An Efficient Universal Generating Function-Based Analyzing Approach for Multistate System with Imperfect Coverage Failure

A system with more than two states is called a multistate system (MSS), and such systems have already become a general trend in the arena of complex industrial products and/or systems. Fault-tolerant technology often plays a very important role in improving the reliability of an MSS. However, the existence of imperfect coverage failure (ICF) in a work-sharing group (WSG) decreases the reliability of MSS. A method is proposed to assess the reliability and sensitivity of an MSS with ICF. The components in a WSG can cooperate so as to improve overall efficiency by increasing performance levels. Using the technique of the universal generating function (UGF), a component’s UGF expression with ICF can be incorporated in two steps. During the computation of the system’s UGF, an algorithm based on matrix (ABM) is developed to reduce the computational complexity. Consequently, indices of reliability can be easily calculated based on the UGF expression of an MSS. Sensitivity analysis can help engineers judge which WSG should be eliminated first under various resource limitations. Examples illustrate and validate this method.

Vector dynamics influence spatially imperfect genetic interventions against disease

Background and objectives Genetic engineering and similar technologies offer promising new approaches to controlling human diseases by blocking transmission from vectors. However, in spatially structured populations, imperfect coverage of the vector will leave pockets in which the parasite may persist. Movement by humans may disrupt this local persistence and facilitate eradication when these pockets are small, spreading parasite reproduction outside unprotected areas and into areas that block its reproduction. Here we consider the sensitivity of this process to biological details: do simple generalities emerge that may facilitate interventions? Methodology We develop formal mathematical models of this process similar to standard Ross-Macdonald models, but (i) specifying spatial structure of two patches, with vector transmission blocked in one patch but not in the other, (ii) allowing temporary human movement (travel instead of migration), and (iii) considering two different modes of mosquito biting. Results We find that there is no invariant effect of disrupting spatial structure with travel. For both biting models, travel out of the unprotected patch has different consequences than travel by visitors into the patch, but the effects are reversed between the two biting models. Conclusions and implications Overall, the effect of human travel on the maintenance of vector-borne diseases in structured habitats must be considered in light of the actual biology of mosquito abundances, biting dynamics, and human movement patterns. Lay summary Genetic interventions against pathogens transmitted by insect vectors are promising methods of controlling infectious diseases. These interventions may be imperfect, leaving pockets where the parasite persists. How will human movement between protected and unprotected areas affect persistence? Mathematical models developed here show that the answer is ecology-dependent, depending on vector biting behavior.

On the retrial queue with imperfect coverage and delay reboot

This paper presents a design for a fault-tolerant call center consisting of a multi-server retrial queue, and including detection, location and coverage variables. Basically, incoming calls are immediately detected and located. However, it is not always possible to detect and locate because of some fault issues. If incoming calls are not detected and located, the system is cleared by a reboot. Once incoming calls are detected and located, they are attended to when a consultant is available; otherwise, they join a retrial orbit and generate repeated attempts till a free consultant is found. We analyze the presented model as a quasi-birth-and-death process and develop various performance indices. The optimal number of consultants and optimal service rate are searched by constructing an average cost function. A heuristic search technique is employed to obtain the optimization approximate solution at a minimum cost. Numerical illustrations are given to demonstrate the optimization procedure and the effects of varying parameters on performance indices.

Vector dynamics influence spatially imperfect genetic interventions against disease

Background and objectivesGenetic engineering and similar technologies offer promising new approaches to controlling human diseases by blocking transmission from vectors. However, in spatially structured populations, imperfect coverage of the vector will leave pockets in which the parasite can persist. Yet movement by humans may disrupt this local persistence and facilitate eradication when these pockets are small, essentially distributing parasite reproduction out of unprotected areas and into areas that block its reproduction.MethodologyWe develop formal mathematical models of this process similar to standard Ross-Macdonald models, but (i) specifying spatial structure of two patches, with transmission blocked in one patch but not in the other, (ii) allowing temporary human movement (travel instead of migration), and (iii) considering two different modes of mosquito biting.ResultsWe find that there is no invariant effect of disrupting spatial structure with travel. For both biting models, travel out of the unprotected patch has different consequences than travel by visitors into the patch, but the effects are reversed between the two biting models.Conclusions and implicationsOverall, the effect of human travel on the maintenance of vector-borne diseases in structured habitats must be considered in light of the actual biology of mosquito abundances and biting dynamics.Lay summaryGenetic interventions against pathogens transmitted by insect vectors are promising methods of controlling infectious diseases. These interventions may be imperfect, leaving pockets where the parasite persists. How will human movement between protected and unprotected areas affect persistence? Mathematical models developed here show that the answer is ecology-dependent, depending on vector biting behavior.

Transient analysis of computing system with reboot and recovery delay

PurposeThe purpose of this paper is to present a sensitivity analysis of fault-tolerant redundant repairable computing systems with imperfect coverage, reboot and recovery process.Design/methodology/approachIn this investigation, the authors consider the computing system having a finite number of identical working units functioning simultaneously with the provision of standby units. Working and standby units are prone to random failure in nature and are administered by unreliable software, which is also likely to unpredictable failure. The redundant repairable computing system is modeled as a Markovian machine interference problem with exponentially distributed failure rates and service rates. To excerpt the failed unit from the computing system, the system either opts randomized reboot process or leads to recovery delay.FindingsTransient-state probabilities have been determined with which the authors develop various reliability measures, namely reliability/availability, mean time to failure, failure frequency, and so on, and queueing characteristics, namely expected number of failed units, the throughput of the system and so on, for the predictive purpose. To spectacle the practicability of the developed model, a numerical simulation, sensitivity analysis and so on for different parameters have also been done, and the results are summarized in the tables and graphs. The transient results are helpful to analyze the developing model of the system before having the stability of the system. The derived measures give direct insights into parametric decision-making.Social implicationsThe conclusion has been drawn, and future scope is remarked. The present research study would help system analyst and system designer to make a better choice/decision in order to have the economical design and strategy based on the desired mean time to failure, reliability/availability of the systems and other queueing characteristics.Originality/valueDifferent from previous investigations, this studied model provides a more accurate assessment of the computing system compared to uncertain environments based on sensitivity analysis.