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The Anatomy Study of Efficient Agreement
in a Cloud Computing Environment with Fallible Processes
Shu-Ching Wang
Chaoyang University of Technology Taiwan, R.O.C.
Kuo-Qin Yan*
Chaoyang University of Technology Taiwan, R.O.C.
(*: Corresponding author)
Chia-Ping Huang
Chaoyang University of Technology Taiwan, R.O.C.
Abstract—Fault-tolerance is an important research topic in
the study of distributed systems. To counter the influence of
faulty components, it is essential to reach a common agreement
in the presence of faults before performing certain tasks.
However, the agreement problem is fundamental to fault-
tolerant distributed systems. In previous studies, protocols
dealing with the agreement problem have focused on a
network topology with faulty hardware components. However,
cloud computing, an Internet-based development in which
dynamically scalable and often virtualized resources are
provided as a service over the Internet has become a significant
issue. Therefore, previous protocols for the agreement problem
with fallible hardware are not suitable for a cloud computing
environment with fallible processes. To enhance fault tolerance,
the agreement problem in a cloud computing environment with
fallible processes is revisited in this study. The proposed
protocol can solve the agreement problem with a minimal
number of rounds of message exchange and tolerates a
maximal number of faulty processes.
Keywords- Agreement problem; Byzantine agreement;
Consensus problem; Interactive consistency; Distributed system;
Fault-tolerance; Cloud computing
I. INTRODUCTION
Cloud computing is a new concept in distributed systems.
It is currently used mainly in business applications in which
computers cooperate to perform a specific service together.
In addition, the internet applications are continuously
enhanced with multimedia, and vigorous development of the
device quickly occurs in the network system [1,6]. As
network bandwidth and quality outstrip computer
performance, various communication and computing
technologies previously regarded as being of different
domains can now be integrated, such as telecommunication,
multimedia, information technology, and construction
simulation. Thus, applications associated with network
integration have gradually attracted considerable attention.
Similarly, cloud computing facilitated through distributed
applications over networks has also gained increased
recognition. In a cloud computing environment, users have
access to faster operational capability on the Internet [1],
and the computer systems must have high stability to keep
pace with this level of activity. However, cloud computing has greatly encouraged
distributed system design and application to support user-
oriented service applications [5]. Therefore, the users can use the application platform of cloud computing to execute the personal software or program in their capacity of account [7]. The processes in the cloud computing environment must be synchronously completed. To ensure the cloud computing environment is reliable, a mechanism to ensure that all nodes can reach an agreement is thus necessary.
The Internet platform of cloud computing provides many applications for users. Therefore, each node of a cloud computing environment needs to run many processes and needs to execute user’s requests synchronously. In the cloud computing environment, many users can execute application services simultaneously. Therefore, the high fault-tolerant capability of a cloud computing environment needs to be considered. However, in the cloud computing environment, nodes receive the user’s requests maybe influence by the disorderly faulty processes. Hence, to remove the affect of disorderly faulty processes needs to be mitigated. In a cloud computing environment, achieving perfect reliability must be accomplished by allowing a given set of nodes to reach a common agreement even in the presence of faulty processes.
The agreement problem is one of the most important
issues for designing a fault-tolerant distributed system [3].
The definition of the problem is to make the correct nodes in
an n nodes distributed system to reach agreement. Each
node i has its initial value vi and agrees on a set of common
values. Therefore, agreement has been achieved if the
following conditions are met:
Agreement: Each correct node agrees on a set of
common values V=[v1, v2, …, vn].
Validity: If the initial value of each correct node is vi,
then the i-th value in the common vector V
should be vi. Previous solutions of the agreement problem focused on a
network topology with faulty hardware components. However, previous studies of the agreement problem [3,6] do not specifically address the cloud computing with faulty processes to order the application of internet. Therefore, the agreement problem in a cloud computing environment with disorderly faulty processes is revised in this study. The proposed protocol is named Protocol of Fallible Processes (PFP in short) and it can lead an agreement of all correct nodes in a cloud computing environment.
The rest of this paper is organized as follows. Section 2 discusses the applications of cloud computing and the topology of cloud computing. Then, the proposed protocol
PFP is illustrated in detail in Section 3. In Section 4, an example of the execution of PFP is given. Section 5 demonstrates the correctness and complexity of PFP. Section 6 concludes this paper.
II. RELATED WORK
The previous studies of the agreement problem [6] do not specifically address cloud computing to order the application of internet. Hence, in this section, the applications of cloud computing are illustrated first. Then, the network construction of cloud computing is discussed.
A. Practical Applications
Cloud computing is a style of computing where massively scalable IT-related capabilities are provided to multiple external customers “as a service” using internet technologies [7]. The cloud providers have to achieve a large, general-purpose computing infrastructure; and virtualization of infrastructure for different customers and services to provide the multiple application services. The ZEUS Company has developed several types of software [10] that can create, manage, and deliver exceptional online services from physical and virtual datacenters or from any cloud environment, such as ZXTM [10] and ZEUS Web Server (ZWS) [10], as shown in Fig 1 [10].
Fig. 1 The resource of cloud infrastructure with virtualization [10]
A cloud infrastructure virtualizes large-scale computing
resources and packages them up into smaller quantities [10]. Furthermore, the ZEUS Company develops software that can let the cloud provider easily and cost-effectively offer every customer a dedicated application delivery solution. The ZXTM software is much more than a shared load balancing service and it offers a low-cost starting point in hardware development, with a smooth and cost-effective upgrade path to scale as your service grows [10].
The ZEUS provided network framework can be utilized to develop new cloud computing methods, and is utilized in the current work. In this network composition that can support the network topology of cloud computing used in our study. According to the ZEUS network framework can testify the construction of network topology that we proposed in this paper, which let the company has to be considered. Hence, the proposed network topology of cloud computing that has the trustworthy example with the company provided to support our study.
B. Network Construction
Cloud computing is a new distributed system concept that has been implemented by businesses such as Google [9] and Amazon [8]. Google provides various applications on their internet platform [9]. In previous literature, the agreement problem has been solved in various network topologies. However, previous studies of agreement problems [3,6] are not specifically address cloud computing to order the application of internet. Hence, in this paper, the topology of a cloud computing environment is applied. Subsequently, the agreement problem with fallible processes is discussed. The nodes of cloud computing are interconnected with the internet; the network is assumed reliable and synchronous. Fig. 2 is the topology of cloud computing used in our study. The topology is composed of two levels, as follows: (1) The nodes in an A-Level group receive the request from
users of different types of applications. Therefore, the nodes of an A-Level group have higher computational capability than the nodes in a B-Level group. In addition, nodes in an A-Level group compute enormous amounts data and can communicate with other nodes in the same group directly through transmission media.
(2) According to the properties of nodes, the nodes are clustered into a cluster Bi in a B-Level group, where 1≤i≤cn and cn is the total number of clusters in a B-Level group.
(3) For the reliable communication, multiple inter transmission media are used to connect the nodes between an A-Level group and a B-Level group. In A-Level group, each node forwards the message to all nodes in the corresponding cluster of the B-Level group.
Fig. 2. Example of topology of cloud computing
However, a process is said to be correct if it follows the
protocol specifications during the execution of a protocol;
otherwise, the process is faulty. The fault symptom of
process is called disorderly faults. The behavior of a
disorderly fault is the fault can cause other components
cannot complete work correctly and synchronously. A
disorderly faulty process takes place when a node fails to
transmit the fake messages and other nodes receive the same
fake messages. However, the behavior of disorderly faulty
process is unpredictable and to confuse other nodes to
receive incorrect messages to complete a specific service for
user. Therefore, the disorderly faulty processes will
influence each node in the system finish user’s request
synchronization. Here, a solution of the agreement problem
in the cloud computing environment with disorderly faulty
processes is presented.
III. THE PROPOSED PROTOCOL
In this study, the proposed protocol named Protocol
of Fallible Processes (PFP), is invoked to solve the
agreement problem in a cloud computing with fallible
processes. Based on the network topology of cloud
computing, PFP provides each node to transmit
messages to other nodes without influence from
disorderly faulty processes and the proposed protocol is
shown in Fig. 3. The PFP executes the follow steps:
Step 1: The nodes of the A-Level group execute the
Agreement Process (for the node i in the A-Level
group with initial value vi; 1≤i≤nA) and nA is the
total number of nodes in the A-Level group then an
agreement vector DEC can be acquired.
Step 2: Each element of DEC is mapped to a specific
application that will be executed in the cluster of
the B-Level group. Then, each node of the cluster
in A-Level group sends the specific element of
DEC to the nodes of a specific application having
the cluster of B-Level group.
Step 3: Each node k in the same cluster of B-Level group
receives the element values from nodes of A-Level
group.
Step 4: The nodes of B-Level group’s cluster execute the
Poll Process then the agreement value can be
obtained. The PFP is proposed to solve the agreement problem
when caused by disorderly faulty processes that may send incorrect messages to influence the cloud computing environment to reach agreement. When the disorderly faulty processes exist in the cloud computing environment then two rounds of message exchange required can be estimated to solve the agreement problem. In the cloud computing topology, the main work of an A-Level group’s nodes is collecting user requests. Each node in an A-Level group receives the various requests from users, while the nodes in a B-Level group’s cluster provide many services for users.
Each node in an A-Level group that uses the service request as the initial value executes the PFP to obtain the common vector DEC. Then each node of the A-Level group forwards the element of vector DEC to the nodes in the B-Level group. However, the specific service request can be conformed by the nodes of the same group.
Each node in the same cluster of a B-Level group receives the element from the nodes of the A-Level group. In the B-Level group, nodes may receive the fake value by the disorderly faulty processes in an A-Level group. The nodes in a B-Level group receive the fake value from failure processes of A-Level group through the transmission media.
Therefore, the number of A-Level group’s failure processes must be less than half with those processes.
Sequentially, each node in the same cluster of a B-Level group takes the majority value of the received element values (DEC). Hence, the agreement can be achieve by the common agreement value.
PFP protocol
The nodes of A-Level group execute Agreement Process.
The nodes of B-Level’s group execute Poll Process.
Agreement Process
Message Exchange Phase:
r = 1
Node i broadcasts vi, then receives the initial value from the other nodes
in A-Level group, and construct vector Vi.
r = 2
Node i broadcasts Vi, then receives column vectors broadcasted by other
nodes, and construct MATi.
Decision Making Phase:
(1) Take the majority value of each column k of MATi to MAJk.
(2) Search for any MAJk. If (∃MAJk=¬vi), then DECi=φ; else if (∃MAJk=λ)
AND (vki=vi), then DECi=φ; else DECi=vi, and terminate.
(3) Each node i sends the specific element of DECi to the nodes of a
specific application having the cluster of B-Level group.
Function MAT
(1) Receive the initial value vj from node j, for 1≤j≤n and j≠i.
(2) Construct the vector Vi=[v1, v2,…, vn], 1≤j≤n and j≠i.
(3) Broadcast Vi to all nodes, and receive column vector Vj from node j,
1≤j≤n.
(4) Construct a MATi (Setting the vector vj in column j, for 1≤j ≤n).
Poll Process
(1) The node k in the cluster of the B-Level group receives the element
value of DEC with a specific application needs to be serviced.
(2) To take a majority value MAJk (1≤k≤nBj, where nBj is the number of
nodes in cluster j of the B-Level group) of the received element
values.
(3) The common value vk with the node k in cluster j of the B-Level
group can be obtained.
Fig. 3 Protocol PFP
IV. EXAMPLES OF EXECUTING PFP
An example of an A-Level group in the topology of cloud computing is shown in Fig. 4. The nodes in an A-Level group receive service requests. PFP requires two rounds to exchange the messages in an A-Level group. Each node can obtain the initial value in the A cluster as shown in Fig. 5. In the first round of the Message Exchange Phase, each node receives the initial value from other nodes to construct vector Vi, as shown in Fig. 6. In the second round of the Message Exchange Phase, each node broadcasts its vector Vi, and receives the vectors from other nodes to construct the matrix MATi, as shown in Fig. 7. Finally, the common value DECi (=1) is obtained by taking the majority value on matrix MATi.
The node in A-level group broadcasts the DECi (=1) value to the cluster of a B-level group. All nodes in the cluster of a B-Level group receive the element DECi from the nodes of an A-Level group for the specific applications needing to be serviced, as shown in Fig 8. Subsequently, the POLL function is applied to take a majority value. Then, the agreement value is gotten, as shown in Fig. 8.
Fig. 4. Example of cluster A in an A-Level group with the 1st round
Fig. 5. The initial value of each node in A cluster
Fig. 6. Each node in the A cluster at the 1st round
Fig. 7. Construct MAT in 2nd round and MAJ of MAT as decision value
Fig. 8. Each node of BⅡ-1 cluster receives element of DECA from an A-
Level group node
V. THE CORRECTNESS AND COMPLEXITY
The protocol is proposed and the following proofs for the agreement and validity property are given in this section. The following lemmas and theorems are used to prove the correctness and complexity of the PFP. Lemma 1. If the initial value of node i is vi, whether the process is correct or not, the majority value at the i-th row of
MATj, 1≤j≤nA, should be either vi or cannot be determined
with vij=¬ vi. Proof: When process is under the influence of disorderly fault, we consider the following two cases after the first round is run. Case 1: vij = vi.
Since there are at most nA/2-1 disorderly faulty
processes connected with node j, at most nA/2-1 values that
may be ¬ vi’s in the second round. The number of vi’s is nA-
(nA/2-1) =(nA+1)/2 in the i-th row; therefore, the majority of the i-th row in MATi is vi.
Case 2: vij = ¬¬¬¬ vi.
There are at most nA/2-1 faulty processes Therefore, in
the second round, the total number of ¬vi‘s does not exceed
(nA/2-1)+1=nA/2 and the number of vi‘s is at least nA-
(nA/2-1)=(nA+1)/2. If nA is an even number, then
nA/2=nA/2, the majority of the i-th row in MATj cannot
be determined. If nA is an odd number, then nA/2<nA/2. Hence, the majority of the i-th row in MATj is vi.
Lemma 2. If (¬∃MAJk=¬ vi) and {(∃MAJk=?) and (vki = vi)}
in MATi, then DECi=φ is correct. Proof: If MAJk does not exist or cannot be determined,
there are exactly nA/2 v’s and n/2 ¬v’s in the k-th row. Let vki
=vi in MATi, then, all nA/2 ¬v’s should be received in the
second round. Notably, nA/2-1 faulty processes are in the system. Therefore, in the second round, node i at least receives a value from node k without any disturbance. The initial value of node k should disagree with the initial value
of node i; hence it is correct to choose DECi=φ. If vki =¬vi,
we claim that ¬vi ought to be passed by a faulty process
from node k, and the initial value of node be ¬vki =vi. To prove, if faulty process is correct, then the initial value of
node k should be ¬vi. By Lemma 1, the majority value of the
k-th row in MATi is ¬vi. This is contradiction with the
condition of (¬∃MAJk=¬vi. If the initial value of node k was
¬vi, then, by Lemma 1, MAJk should be either ¬vi or cannot be determined for vki=vi. It is a contradiction. Theorem 1. PFP is valid. Proof: According to Lemmas 1 and 2, the validity of PFP is confirmed. Theorem 2. Protocol PFP can reach an agreement. Proof:
Agreement:
Part 1: If a node agrees on φ, then all nodes should agree
on φ. If the node i with initial value vi agrees on φ, by
Theorem 1, at least there is a node k with initial value ¬vi in the environment. By Lemma 2, the majority value in
the k-th row of MATj, 1≤j≤nA, should be either ¬vi or ? (Cannot be determined) for vjk =vi. All nodes with initial value vi are agreement. Similarly, for the node i with
initial value ¬vi, the majority value of the i-th row in
MATj, 1≤j≤nA, should be either vi or cannot be
determined with ¬vij = vi. All nodes with initial value ¬vi
agree on φ, too. Part 2: If a node agrees on vi, then all nodes should agree on vi. If the node i with initial value vi and DECi= vi, but
there exists some node j, j≠i, which has DECj ≠ vi. Therefore, such a situation is impossible. To demonstrate
this impossibility, if DECi =φ, by Part 1, then DECi =φ.
This contradicts the above assumption. If DECi =¬vi,
unless the initial value of node j is ¬vi; otherwise, it is impossible according to the definition of a agreement
problem. However, if the initial value of node j is ¬vi, by
Lemma 2, MAJk equals to ¬vi or cannot be determined
with vji =vi in MAT. Then, DECi =φ, it is a contradiction. Hence, all nodes should agree on the same value by the definition of agreement problem.
Validity: To prove this case, the initial value of all nodes
should be the same. If there is a value ¬vi in MATj,
1≤j≤nA, then the value must be attributed to a faulty
process. There are at most nA/2-1 faulty processes;
hence, there is at most nA/2-1 ¬vi‘s in each row. Since
the value received in the first round may be ¬vi, the majority of each row for all MATj should be vi. Therefore, all nodes should agree on vi.
Theorem 3. The maximal number of allowable faulty processes by PFP is TF= TFA+ TFB. TFA is the total number of allowable faulty processes in A-Level group and TFA
=nA/2-1 where nA is the number of nodes in an A-Level group. TFB is the total number of allowable faulty processes
in B-Level group and TFB = ∑=
−nc
jBjn
1
)1( .
Proof: In the A-Level group, if the allowable faulty
processes TFA is greater than nA/2-1, then the nodes in A-Level group cannot reach agreement. However, when a node of cluster j in B-Level group exists, then the specific application can possibly be carried out where 1≤j≤cn and cn is the number of clusters in B-Level group. Therefore, the
fault tolerant capability of B-Level group is ∑=
−nc
jBjn
1
)1(
where nBj is the number of nodes in group j of B-Level group. Hence, the maximal number of allowable faulty processes by PFP is TF= TFA+ TFB. Theorem 4. PFP requires 3 rounds to solve the agreement in
a cloud-computing environment.
Proof: The nodes in A-Level group need 2 rounds to
exchange message in the Message Exchange Phase. In
addition, in the Decision Making Phase, each node in A-
Level group sends the specific element of DEC to the nodes
in a B-Level group. Therefore, an additional round of
message exchange is required. In conclusion, the minimum
number of rounds of PFP is 3. Moreover, the number rounds
required is optimal.
VI. CONCLUSIONS
Cloud computing is a new concept of distributed systems [1,2,9]. It has greatly encouraged distributed system design and practice to support user-oriented services with application [5,7]. In the Internet platform of cloud computing where each node needs to complete the user’s requests synchronously and to reach the common agreement as specific service. Fault-tolerance is an important research topic in the study of distributed systems and it is a fundamental problem in distributed systems; there are many relative literatures in the past [3,6]. According to previous studies, network topology plays an important role in the agreement problem, but the results cannot cope with a cloud computing environment and the agreement problem thus needs to be reinvestigated. Moreover, in this paper, the agreement problem with disorderly faulty processes has been solved by the proposed protocol.
The proposed Processes Failure of Cloud computing (PFP in short) ensures that all nodes in a cloud computing environment can reach a common value. Moreover, the new protocol PFP is adapted to the cloud computing environment and the solution of PFP is applied to solve the disorderly faulty processes existence. PFP can derive the bound of allowable disorderly faulty processes. PFP uses the minimum number of rounds of message exchange and tolerates the maximum number of allowable disorderly faulty processes in a cloud computing environment. Furthermore, the fault-tolerance capacity is enhanced by PFP.
Merely considering processes faults in the agreement problem is insufficient for the highly reliable distributed system of a cloud computing environment. A related closely problem called the Fault Diagnosis Agreement (FDA) problem. The objective of solving the FDA problem is to make each node can detects or locates the common set of disorderly faulty processes in the distributed system. Therefore, solving the FDA problem for the highly reliable distributed system underlying topology of cloud computing environment is included in our future work.
ACKNOWLEDGMENT
This work was supported in part by the Taiwan National
Science Council under Grants NSC97-2221-E-324–007.
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