parameters

Main indicators of a stress-strain state of a rubber-cable belt, the rubber-cable rope for a random placement pattern and the size of the part with broken cables, including partially removed cables, with cable breakages and their random amount, different conditions of belt interaction in its cross-sections of connection to structural elements of a conveyor and a lifting machine to ensure control of its tractive ability during the life cycle. Performed researches clarify the idea of the interaction mechanism of reinforcing elements in composite materials of layered structure with hard and soft layers. Obtained results can be used for development and justification of a unified technology of creation and engineering support of operation of lifting and transporting machines with flat tractive-bearing elements with increased life-span, level of efficiency and operational safety in systems of extraction, transportation and processing of minerals.

Varieties of Noisy Harmonic Grammar

Noisy Harmonic Grammar (NHG) is a framework for stochastic grammars that uses the GEN-cum-EVAL system originated in Optimality Theory. As a form of Harmonic Grammar, NHG outputs as winner the candidate with the smallest harmonic penalty (weighted sum of constraint violations). It is stochastic because at each "evaluation time," constraint weights are nudged upward or downward by a random amount, resulting in a particular probability distribution over candidates. This “classical” form of NHG can be modified in various ways, creating alternative theories. I explore these variants in a variety of simple simulations intended to reveal key differences in their behavior; maxent grammars are also included in the comparison. In conclusion I offer hints from the empirical world regarding which of these rival theories might be correct.

The Lifetime Model of the One-Unit-System with Two Kinds of Wear-Out

A system at inception is endowed with a random amount of resource, the process of the lapse of system life can be viewed as that of the depletion of random resource caused by the wear-out effect. This thesis considers the wear-out process of the system as the sum of an additive compound nonhomogeneous poisson shock wear-out and a continuous routine wear-out in time t. With the introduction of the concept of random resource, a wear-out model is built. Moreover, the aging properties of the system lifetime are studied in this model.

On (s,S) inventory system with random lead time and repeated demands

We consider an (s,S) inventory system with random lead time and repeated demands of unsatisfied demands from the orbit. Whenever the inventory level falls to the level s, an order is placed to bring the level to S. The quantity ordered is M=S−s. Demands to the system are served immediately if there is a positive inventory. Otherwise it will go to a pool of unsatisfied customers called orbit. After a random amount of time, that demand is retried for service. We assume a Markovian setup for the time between consecutive arrivals, replenishments, and retrials. We obtained the condition for ergodicity of the system, steady state system size probabilities, expected length of the busy period of the system, expected inventory level, expected number of customers waiting in the orbit, expected waiting times, and so forth. A control problem is studied and some numerical illusrtations are provided.

Multivariate Counting Processes: Copulas and Beyond

Multivariate stochastic processes with Poisson marginals are of interest in insurance and finance; they can be used to model the joint behaviour of several claim arrival processes, for example. We discuss various methods for the construction of such models, with particular emphasis on the use of copulas. An important class of multivariate counting processes with Poisson marginals arises if the events of a background Poisson process with constant intensity are moved forward in time by a random amount and possibly deleted; here we think of the events of the background process as triggering later claims in different categories. We discuss structural aspects of these models, their dependence properties together with stochastic order aspects, and also some related computational issues. Various actuarial applications are indicated.