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Performance analysis of cloud computing services considering resources sharing among virtual machines

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Abstract

Cloud computing is a novel paradigm for the provision of service on demand. Through the use of virtualization, physical resources are converted into “resources pool” which provides service on demand. Due to the complexity and diversity of user requests of the cloud computing system, its performance is difficult to model and analyze. Although there are some researches on cloud service performance, very few of them addressed the issues of resources sharing among VMs and its impact on service performance. This paper presents a model for performance analysis of cloud services. The model considers the resources sharing among VMs. In addition, various types of failures, such as VMs failures, physical servers failures and network failures are also considered. The service requests are also relaxed compared with prior research. A service request is divided into many subtasks and each subtask consists of a series of data processing and transmission. The average service time of service requests is obtained. And a numerical example is presented.

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Abbreviations

\(\lambda \) :

The arrive rate of service requests

\(g\) :

The number of subtasks of a service request

\(r_{j}\) :

The service rate of the \(j\)-th physical server

\(s_{ij}\) :

The proportion of the \(\mathrm{VM}_{i}\)’s resources to the \(j\)-th physical server

\(R_{s}\) :

The service rate vector of the cloud system

\(S_{k}\) :

The \(k\)-th subtask

\(\mathrm{VM}_{i}\) :

The \(i\)-th VM

\(M_{j}\) :

The \(j\)-th physical server

\(N_{j}\) :

The number of VMs that can be created on the physical server \(j\)

\(\mu _{i}\) :

The service rate for the system to stay at state \(i\)

\(M_\mathrm{total}\) :

The total number of VMs can be created by the cloud center

\(M^\mathrm{max}_{j}\) :

The maximum number of VMs that can be created on server \(j\)

\(\lambda _{v}\) :

The failure rate of VMs

\(\mu _{v}\) :

The recovery rate of VMs

\(\lambda _{p}\) :

The failure rate of physical servers

\(\mu _{p}\) :

The recovery rate of physical servers

\(\lambda _{c}\) :

The failure rate of communication links

\(\mu _{c}\) :

The recovery rate of communication links

\(N\) :

The capacity of the request queue

\(P(e)\) :

The probability of event e

\(q_{n}\) :

The steady probability for the system to stay at state \(n\)

\(P_\mathrm{block}\) :

The probability for the blocking failure

\(\omega _{k}\) :

The processing time of subtask \(k\)

\(wl_{k}\) :

The workload of subtask \(k\)

\(d_{k}\) :

The data size of subtask \(k\) needed to be transmitted

\(B_{j}\) :

The available bandwidth of the physical server \(M_{j}\)

\(\widetilde{\omega }^{v}_{k}\) :

The processing time of suktask \(k\) when there is VM failure

\(\widetilde{h}^{c}_{k}\) :

The processing time of suktask \(k\) when there is VL failure

\(\widetilde{\mathrm{VR}}^{y}_{i}\) :

The the \(y\)-th recovery time of the \(\mathrm{VM}_{i}\)

\(T^\mathrm{avg}_{i}\) :

The average waiting time of the \(i\)-th resources request

mod:

The modulus operator

\(B_{j}\) :

The available bandwidth of the physical server \(M_{j}\)

\(m\) :

The total number of servers of the cloud center

\(W_{i}\) :

The allocation matrix of the \(i\)-th service request

\(N_{j}\) :

The number of VMs that running on the physical server \(M_{j}\)

\(T^{vf}\) :

The completion time if VMs failure

\(T^{sf}\) :

The completion time if physical server failure

\(T^{cf}\) :

The completion time if network failure

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Acknowledgments

This work is supported by Innovation Action Plan supported by Science and Technology Commission of Shanghai Municipality (No. 11511500200).

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Authors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, Shanghai , 200444, China

    Xiaodong Liu, Weiqin Tong & Xiaoli Zhi

  2. Department of Computer Science and Engineering, Henan Institute of Engineering, Zhengzhou , 451191, China

    Xiaodong Liu

  3. China Telecom Corporation Ltd., Shanghai Branch, Shanghai , 200085, China

    Fu ZhiRen & Liao WenZhao

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  1. Xiaodong Liu
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  2. Weiqin Tong
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  3. Xiaoli Zhi
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  4. Fu ZhiRen
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  5. Liao WenZhao
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Correspondence to Xiaodong Liu.

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Liu, X., Tong, W., Zhi, X. et al. Performance analysis of cloud computing services considering resources sharing among virtual machines. J Supercomput 69, 357–374 (2014). https://doi.org/10.1007/s11227-014-1156-3

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