CN111512332A - Topological construction method and system for meeting partition tolerance under alliance chain consensus - Google Patents

Topological construction method and system for meeting partition tolerance under alliance chain consensus Download PDF

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CN111512332A
CN111512332A CN201980005054.8A CN201980005054A CN111512332A CN 111512332 A CN111512332 A CN 111512332A CN 201980005054 A CN201980005054 A CN 201980005054A CN 111512332 A CN111512332 A CN 111512332A
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李挥
王菡
邬江兴
伊鹏
陆平
安辉耀
黄健森
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Shenzhen Cestbon Technology Co ltd
Peking University Shenzhen Graduate School
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Abstract

The invention is suitable for the field of network construction technology improvement, and provides a topological construction method meeting partition tolerance under alliance chain consensus, which comprises the following steps: s1, combining the alliance chain consensus mechanism with the network topology structure to enable the alliance chain consensus to meet partition tolerance in probability; s2, abstracting the partition tolerance of the system into a type of a convergent Markov process and acquiring the steady-state probability of the system; s3, estimating the probability and the minimum repair time of partition faults and unsatisfied consistency or availability at a certain time according to the number of the fault channels to obtain the partition tolerance probability and the average minimum repair time of the system; and S4, analyzing the resource overhead and the partition tolerance under different network topology structures according to the obtained partition tolerance probability and the average minimum repair time, and constructing a network topology structure with proper scale and high partition tolerance for the alliance chain consensus with different requirements. The coexistence of the three factors of CAP can be realized, and the method has high practical significance.

Description

Topological construction method and system for meeting partition tolerance under alliance chain consensus
Technical Field
The invention belongs to the field of network construction technology improvement, and particularly relates to a topological construction method meeting partition tolerance under alliance chain consensus.
Background
A block chain refers to a mode for implementing and managing transaction processing by constructing a block chain type data structure which is not fakeable, falsifiable and traceable through transparent and trusted rules in a Peer-to-Peer network (also called Peer-to-Peer network) environment. According to the early discussion of the blockchain, in a narrow sense, the blockchain is a chain-type data structure formed by combining data blocks in a sequential connection mode according to a time sequence, and is a distributed account book which is guaranteed to be not falsifiable and counterfeitable in a cryptographic mode; broadly, a blockchain is a completely new distributed infrastructure and computing approach that utilizes blockchain data structures to verify and store data, distributed node consensus algorithms to generate and update data, cryptographic approaches to secure data transmission and access, and intelligent contracts composed of automated script code to program and manipulate data.
The blockchain is essentially a decentralized, distributed ledger, and as early as before the blockchain appeared, the idea of distribution has been proposed and matured increasingly.2000, Eric Brewer, at some seminar, does not have the guess of Consistency (C: Consistency), Availability (a: Availability), and Partition tolerance (P: Partition tolerance) to be fully satisfied simultaneously in a distributed system.2002, L ynch et al, have demonstrated this guess and raised it to the CAP theorem, which abstracts the three factors of Consistency, Availability, and Partition tolerance to important features of the distributed system design for the first time.
Due to the fact that the network environment of the block chain is quite complex, the main flow block chain consensus algorithm of PoW and the like meets high availability and partition tolerance by weakening strict consistency into long-time final consistency, but the TPS performance of the system is limited. Therefore, some high performance blockchain systems such as EOS choose to sacrifice part of partition tolerance in exchange for TPS performance improvement by controlling the number of nodes participating in accounting. Both of the above approaches simply select two factors as the main enhancement points in consistency, availability and partition tolerance, while weakening the third factor significantly, leaving much room from the CAP limit.
The bit currency adopts a point-to-point distributed network architecture based on the Internet, and each node has a network routing function. When a new node needs to be accessed into the bitcoin network, the following steps are executed:
1. a DNS seed or seed command is used to find a valid node in the bitcoin network.
2. And sending a version message containing basic authentication content to the found valid bitcoin node to perform an initial handshake communication process, and establishing connection.
3. The IP address of the node is sent to the connected nodes, and the nodes forward the IP address to the respective connecting nodes after receiving the IP address, so that more nodes in the network receive the new node.
4. A list of its known node IP addresses is requested from the connected nodes to find more connectable nodes.
5. Periodically sending information to the nodes which have established connection to maintain connection, if no communication is carried out with a certain node for 90 minutes, the nodes are considered to be disconnected, and a new node is searched for. Since bitcoin communication is based on the TCP protocol, the number of TCP connections per node is limited, and therefore an excess number of IP addresses may be ignored.
After the startup is completed, the node remembers the node which is successfully connected recently, and can quickly reestablish connection with the previous node after the startup is restarted. And (4) if the previous nodes can not be connected, restarting to execute from the step (1).
In the communication process between the bit currency block chain nodes, the topological structure of the network is not required to be maintained, namely the network is not required to be abstracted in a logic sense, and a flooding strategy is adopted for data transmission. The flooding idea is simple and easy to realize, the negative influence of the behaviors of node addition, node departure, node failure and the like on the whole system is small, and the network reliability is high. However, since the mesh structures are interconnected, flooding may cause the nodes to repeatedly receive the same data for many times, resulting in redundant reception of node information, and a large amount of useless repeated data transmission consumes network resources.
A class of Authority certification (PoA) consensus algorithm based on a federation chain was proposed in 2017 by Gavin Wood, a pioneer and predecessor technical officer in the united foundries of etherhouses, and is currently used in the test network Kovan of etherhouses. The consensus process for PoA is: firstly, a group of initial authorized signers is specified in a created block, and the signers start to sign the generated block and broadcast uplink after mine excavation is started. If other authorized signers object to the block generation, the signer of the block is voted for kicking, and the accounting right of the signer corresponding to the block is cancelled when the number of votes exceeds 50% of the total number of the signers.
In order to reduce the loss of a malicious SIGNER, the same SIGNER can only sign one of (SIGNER _ COUNT/2) +1 blocks. IN order to reduce the probability OF divergence, one signer is IN an IN-TURN state at each altitude, other signers are IN an OUT-OF-TURN state, the signer IN the IN-TURN state can broadcast own blocks immediately, and the signer IN the OUT-OF-TURN state generates the blocks and broadcasts the blocks after randomly delaying for a period OF time.
PoA consensus relies on an efficient and trustworthy authentication mechanism. Considering that the identity of the signer is public to the whole network, once an attacker attacks more than half of the signers, the system cannot guarantee the correctness of the block. On the other hand, compared to the conventional PBFT consensus algorithm, the PoA consensus algorithm achieves high availability and partition tolerance by weakening the consistency requirement to be non-consistency (Aura client) or final consistency (Clique client).
Disclosure of Invention
The invention aims to provide a topological construction method meeting partition tolerance under alliance chain consensus, and aims to solve the technical problems.
The invention is realized in such a way that a topological construction method meeting partition tolerance under alliance chain consensus comprises the following steps:
s1, combining the alliance chain consensus mechanism with the network topology structure to enable the alliance chain consensus to meet partition tolerance in probability;
s2, abstracting the partition tolerance of the system into a type of a convergent Markov process and acquiring the steady-state probability of the system;
s3, estimating the probability and the minimum repair time of partition faults and unsatisfied consistency or availability at a certain time according to the number of the fault channels to obtain the partition tolerance probability and the average minimum repair time of the system;
and S4, analyzing the resource overhead and the partition tolerance under different network topology structures according to the obtained partition tolerance probability and the average minimum repair time, and constructing a network topology structure with proper scale and high partition tolerance for the alliance chain consensus with different requirements.
The further technical scheme of the invention is as follows: in step S2, the Markov process converges to a steady state distribution of an independent initial distribution, and obtaining the steady state probability of the system under a single network topology includes the following steps:
s21, multiplying the state transition matrix P by itself circularly;
s22, judging whether the matrix 2-norm of the difference between two continuous products is smaller than the set convergence precision, if so, considering the power value of the P at the moment as a steady-state probability matrix P*If not, the process returns to step S21.
The further technical scheme of the invention is as follows: the MTBF and MTTR of each analysis element in the step S3 are independent processes without memory and have constant mean values; the method for acquiring the partition tolerance probability of the system under the single network topology structure comprises the following steps:
s311, sampling for each possible state of the steady-state system for N times respectively;
s312, estimating the probability that partition faults occur and the consistency or the availability is not met in each state;
s313, calculating the partition tolerance probability of the system according to a total probability formula, wherein the total probability formula is as follows:
Figure BDA0002446282920000031
l represents the total number of channels and i represents that there are and only i channels in the steady state system are in a failure state.
The further technical scheme of the invention is as follows: the method for acquiring the average minimum repair time of the system under the single network topology structure comprises the following steps:
s321, calculating the minimum repair time for each sample which has partition faults and does not meet consistency or availability;
and S322, multiplying the weight of the sample in the total system partition tolerance problem to obtain the average minimum repair time of the system.
The further technical scheme of the invention is as follows: in a hierarchical network topology structure, according to a consensus process, the partition tolerance of a lower-level domain is not only influenced by the network topology structure of the lower-level domain, but also related to the partition tolerance of a higher-level domain; partition tolerance probability of the system is
Figure BDA0002446282920000041
The average minimum repair time of the system is
Figure BDA0002446282920000042
Wherein the content of the first and second substances,
Figure BDA0002446282920000043
the partition tolerance probability of each domain is expressed,
Figure BDA0002446282920000044
representing the average minimum repair time for each domain.
Another object of the present invention is to provide a topology construction system satisfying partition tolerance under federation chain consensus, the topology construction system comprising
The combination module is used for combining the alliance chain consensus mechanism with the network topology structure so that the alliance chain consensus meets the partition tolerance in probability;
the convergence module is used for abstracting the partition tolerance of the system into a type of a converged Markov process and acquiring the steady-state probability of the system;
the sampling estimation module is used for estimating the probability that the number of the fault channels has partition faults at a certain time and does not meet the consistency or availability and the minimum repair time to obtain the partition tolerance probability and the average minimum repair time of the system;
and constructing a network module for analyzing the resource overhead and the partition tolerance under different network topology structures according to the obtained partition tolerance probability and the average minimum repair time, and constructing a network topology structure with proper scale and high partition tolerance for the alliance chain consensus with different requirements.
The further technical scheme of the invention is as follows: the Markov process in the convergence module converges to a steady state distribution of an independent initial distribution, and the obtaining of the steady state probability of the system under a single network topology structure comprises
A cyclic multiplication unit for multiplying the state transition matrix P with itself cyclically;
a judging unit for judging whether the matrix 2-norm of the difference between two successive products is less than the set convergence precision, if so, the power value of P at the moment is considered as a steady-state probability matrix P*And if not, returning to the cyclic multiplication unit.
The further technical scheme of the invention is as follows: MTBF and MTTR of each analysis element in the sampling estimation module are independent processes without memory and have constant mean values; obtaining partition tolerance probabilities for a system under a single network topology includes
A sampling unit for respectively sampling N times for each possible state of a steady-state system;
an estimating unit for estimating a probability that a partition failure occurs and that consistency or availability is not satisfied in each state;
and the calculating unit is used for calculating the partition tolerance probability of the system according to a total probability formula, wherein the total probability formula is as follows:
Figure BDA0002446282920000051
l represents the total number of channels and i represents that there are and only i channels in the steady state system are in a failure state.
The further technical scheme of the invention is as follows: obtaining an average minimum repair time for a system under a single network topology includes
Calculating a minimum repair time unit for calculating a minimum repair time for each sample that has a partition failure and does not satisfy consistency or availability;
and calculating an average minimum repair time unit for multiplying the weight of the sample in the total system partition tolerance problem to obtain the average minimum repair time of the system.
The further technical scheme of the invention is as follows: in a hierarchical network topology structure, according to a consensus process, the partition tolerance of a lower-level domain is not only influenced by the network topology structure of the lower-level domain, but also related to the partition tolerance of a higher-level domain; partition tolerance probability of the system is
Figure BDA0002446282920000052
The average minimum repair time of the system is
Figure BDA0002446282920000053
Wherein the content of the first and second substances,
Figure BDA0002446282920000054
the partition tolerance probability of each domain is expressed,
Figure BDA0002446282920000055
representing the average minimum repair time for each domain.
The invention has the beneficial effects that: the network topology structure is combined with the alliance chain consensus mechanism, so that the alliance chain consensus meets the partition tolerance in probability, the coexistence of three factors of CAP can be realized, and the practical significance is high; the mean fault interval time and the mean fault repairing time which are kept unchanged in a period of time are used as parameters, and the prediction accuracy of the Markov model on the system state probability distribution trend is improved; the probability that the number of the fault channels is subjected to partition faults at a certain time and does not meet the consistency or availability and the minimum repair time are estimated, and the self-partition tolerance and the network topological structure characteristics of the consensus mechanism are adapted to the maximum extent.
Drawings
Fig. 1 is a Markov state transition diagram representation of a general network topology.
Fig. 2 is a domain number diagram of a hierarchical network topology according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of partition tolerance probability of a multi-dimensional super-square network topology according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of an average minimum repair time of a multi-dimensional super-square network topology according to an embodiment of the present invention.
Fig. 5 is a schematic diagram of partition tolerance probability of a multi-point fully-connected network topology according to an embodiment of the present invention.
Fig. 6 is a schematic diagram of an average minimum repair time of a multipoint fully connected network topology according to an embodiment of the present invention.
Fig. 7 is a schematic diagram of a lower boundary situation of a hierarchical network topology according to an embodiment of the present invention.
Fig. 8 is a schematic diagram of a fully symmetric hierarchical network topology according to an embodiment of the present invention.
Fig. 9 is a schematic diagram of a semi-symmetric hierarchical network topology according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of an asymmetric hierarchical network topology according to an embodiment of the present invention.
Fig. 11 is a flowchart of a topology construction method satisfying partition tolerance under federation chain consensus provided by the embodiment of the present invention.
Detailed Description
As shown in fig. 11, the topology construction method satisfying partition tolerance under federation chain consensus provided by the present invention is detailed as follows:
the existing block chain system only strengthens two factors of consistency, usability and partition tolerance at a consensus level, and is accompanied by great weakening of a third factor, and the third factor still has a distance from the CAP limit. In addition, in the data communication layer, the currently mainstream blockchain system does not consider how to maintain the network topology structure, which brings potential network communication hidden danger and resource waste.
The invention also provides a partition tolerance calculation method, which abstracts the partition tolerance problem of the system into a type of convergent Markov process, and uses simulation software such as MAT L AB and the like to sample and calculate the probability and the average minimum repair time that the network does not meet the consistency or the availability when the partition fault occurs.
According to the technical scheme, on the basis of not influencing the consistency and the availability of the consensus algorithm, the network topology structure and the alliance chain consensus mechanism are combined, so that the alliance chain consensus meets the partition tolerance in probability, the coexistence of three factors of CAP can be realized, and the method has high practical significance.
A partition tolerance calculation method is provided, the partition tolerance problem of a system is abstracted into a type of a convergent Markov process, and the average fault interval time and the average fault repairing time which are kept unchanged in a period of time are used as parameters, so that the prediction accuracy of a Markov model on the system state probability distribution trend is improved.
The partition tolerance of different consensus mechanisms is different, and the possible partition faults under different network topologies are also different, so that the fault probabilities of the different consensus mechanisms have different characteristics.
The partition tolerance under the hierarchical network topology structure is further deduced by a calculation method under the single network topology structure, so that the method is not only suitable for a general single-chain architecture, but also suitable for multi-chain and cross-chain architectures, and has a wide application prospect.
The resource overhead and the partition tolerance under different network topological structures are specifically analyzed, and a single or hierarchical network topological structure which is suitable in scale and high in partition tolerance is constructed for union link consensus with different requirements. The domains at different hierarchies may adopt the same or different network topologies and parameters, and the network topologies of the domains at the same hierarchy may not be completely the same.
Evaluating a communication network is generally based on the following basic assumptions:
1. all elements involved in the analysis have only two states: operation and failure.
2. The failure and repair of each analysis element are independent of each other.
3. MTBF (Mean Time Between Failures) and MTTR (Mean Time To Repair Time) of each analysis element are independent processes without memory and Mean values are constant.
MTBF is much greater than MTTR.
Based on the above assumptions, since each element is in the multiple processes of work-fail-repair, a Markov process can be used for mathematical description. The parameters are defined as follows:
v: total number of network nodes.
l: total number of network channels.
k: the alliance chain consensus mechanism meets the number of consensus nodes with minimum requirements on consistency and availability, namely if and only if the number of consensus nodes in a certain partition is larger than or equal to k, the alliance chain consensus mechanism meets the consistency and the availability.
λ: probability of failure interruption per unit time of channel, i.e.
Figure BDA0002446282920000071
μ: probability of a channel in a system being repaired per unit time in a failed state, i.e. repair rate
Figure BDA0002446282920000072
Partition tolerance probability and average minimum repair time of single network topology
For a network topology (such as a multi-dimensional super-square structure or a multi-point full-connection structure) comprising v nodes and l channels, a Markov state transition diagram is made, as shown in FIG. 1. The ith system state indicates that there are and only i channels in the network in a failure state (0 ≦ i ≦ l).
The state transition matrix of the Markov model is a matrix P of size (l +1) × (l +1), where the element PjiRepresenting the probability of transitioning from the ith system state to the jth system state. Let m denote the number of failed channels in state i and state j, the value range of m is [ max { i + j-l, 0}, min { i, j }]。
Figure BDA0002446282920000073
The state transition matrix P of the above Markov model satisfies three characteristics:
1. p satisfies randomness because all elements of P are equal to or greater than 0 and the sum of the elements of a column represents the sum of the probabilities of all possible next hops in a given initial state, i.e., the sum of the columns of P is 1.
2. P satisfies irreducibility because failure and repair are independent of each other, and each system state can come from any other state, i.e., the Markov state transition diagram is fully connected.
3. As can be seen from fig. 1, there is no simple loop between system states, so P satisfies aperiodic.
Thus, the Markov process eventually converges to a steady state profile that is independent of the initial profile. Algorithm 1 describes an iterative calculation process of the steady-state probability of the system. Multiplying the state transition matrix P circularly with the state transition matrix P, and if the matrix 2-norm of the difference between two continuous products is smaller than the given convergence precision, considering the power value of the P at the moment as a steady-state probability matrix P*。
Figure BDA0002446282920000081
Since the MTBF and MTTR of each analysis element are independent processes without memory and have constant mean values, the probability that the number of failed channels is partitioned and fails to meet consistency or availability at a certain time can be estimated by sampling. Algorithm 2 describes the partition tolerance probability calculation process for a system under a single network topology. For various states possibly existing in the system in a steady state, sampling for N times respectively, estimating the probability that the system has partition faults and does not meet the consistency or the availability, and calculating the partition tolerance probability of the system according to a full probability formula.
Figure BDA0002446282920000091
The minimum repair time is defined as the minimum time required for the system to repair a portion of the channel in the event of a failure of some kind so that the system meets consistency and availability. Algorithm 3 describes the average minimum repair time calculation process for a system under a single network topology. On the basis of the algorithm 2, for each instance which has a partition fault and does not meet the consistency or availability, the minimum repair time is calculated, and then the weight of the instance in the total system partition tolerance problem is multiplied to obtain the average minimum repair time of the system.
Figure BDA0002446282920000101
Second, partition tolerance probability and minimum average repair time of hierarchical network topology
In a hierarchical network topology, after a lower domain node generates a block in the local domain, the block is transferred to an upper domain node to continue the higher level of consensus. For an n-level network topology, the domains are assigned (i)1i2i3…) as shown in fig. 2.
The partition tolerance of the lower-level domain is not only influenced by the network topology of the lower-level domain, but also related to the partition tolerance of the higher-level domain. Order to
Figure BDA0002446282920000102
Representing the partition tolerance probability of each domain. The partition tolerance probability of the system is
Figure BDA0002446282920000111
In the same way, order
Figure BDA0002446282920000112
Representing the average minimum repair time for each domain. The average minimum repair time of the system is
Figure BDA0002446282920000113
Taking a digital optical cable system as an example, the partition tolerance probability and the average minimum repair time when a voting certification consensus mechanism (Proof of office, PoV) in a alliance chain adopts a super square network topology and a fully connected network topology are respectively calculated below.
According to the regulation of national standard, the digital optical cable communication system with the automatic switching function of the main and standby systems should meet the annual index shown in table 1, so the parameter pair (lambda, mu) ∈ { (4.5662 × 10)-4，4.1667×10-2)，(2.7397×10-4，6.9444×10-2)，(3.8358×10-5，4.9603×10-1)，(2.5571×10-5，7.4405×10-1)}。
TABLE 1 digital optical cable communication system reliability index
Link length/km 5000 3000 420 280
Number of bidirectional full-range faults 4 2.4 0.336 0.224
MTBF/h 2190 3650 26070 39107
φ/fit 456620 273970 38358 25570
MTTR/h 24 14.4 2.016 1.344
F/％ 0.274 0.164 0.023 0.015
A/％ 99.726 99.836 99.977 99.985
The resource overhead of the two network topologies of multidimensional super square and multipoint full connection are shown in table 2.
TABLE 2 resource overhead for multidimensional hyper-square and multi-drop fully-connected network topologies
Figure BDA0002446282920000114
In the context of the common consensus of PoV,
Figure BDA0002446282920000115
the calculated results of the partition tolerance probability and the average minimum repair time are shown in fig. 3-6.
Consider continuing the 4 hierarchical network topologies exemplified in fig. 7-10. FIG. 7 shows a lower boundary case of the method, i.e., the topological structure of the top, second and third level domains are 2-dimensional hyper-squares; FIG. 8 shows a fully symmetric 3-level topology construction method, where the topological structures of the top, second and third level domains are all 3-dimensional ultrasquares; FIG. 9 shows a semi-symmetric 2-level topology construction method, where the topology structures between the same level domains are the same, but the topology structure of the top level domain is 4-dimensional super-square, and the topology structure of the second level domain is 3-dimensional super-square; fig. 10 shows an asymmetric 2-level topology construction method, where the topological structures of the upper level domain, the lower level domain, and the same level domain are all different, specifically, the top level domain adopts a 4-dimensional super-square structure, and at the same time, 4, 8, and 4 secondary domains respectively adopt 4-dimensional super-square, 3-dimensional super-square, and 7-point full-connection structures.
Assume that the top, second and third level link lengths of the topologies in fig. 7-10 are 5000km, 3000km and 420km, respectively. Using the results of the partition tolerance calculation of the multidimensional super square and the multipoint full connection in fig. 3 to 6, the partition tolerance probability and the average minimum repair time of the 4 hierarchical network topologies in fig. 7 to 10 are further calculated as follows:
(1) lower boundary condition
p＝1-[(1-p1)+p1*(1-p11)*4+p1*p11*(1-p111)*4*4]≈1-4×10-4I.e., a partition failure may occur approximately every 3 months.
t＝[t1*(1-p1)+t11*p1*(1-p11)*4+t111*p1*p11*(1-p111)*4*4]I.e.,/(1-p) ≈ 21h, the average minimum repair time after a partition failure occurs is about 21 hours.
(2) Fully symmetric 3-level topology
p＝1-[(1-p1)+p1*(1-p11)*8+p1*p11*(1-p111)*8*8]≈1-5×10-8I.e., a partition failure may occur approximately every 2,283 years.
t＝[t1*(1-p1)+t11*p1*(1-p11)*8+t111*p1*p11*(1-p111)*8*8]And/(1-p) ≈ 23h, i.e., the average minimum repair time after a partition failure occurs is about 23 hours.
(3) Semi-symmetrical 2-level topology
p＝1-[(1-p1)+p1*(1-p11)*16]≈1-1×10-8I.e., a partition failure may occur approximately every 11,416 years.
t＝[t1*(1-p1)+t11*p1*(1-p11)*16]And/(1-p) ≈ 14h, i.e., the average minimum repair time after a partition failure occurs is about 14 hours.
(4) Asymmetric 2-level topology
p＝1-[(1-p1)+p1*(1-p11)*4+p1*(1-p12)*8+p1*(1-p13)*4]≈1-6×10-9I.e., a partition failure may occur approximately every 19,026 years.
t＝[t1*(1-p1)+t11*p1*(1-p11)*4+t12*p1*(1-p12)*8+t13*p1*(1-p13)*4]And/(1-p) ≈ 14h, i.e., the average minimum repair time after a partition failure occurs is about 14 hours.
Another object of the present invention is to provide a topology construction system satisfying partition tolerance under federation chain consensus, the topology construction system comprising
The combination module is used for combining the alliance chain consensus mechanism with the network topology structure so that the alliance chain consensus meets the partition tolerance in probability;
the convergence module is used for abstracting the partition tolerance of the system into a type of a converged Markov process and acquiring the steady-state probability of the system;
the sampling estimation module is used for estimating the probability that the number of the fault channels has partition faults at a certain time and does not meet the consistency or availability and the minimum repair time to obtain the partition tolerance probability and the average minimum repair time of the system;
and constructing a network module for analyzing the resource overhead and the partition tolerance under different network topology structures according to the obtained partition tolerance probability and the average minimum repair time, and constructing a network topology structure with proper scale and high partition tolerance for the alliance chain consensus with different requirements.
The Markov process in the convergence module converges to a steady state distribution of an independent initial distribution, and the obtaining of the steady state probability of the system under a single network topology structure comprises
A cyclic multiplication unit for multiplying the state transition matrix P with itself cyclically;
a judging unit for judging whether the matrix 2-norm of the difference between two successive products is less than the set convergence precision, if so, the power value of P at the moment is considered as a steady-state probability matrix P*And if not, returning to the cyclic multiplication unit.
MTBF and MTTR of each analysis element in the sampling estimation module are independent processes without memory and have constant mean values; acquiring the partition tolerance probability of the system under a single network topology structure comprises an adoption unit, a sampling unit and a sampling unit, wherein the adoption unit is used for respectively sampling each possible state of a steady-state system for N times;
an estimating unit for estimating a probability that a partition failure occurs and that consistency or availability is not satisfied in each state;
and the calculating unit is used for calculating the partition tolerance probability of the system according to a total probability formula, wherein the total probability formula is as follows:
Figure BDA0002446282920000137
l represents the total number of channels and i represents that there are and only i channels in the steady state system are in a failure state.
Obtaining an average minimum repair time for a system under a single network topology includes
Calculating a minimum repair time unit for calculating a minimum repair time for each sample that has a partition failure and does not satisfy consistency or availability;
and calculating an average minimum repair time unit for multiplying the weight of the sample in the total system partition tolerance problem to obtain the average minimum repair time of the system.
In a hierarchical network topology structure, according to a consensus process, the partition tolerance of a lower-level domain is not only influenced by the network topology structure of the lower-level domain, but also related to the partition tolerance of a higher-level domain; partition tolerance probability of the system is
Figure BDA0002446282920000131
Figure BDA0002446282920000132
The average minimum repair time of the system is
Figure BDA0002446282920000133
Figure BDA0002446282920000134
Wherein the content of the first and second substances,
Figure BDA0002446282920000135
the partition tolerance probability of each domain is expressed,
Figure BDA0002446282920000136
representing the average minimum repair time for each domain.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (10)

1. A topological construction method meeting partition tolerance under alliance chain consensus is characterized by comprising the following steps:
s1, combining the alliance chain consensus mechanism with the network topology structure to enable the alliance chain consensus to meet partition tolerance in probability;
s2, abstracting the partition tolerance of the system into a type of a convergent Markov process and acquiring the steady-state probability of the system;
s3, estimating the probability and the minimum repair time of partition faults and unsatisfied consistency or availability at a certain time according to the number of the fault channels to obtain the partition tolerance probability and the average minimum repair time of the system;
and S4, analyzing the resource overhead and the partition tolerance under different network topology structures according to the obtained partition tolerance probability and the average minimum repair time, and constructing a network topology structure with proper scale and high partition tolerance for the alliance chain consensus with different requirements.
2. The topology construction method meeting partition tolerance under alliance chain consensus as claimed in claim 1, wherein the Markov process converges to a steady state distribution of an independent initial distribution in step S2, and the step of obtaining the steady state probability of the system under a single network topology comprises the steps of:
s21, multiplying the state transition matrix P by itself circularly;
s22, judging whether the matrix 2-norm of the difference between two continuous products is smaller than the set convergence precision, if so, considering the power value of the P at the moment as a steady-state probability matrix P*If not, the process returns to step S21.
3. The topology construction method satisfying partition tolerance under federation chain consensus as recited in claim 2, wherein the MTBF and MTTR of each analysis element in the step S3 are both memory-free independent processes with constant mean; the method for acquiring the partition tolerance probability of the system under the single network topology structure comprises the following steps:
s311, sampling for each possible state of the steady-state system for N times respectively;
s312, estimating the probability that partition faults occur and the consistency or the availability is not met in each state;
s313, calculating the partition tolerance probability of the system according to a total probability formula, wherein the total probability formula is as follows:
Figure FDA0002446282910000021
l represents the total number of channels and i represents that there are and only i channels in the steady state system are in a failure state.
4. The topology construction method satisfying partition tolerance under alliance chain consensus as claimed in claim 3, wherein obtaining the average minimum repair time of the system under a single network topology comprises the steps of:
s321, calculating the minimum repair time for each sample which has partition faults and does not meet consistency or availability;
and S322, multiplying the weight of the sample in the total system partition tolerance problem to obtain the average minimum repair time of the system.
5. A topology construction method satisfying partition tolerance under alliance chain consensus as claimed in any one of claims 1-4, wherein in hierarchical network topology, according to the consensus process, the partition tolerance of lower level domain is not only affected by own network topology but also related to the partition tolerance of higher level domain; partition tolerance probability of the system is
Figure FDA0002446282910000022
The average minimum repair time of the system is
Figure FDA0002446282910000031
Wherein the content of the first and second substances,
Figure FDA0002446282910000032
the partition tolerance probability of each domain is expressed,
Figure FDA0002446282910000033
representing the average minimum repair time for each domain.
6. A topological construction system meeting partition tolerance under alliance chain consensus is characterized in that the topological construction system comprises
The combination module is used for combining the alliance chain consensus mechanism with the network topology structure so that the alliance chain consensus meets the partition tolerance in probability;
the convergence module is used for abstracting the partition tolerance of the system into a type of a converged Markov process and acquiring the steady-state probability of the system;
the sampling estimation module is used for estimating the probability that the number of the fault channels has partition faults at a certain time and does not meet the consistency or availability and the minimum repair time to obtain the partition tolerance probability and the average minimum repair time of the system;
and constructing a network module for analyzing the resource overhead and the partition tolerance under different network topology structures according to the obtained partition tolerance probability and the average minimum repair time, and constructing a network topology structure with proper scale and high partition tolerance for the alliance chain consensus with different requirements.
7. The system of claim 6, wherein the Markov process in the convergence module converges to a steady state distribution of independent initial distributions, and obtaining the steady state probability of the system under a single network topology comprises
A cyclic multiplication unit for multiplying the state transition matrix P with itself cyclically;
a judging unit for judging whether the matrix 2-norm of the difference between two successive products is less than the set convergence precision, if so, the power value of P at the moment is considered as a steady-state probability matrix P*And if not, returning to the cyclic multiplication unit.
8. The topology construction system meeting partition tolerance under federation chain consensus as recited in claim 7, wherein the MTBF and MTTR of each analysis element in the sample estimation module are both memory-free independent processes with constant mean; obtaining partition tolerance probabilities for a system under a single network topology includes
A sampling unit for respectively sampling N times for each possible state of a steady-state system;
an estimating unit for estimating a probability that a partition failure occurs and that consistency or availability is not satisfied in each state;
and the calculating unit is used for calculating the partition tolerance probability of the system according to a total probability formula, wherein the total probability formula is as follows:
Figure FDA0002446282910000041
l represents the total number of channels and i represents that there are and only i channels in the steady state system are in a failure state.
9. The method of claim 8, wherein obtaining an average minimum repair time for a system under a single network topology comprises
Calculating a minimum repair time unit for calculating a minimum repair time for each sample that has a partition failure and does not satisfy consistency or availability;
and calculating an average minimum repair time unit for multiplying the weight of the sample in the total system partition tolerance problem to obtain the average minimum repair time of the system.
10. A topology construction method satisfying partition tolerance under alliance chain consensus as claimed in any one of claims 1-4, wherein in hierarchical network topology, according to the consensus process, the partition tolerance of lower level domain is not only affected by own network topology but also related to the partition tolerance of higher level domain; partition tolerance probability of the system is
Figure FDA0002446282910000051
The average minimum repair time of the system is
Figure FDA0002446282910000052
Wherein the content of the first and second substances,
Figure FDA0002446282910000053
the partition tolerance probability of each domain is expressed,
Figure FDA0002446282910000054
representing the average minimum repair time for each domain.
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