=Paper=
{{Paper
|id=Vol-2590/paper15
|storemode=property
|title=Analysis of the Cluster Operating Time With the Migration of Virtual Machines
|pdfUrl=https://ceur-ws.org/Vol-2590/paper15.pdf
|volume=Vol-2590
|authors=Vladimir Bogatyrev,Aleksej Derkach
|dblpUrl=https://dblp.org/rec/conf/micsecs/BogatyrevD19
}}
==Analysis of the Cluster Operating Time With the Migration of Virtual Machines==
https://ceur-ws.org/Vol-2590/paper15.pdf
Analysis of the Cluster Operating Time With
the Migration of Virtual Machines?
Vladimir Bogatyrev1,2[0000−0003−0213−0223] and Aleksey
Derkach2[0000−0002−0108−319X]
1
Saint-Petersburg State University of Aerospace Instrumentation, Saint-Petersburg,
Russia
vladimir.bogatyrev@gmail.com
http://new.guap.ru
2
ITMO University, Saint-Petersburg, Russia
alexitmo1@gmail.com
http://www.ifmo.ru/ru/
Abstract. A Markov model of reliability of a fault-tolerant cluster has
been considered, using virtualization technologies that ensure the conti-
nuity of the computational process in the event of a failure of the servers‘
physical resources and the impossibility of recovering from the interrup-
tion of the computational process. The probability of maintaining the
system’s operability under the condition of ensuring the continuity of the
computing process for different service organization options was anilized.
The mean time time to failure of such sistems was found. The purpose
of the work is to increase the functional reliability of computing systems
of a cluster architecture while increasing the time to failure, taking into
account the requirements for ensuring the continuity of the computing
process. A fault tolerance is considered as an object of study. A vir-
tual machine is running on the cluster. The system involves launching a
shadow copy of the VM on the backup server, which al-lows after the fail-
ure of the primary server to continue its implementation on the backup
server.The proposed models can be used to assess the level of system re-
liability and are important in choosing a system configuration for certain
conditions. Assessing the migration of virtual machines in the event of
a failure of physical servers will allow you to calculate and evaluate the
possible damage when using various models.
Keywords: Virtualization · Cluster · Migration · Virtual machines ·
Mean time to failure.
1 Introduction
For cluster computing systems, especially real-time, the key is to ensure reli-
ability and fault tolerance while maintaining the continuity of the computing
?
Copyright c 2019 for this paper by its authors. Use permitted under Creative Com-
mons License Attribution 4.0 International (CC BY 4.0)
2 V. Bogatyrev et al.
process. The achievement of high and stable performance indicators, reliability,
fault tolerance [1-3] and security [4] of computer systems is facilitated by the use
of technologies for consolidation of clustering and virtualization resources [5-6],
accompanied by replication and migration of virtual machines between physical
servers. Migration and replication of virtual machines speeds up the reconfigu-
ration process after failures of physical resources and contributes to supporting
the continuity of the computing process required for managing cyber-physical
systems and real-time technological processes.
2 Cluster fault tolerance technology with continuous
computing
One of the effective ways to achieve fault tolerance of computing systems and pro-
cesses is the migration of virtual resources between the physical nodes (servers)
of a computing system of a cluster architecture. In a cluster with replication
of virtual machines (VMs) on different physical nodes, they can migrate be-
tween cluster nodes in the event of failure of physical resources without stopping
calculations on servers [7-8, 17-19].
Virtualization allows to optimize the use of computing resources, increases
the scalability, fault tolerance and extensibility of the infrastructure, due to the
rapid redistribution of the virtual resource [9-10].
Recovery time during VM migration after failures depends on the structure
of the data storage.With shared storage for all physical nodes of the cluster, only
RAM, virtual processor registers, and VM virtual device states are transferred
during migration [5-6]. Information is transferred from hard disks in case of the
data storage is localized for each node of the cluster.
Fault tolerance ensures the continuity of the computing process (service) in
the cluster after the failure of one of the physical servers with the support of two
copies of the VM, which, in RAM, are located on different physical servers, so
that in case of failure of one of them, continue to work on the second. During the
functioning of the VM on the main servers, the backup copy must support the
actual copy of the RAM [12-14] of the active VMs. In this case, the virtual disk
images of the VM should be stored on a dedicated or distributed data storage
with synchronous data replication. VMware Fault Tolerance, Kemari for Xen
and KVM [11, 12] software products support fault tolerance technology.
The purpose of the work is to increase the functional reliability of computing
systems of a cluster architecture while increasing the time to failure, taking into
account the requirements for ensuring the continuity of the computing process.
By functional reliability, we mean the ability of systems to perform the re-
quired functions, taking into account not only the operability of the resources
required for their implementation, but also ensuring the necessary conditions for
their implementation. Requirements to ensure the continuity of the computa-
tional process in the inadmissibility of interruptions of the reservation system
at the time of recovery are proposed as conditions of operation. Thus, in the
systems under consideration, recovery is possible only if it is combined with the
Title Suppressed Due to Excessive Length 3
implementation of the required functions by non-failed nodes. The system enters
a non-recoverable state if it is impossible to reconfigure with the activation of
the required number of operability resources. For such systems, the reliability
indicator is the time to failure, including taking into account violations of the
continuity of the computing process, provided that the permissible reconfigura-
tion time, including the costs of migration of virtual machines, is exceeded.
3 Cluster organization and options for its recovery
The cluster architecture computer system contains servers (Fig.1). Each server
is connected directly to one local storage device (local server storage device).
In the system to ensure automatic reconfiguration, aimed at supporting the
continuity of computing processes based on dynamic migration, pairs of physical
servers of the primary and secondary are allocated in the cluster. The main
server performs the required tasks critical to the continuity of the computing
process. The backup server is designed to perform dynamic reconfiguration with
ensuring the continuity of the computing process in case of possible failures of
the primary server. The backup server, in addition to implementing dynamic
system reconfiguration, performs some background tasks that are not critical to
the continuity of the computational process and to the time of query execution).
If the backup server fails, the background tasks that it performs may be lost
or redistributed to the main server if they are performed non-priority in the
background.
With the simplest implementation of a fault tolerance cluster, it is equipped
with a pair of servers, one of which is designated as the main, and the second as
the backup.
Fault tolerance technology involves launching a backup copy of the primary
server VM on the backup server and transferring the calculations to the backup
server in case of primary server or storage device failure.
Consider system options that provide (option A) and do not provide (option
B) the restoration of physical nodes for states in which the continuity of the
computing process is ensured during reconfiguration of the cluster, which allows
us to select a working server and associated storage device for the implementation
of the calculations.
For the options under consideration, in the event of a transition to a failure
state with the impossibility of implementing the required functions at least with
a minimal workable configuration, it is considered that the computational process
is interrupted for a time exceeding the maximum permissible value, which entails
a transition to a state of unrecoverable failure.
Let us consider cluster systems while ensuring fault-tolerant functioning with
pairwise integration of physical servers into duplicated systems supporting the
processes of virtual machine migration and data replication. For each pair of
pairs in the cluster interacting to support dynamic reconfiguration of the servers
(duplicated system), state and transition diagrams for a variant of organization
A and B of a duplicated cluster system with recovery disciplines are shown in
4 V. Bogatyrev et al.
Fig. 2 and 3 . The diagram shows the failure and recovery rates of the server
λ0 and µ0 ; disk λ1 , µ1 ; commutator λ2 , µ2 . The actual data replica is loaded
onto the recovered disk (synchronization of the distributed storage system) with
an intensity of 3. The VM startup time on the backup server and the user
application loading on it are negligibly small in comparison with the loading
of the current data replica, there-fore, in this study, an instant switch between
servers is assumed.
The system of differential equations in accordance with the state diagram
and transitions in Fig. 2 and have the form:
P00 (t) = −(2λ0 + λ2 + 2λ1 )P0 (t) + µ3 P4 (t),
P10 (t) = −(λ1 + λ0 + µ0 )P1 (t) + 2λ0 P0 (t) + λ0 P4 (t),
P20 (t) = −(λ1 + λ0 + µ2 )P2 (t) + λ2 P0 (t) + λ2 P4 (t),
P30 (t) = −(λ1 + λ0 + µ1 )P3 (t) + λ1 P4 (t) + 2λ1 P0 (t),
P40 (t) = −(2λ0 + λ2 + 2λ1 + µ3 )P4 (t) + µ1 P3 (t) + µ0 P1 (t) + µ2 P2 (t),
P50 (t) = −(λ1 + λ0 )(P1 (t) + P2 (t) + P3 (t) + P4 (t)).
For option B:
P00 (t) = −(2λ0 + λ2 + 2λ1 )P0 (t),
P10 (t) = −(λ1 + λ0 )P1 (t) + 2λ0 P0 (t),
P20 (t) = −(λ1 + λ0 )P2 (t) + λ2 P0 (t),
P30 (t) = −(λ1 + λ0 )P3 (t) + 2λ1 P0 (t),
P40 (t) = −(λ1 + λ0 )(P1 (t) + P2 (t) + P3 (t)).
4 Calculation of the probability of operability of
duplicated systems
The presented systems of differential equations make it possible to determine
the dependence of the probabilities of all states from time.
The probability of the system working while maintaining the continuity of
the computing process for option A and B is defined as:
4
X
P (t) = Pi (t),
i=0
and for option B is defined as:
3
X
P (t) = Pi (t).
i=0
Title Suppressed Due to Excessive Length 5
Fig. 1. Cluster model.
6 V. Bogatyrev et al.
Fig. 2. State and transition graph of a duplicated system with ensuring the continuity
of the computing process for organization option A.
Title Suppressed Due to Excessive Length 7
Fig. 3. State and transition graph of a duplicated system with ensuring the continuity
of the computing process for organization option B.
8 V. Bogatyrev et al.
Fig. 4. The probability of maintaining the system’s operability under the condition of
ensuring the continuity of the computing process for ser-vice organization options A
and B.
The results of calculating the probability of duplicated computer systems‘
operability provided that the computing process is continuous for options A
(the curve 1) and B (the curve 2) of the maintaining process‘ organization are
presented in Fig. 3.
The calculations were performed with the following failure rates λ0 = 1.115 ·
10−5 (1/h) , λ1 = 3.425 · 10−6 (1/h), λ2 = 2.3 · 10−6 (1/h), and recovery rates
µ0 = 0.33 (1/h) , µ1 = 0.17 (1/h) , µ2 = 0.33 (1/h) , µ3 = 1 (1/h).
The presented dependences make it possible to evaluate the effect on the
probability of maintaining the operability of a duplicated system, restrictions on
the inadmissibility of interruption of the computational process, and the impact
of restoration work while maintaining the possibility of continuity of the process
of performing the required functions.
5 Calculation of the probability of operability of
duplicated systems
The mean time between failures and the probability of working without failures
are related by the relation [15]:
Z∞
T = P (t)dt.
0
Title Suppressed Due to Excessive Length 9
The average operating time to failure in accordance with the methodology of
[15] is found as follows. The mean time to failure can be obtained by integrating
the system of differential equations for a model with an absorbing state, the
initial conditions P1 (0) = 1, . . . Pk (0) = 0, Pn (0) = 0 for a model with n states.
For the systems under study, integrating the left and right sides of the sys-
tems of equations (1), (2) for the models under consideration. Given that in the
presence of an absorbing state, Pi (∞) = 0, we have [16]:
−(2λ0 + λ2 + 2λ1 )T0 + µ3 T4 = −1,
−(λ1 + λ0 + µ0 )T1 + 2λ0 T0 + λ0 T4 = 0,
−(λ1 + λ0 + µ2 )T2 + λ2 T0 + λ2 T4 = 0,
−(λ1 + λ0 + µ1 )T3 + λ1 T4 + 2λ1 T0 = 0,
−(2λ0 + λ2 + 2λ1 + µ3 )T4 + µ1 T3 + µ0 T1 + µ2 T2 = 0,
−(λ1 + λ0 )(T1 + T2 + T3 + T4 ) = 0.
Thus, for the options for organizing system A, we have:
For option B:
−(2λ0 + λ2 + 2λ1 )T0 = −1,
−(λ1 + λ0 )T1 + 2λ0 T0 = 0,
−(λ1 + λ0 )T2 + λ2 T0 = 0,
−(λ1 + λ0 )T3 + 2λ1 T0 = 0,
−(λ1 + λ0 )(T1 + T2 + T3 ) = 0.
Where Ti is the average time spent in working condition i when starting work
from a operable state. Mean time to failure is determined by summing Ti , for
all operational states [16]:
X
T = Ti .
For the system under consideration, the time to failure with service discipline
A : T1 = 3.891 ∗ 105 hours, and B T2 = 3, 277 ∗ 103 hours.
6 Conclusions
The significance of the impact of ensuring the continuity of the computational
process on duplicated systems of the cluster architecture is demonstrated. The
result of the study was obtained on the basis of Markov models of reliability of a
fault-tolerant cluster with the migration of virtual machines when it is impossible
to recover after the interruption of the computational process. The time to the
first failure of a duplicated system with recovery and without recovery in failure
states of nodes that do not violate the continuity of the computational process to
perform the required functional tasks critical to the continuity of the computing
process is determined.
10 V. Bogatyrev et al.
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