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Combined performance and availability analysis of distributed resources in grid computing

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Abstract

This paper presents a mathematical model to evaluate the performance of grid resources when availability of the resources is taken into account. The proposed model uses continuous time Markov chains (CTMCs) to model the failure-repair behavior of a grid resource. In grid computing environment, a resource not only may fail during task execution, but also it can cancel its membership at any time. Hence, the proposed CTMC considers the availability of a grid resource to a grid user in both failure and membership refusal situations. After modeling the availability of the resource, the mean sojourn time of grid tasks in each of the availability states is estimated. Assigning the mean sojourn times of the tasks as performance levels to each of the CTMC’s states, a Markov reward model (MRM) representing the combined performance and availability measures is obtained. Computing the cumulative state probability of the CTMC and multiplying reward rates of the MRM’s states to each of the corresponding state probabilities, the expected accumulated sojourn time of grid tasks in each of the grid resources is achieved. An illustrative example is presented and the results obtained from the proposed model are reported in cases where various scheduling disciplines are considered inside the grid resource to simultaneously service grid and local tasks.

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Abbreviations

FTCS:

Fault tolerant computer system

CTMC:

Continuous time Markov chain

MRM:

Markov reward model

RMS:

Resource management system

GSPN:

Generalized stochastic Petri net

SAN:

Stochastic activity network

\(t\) :

Time

\(i\) :

Index of the system

\(\alpha \) :

Failure rate of the resource

\(\beta \) :

Repair rate of the resource

\(\lambda _\mathrm{l}\) :

Local tasks arrival rate

\(\mu _\mathrm{l}\) :

Resource service rate for local tasks

\(\lambda _\mathrm{g}\) :

Grid tasks arrival rate

\(\mu _\mathrm{g}\) :

Resource service rate for grid tasks

\(\mu \) :

Total service rate of the resource

\(Z(t)\) :

\(\hbox {t}\ge 0\), a random process representing the related CTMC

\(\Omega \) :

State space of CTMC

\(N\) :

Number of states in CTMC

\(Q\) :

Generator matrix

\(P(t)\) :

Transient probability vector

\(p_{0}\) :

Initial probability vector

\(\pi \) :

Steady state probability vector

\(L(t)\) :

Cumulative state probability vector during time period \(\left[ {0,t} \right) \)

\(X(t)\) :

Instantaneous reward rate of the related MRM

\(r\) :

Reward rate vector over \(Z( t)\)

\(\Phi (t)\) :

Accumulative reward over the period \(\left[ {0,t} \right) \)

\({E\left[ {X(t)}\right] }\) :

Expected instantaneous reward rate

\({E\left[ X \right] }\) :

Expected steady state reward

\({E\left[ {\Phi (t)} \right] }\) :

Expected accumulated reward rate

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Acknowledgments

The authors would like to thank Iran Telecommunication Research Center (ITRC) for their support. This research was also supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the CPRC (Communications Policy Research Center) support program supervised by the KCA (Korea Communications Agency)(KCA-1194100004).

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Authors and Affiliations

  1. Department of Computer Engineering, Sharif University of Technology, Tehran, Iran

    Reza Entezari-Maleki, Ali Mohammadkhan & Ali Movaghar

  2. School of Computer Science and Engineering, Seoul National University, Seoul, South Korea

    Heon Young Yeom

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  1. Reza Entezari-Maleki
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  2. Ali Mohammadkhan
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  3. Heon Young Yeom
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  4. Ali Movaghar
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Correspondence to Reza Entezari-Maleki.

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Entezari-Maleki, R., Mohammadkhan, A., Yeom, H.Y. et al. Combined performance and availability analysis of distributed resources in grid computing. J Supercomput 69, 827–844 (2014). https://doi.org/10.1007/s11227-014-1184-z

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