An analytical approach to the unavailability estimation of protected connections in optical networks
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Most existing methods for unavailability estimation of protected connections in optical networks using shared backup are approximate. This paper presents an analytical approach to the unavailability estimation. The failure state probabilities used by the approach are derived from an analytical way. The computed unavailability values based on the analytical state probabilities are viable.Keywords:
Unavailability
With the network function virtualization technology, a middlebox can be deployed as software on commercial servers rather than on dedicated physical servers. A backup server is necessary to ensure the normal operation of the middlebox. The workload can affect the failure rate of backup server; the impact of workload-dependent failure rate on backup server allocation considering unavailability has not been extensively studied. This paper proposes a shared backup allocation model of middlebox with consideration of the workload-dependent failure rate of backup server. Backup resources on a backup server can be assigned to multiple functions. We observe that a function has four possible states and analyze the state transitions within the system. Through the queuing approach, we compute the probability of each function being available or unavailable for a certain assignment, and obtain the unavailability of each function. The proposed model is designed to find an assignment that minimizes the maximum unavailability among functions. We develop a simulated annealing algorithm to solve this problem. We evaluate and compare the performances of proposed and baseline models under different experimental conditions. Based on the results, we observe that, compared to the baseline model, the proposed model reduces the maximum unavailability by an average of 29% in our examined cases.
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Network function virtualization paradigm enables us to implement network functions provided in middleboxes as softwares which run on commodity servers. This paper proposes an unavailability-aware backup allocation model with shared protection for middleboxes with comprehensively considering the failure, repair, and recovery behaviors of functions and backup servers. Multiple functions can share the backup resources on the backup server. The proposed model aims to find the assignment of backup servers to functions to minimize the maximum unavailability among functions. The multiple situations of failure, repair, and recovery of functions and backup servers lead to several different states for each function. The unavailability of function is estimated through analyzing all states that a function can be in. To compute the unavailability of middlebox for a given backup allocation, an analytical approach is developed based on the queueing theory. With the analytical approach, we introduce a simulated annealing heuristic to solve the backup allocation problem. The results reveal that, compared to a baseline model, the proposed unavailability-aware model reduces the maximum unavailability 11% in average in our examined scenarios.
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Middleboxes work as software which runs on a general-purpose server by adopting a network function virtualization. The unavailability of middlebox is a key metric. The previous study considers allocating backup servers to middleboxes to reduce the unavailability. While it adopts shared protection to save backup capacity, resource sharing has not been sufficiently explored as each middlebox can only use one backup server. This paper presents a backup allocation model in which a function can be protected by two backup servers and a backup server can protect multiple functions under a shared protection strategy to minimize the maximum unavailability among functions. We use Markov chains to analyze the state transitions and make equilibrium-state equations. By solving them, we obtain the probability of each state of the allocation and compute an unavailability of function. We introduce two algorithms to examine the proposed model; one of them uses the performance bound of the maximum unavailability which is analyzed in this paper. Numerical results show that the proposed model reduces the maximum unavailability by 13.9-51.2% compared to a baseline model that allocates one backup server for each middlebox in our examined cases.
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Data center
Backup software
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This paper presents a method to incorporate aging failures in power system reliability evaluation. It includes development of a calculation approach with two possible probability distribution models for unavailability of aging failures and implementation in reliability evaluation. The defined unavailability of aging failures has a consistent form as that for repairable failure. This allows aging failures to be easily included in existing reliability evaluation techniques and tools. The differences between the two models using normal and Weibull distributions have been discussed. The BC Hydro north metro system was used as an example to demonstrate an application of the proposed method and models. The results indicate that aging failures have significant impacts on system reliability, particularly for an "aged" system. Ignoring aging failures in reliability evaluation of an aged power system will result in an overly underestimation of system risk and most likely a misleading conclusion in system planning.
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This paper presents a method for incorporating aging failures in power system reliability evaluation. It includes development of a calculation approach with two possible probability distribution models for unavailability of aging failures and implementation in reliability evaluation. The defined unavailability of aging failures has a consistent form as that for repairable failure. This allows aging failures to be easily included in existing reliability evaluation techniques and tools. Differences between the two models using normal and Weibull distributions have been discussed. The BC Hydro north metro system was used as an example to demonstrate an application of the proposed method and models. The results indicate that aging failures have significant impacts on system reliability, particularly for an "aged" system. Ignoring aging failures in reliability evaluation of an aged power system will result in an overly underestimation of system risk and most likely a misleading conclusion in system planning.
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The paper presents a method to incorporate aging failures in power system reliability evaluation. It includes development of a calculation approach with two possible probability distribution models for unavailability of aging failures and implementation in reliability evaluation. The defined unavailability of aging failures has a consistent form which is the same as that for repairable failures. This allows aging failures to be easily included in existing reliability evaluation techniques and tools. Differences between the two models using normal and Weibull distributions have been discussed. The BC Hydro North Metro system was used as an example to demonstrate an application of the proposed method and models. The results indicate that aging failures have significant impacts on system reliability, particularly for an "aged" system. Ignoring aging failures in reliability evaluation of an aged power system will result in an overly underestimation of system risk and most likely a misleading conclusion in system planning.
Unavailability
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Middleboxes work as software which runs on a general-purpose server by adopting network function virtualization. The unavailability of middlebox is a key metric. The previous study considers allocating backup servers to middleboxes to reduce the unavailability. While it adopts shared protection to save backup capacity, resource sharing has not been sufficiently explored as each middlebox can only use one backup server. This paper presents a backup allocation model in which a function can be protected by two backup servers and a backup server can protect multiple functions under a shared protection strategy to minimize the maximum unavailability among functions. We use Markov chain to analyze the state transitions and make equilibrium-state equations. By solving them, we obtain the probability of each state of the allocation and compute an unavailability of function. We introduce two algorithms to examine the proposed model; one of them uses the performance bound of the maximum unavailability which is analyzed in this paper. Numerical results show that the proposed model reduces the maximum unavailability by 9.5–51.2% compared to a baseline model that allocates one backup server for each middlebox in our examined cases.
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Data center
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Unavailability
Component (thermodynamics)
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Summary form only given. The paper presents a method to incorporate aging failures in power system reliability evaluation. It includes development of a calculation approach with two possible probability distribution models for unavailability of aging failures and implementation in reliability evaluation. The defined unavailability of aging failures has a consistent form as that for repairable failures. This allows aging failures to be easily included in existing reliability evaluation techniques and tools. Differences between the two models using normal and Weibull distributions have been discussed. The BC Hydro north metro system was used as an example to demonstrate an application of the proposed method and models. The results indicate that aging failures have significant impacts on system reliability, particularly for an "aged" system. Ignoring aging failures in reliability evaluation of an aged power system results in an overly underestimation of system risk and most likely a misleading conclusion in system planning.
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The electric generating unit's operational state of both history and scheme should be taken into consideration in the operational reliability evaluation of generating system. The generating unit's ageing failure is taken into account in the paper. The repairable failure unavailability and the ageing failure unavailability are deduced from the unified definition of unavailability, and the forced outage model is obtained by using the theory of multiple failure competing risk failure. The selections of formula for computing unavailability in the reliability evaluation of different cycles are discussed. And they are applied to operational reliability evaluation of generating system, which is based on daily generation scheduling. Simulation analyses are given to indicate the effectiveness of the method. The methods and conclusions can be used in operational reliability evaluation of composite generation and transmission system, and also can be applied into operational reliability evaluation of generating system including wind energy and solar energy.
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Reliability theory
Maintenance engineering
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