Hostname: page-component-788cddb947-kc5xb Total loading time: 0 Render date: 2024-10-09T13:20:35.416Z Has data issue: false hasContentIssue false

NASH EQUILIBRIUM STRATEGIES REVISITED IN SOFTWARE RELEASE GAMES

Published online by Cambridge University Press:  23 June 2020

Yasuhiro Saito
Affiliation:
Department of Maritime Safety Technology, Japan Coast Guard Academy, 5-1 Wakabacho, Kure Hiroshima737-0832, Japan E-mail: yasu-saito@jcga.ac.jp
Tadashi Dohi
Affiliation:
Department of Information Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashihiroshima739-8527, Japan E-mail: dohi@hiroshima-u.ac.jp

Abstract

A software release game was formulated by Zeephongsekul and Chiera [Zeephongsekul, P. & Chiera, C. (1995). Optimal software release policy based on a two-person game of timing. Journal of Applied Probability 32: 470–481] and was reconsidered by Dohi et al. [Dohi, T., Teraoka, Y., & Osaki, S. (2000). Software release games. Journal of Optimization Theory and Applications 105(2): 325–346] in a framework of two-person nonzero-sum games. In this paper, we further point out the faults in the above literature and revisit the Nash equilibrium strategies in the software release games from the viewpoints of both silent and noisy type of games. It is shown that the Nash equilibrium strategies in the silent and noisy of software release games exist under some parametric conditions.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baston, V.J. & Garnaev, A.Y. (1995). Teraoka-type two-person nonzero-sum silent duel. Journal of Optimization Theory and Applications 87: 539552.CrossRefGoogle Scholar
Boland, P.J. & Chuivi, N.N. (2007). Optimal times for software release when repair is imperfect. Statistics & Probability Letters 77(12): 11761184.CrossRefGoogle Scholar
Chiu, K.C., Ho, J.W., & Huang, Y.S. (2009). Bayesian updating of optimal release time for software systems. Software Quality Journal 17: 90120.CrossRefGoogle Scholar
Dalal, S.R. & Mallows, C.L. (1988). When should one stop testing software? Journal of the American Statistical Association 83: 872879.CrossRefGoogle Scholar
Dalal, S.R. & Mallows, C.L. (1994). Some graphical aids for deciding when to stop testing software. IEEE Journal on Selected Areas in Communications 8(2): 169175.CrossRefGoogle Scholar
Dalal, S.R. & McIntosh, A.A. (1994). When to stop testing for large software systems with changing code. IEEE Transactions on Software Engineering 20(4): 318323.10.1109/32.277579CrossRefGoogle Scholar
Dohi, T., Nishio, Y., & Osaki, S. (1999). Optimal software release scheduling based on artificial neural networks. Annals of Software Engineering 8: 167185.CrossRefGoogle Scholar
Dohi, T., Teraoka, Y., & Osaki, S. (2000). Software release games. Journal of Optimization Theory and Applications 105(2): 325346.CrossRefGoogle Scholar
Dohi, T., Yatsunami, Y., Nishio, Y., & Osaki, S. (2000). The effective smoothing techniques to estimate the optimal software release schedule based on artificial neural network. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 105(2): 325346.Google Scholar
Forman, E.H. & Singpurwalla, N.D. (1977). An empirical stopping rule for debugging and testing computer software. Journal of the American Statistical Association 72: 750757.Google Scholar
Forman, E.H. & Singpurwalla, N.D. (1979). Optimal time intervals for testing hypotheses on computer software errors. IEEE Transactions on Reliability R-28: 250253.CrossRefGoogle Scholar
Ho, J.W., Fang, C.C., & Huang, Y.S. (2008). The determination of optimal software release times at different confidence levels with consideration of learning effects. Software Testing, Verification and Reliability 18(4): 221249.CrossRefGoogle Scholar
Hou, R.H., Kuo, S.-Y., & Chang, Y.-P. (1997). Optimal release times for software systems with scheduled delivery time based on the HGDM. IEEE Transactions on Computers 46(2): 216221.CrossRefGoogle Scholar
Karlin, S (1959). Mathematical methods and theory in games, programming, and economics, vol. 2. Reading: Addison-Wesley.Google Scholar
Koch, H.S. & Kubat, P. (1983). Optimal release time for computer software. IEEE Transactions on Software Engineering SE-9(3): 323327.CrossRefGoogle Scholar
Li, X., Li, Y.F., Xie, M., & Ng, S.H. (2011). Reliability analysis and optimal version-updating for open source software. Information and Software Technology 53: 929936.CrossRefGoogle Scholar
Liu, C.-T. & Chang, Y.-C. (2007). Optimal planning for open source software updates. Probability in the Engineering and Informational Sciences 21: 301314.Google Scholar
Luo, C., Okamura, H., & Dohi, T. (2016). Reliability analysis and optimal version-updating for open source software. Journal of Risk and Reliability 230(1): 4453.Google Scholar
Momotaz, B. & Dohi, T. (2018). Optimal stopping time of software system test via artificial neural network with fault count data. Journal of Quality in Maintenance Engineering 24(1): 2236.Google Scholar
Momotaz, B. & Dohi, T. (2018). Optimal release time estimation of software system using Box-Cox transformation and neural network. International Journal of Mathematical, Engineering and Management Sciences 3(2): 177194.Google Scholar
Okumoto, K. & Goel, A.L. (1980). Optimal release time for software systems based on reliability and cost criteria. Journal of Systems and Software 1: 315318.CrossRefGoogle Scholar
Ozekici, S., Altinel, I.K., & Angun, E. (2001). A general software testing model involving operational profiles. Probability in the Engineering and Informational Sciences 15(4): 519533.CrossRefGoogle Scholar
Pham, H. & Zhang, X.M. (1999). A software cost model with warranty and risk costs. IEEE Transactions on Computers 48(1): 7175.CrossRefGoogle Scholar
Ross, S.M. (1985). Software reliability: the stopping rule problem. IEEE Transactions on Software Engineering SE-11: 14721476.CrossRefGoogle Scholar
Saito, Y. & Dohi, T. (2015). Stochastic marksmanship contest games with random termination – survey and application. Journal of the Operations Research Society of Japan 58(3): 223246.CrossRefGoogle Scholar
Sgarbossa, F. & Pham, H. (2010). A cost analysis of systems subject to random field environments and reliability. IEEE Transactions on Systems, Man and Cybernetics, Part C 40(4): 429437.CrossRefGoogle Scholar
Singh, V.B., Sharma, M., & Pham, H. (2018). Entropy based software reliability analysis of multi-version open source software. IEEE Transactions on Software Engineering 44(12): 12071223.CrossRefGoogle Scholar
Singpurwalla, N.D. (1991). Determining an optimal time interval for testing and debugging software. IEEE Transactions on Software Engineering 17(4): 313319.CrossRefGoogle Scholar
Teraoka, Y. (1986). Silent-noisy marksmanship contest with random termination. Journal of Optimization Theory and Applications 49: 477487.CrossRefGoogle Scholar
Wee, N.-S. (1990). Optimal maintenance schedules of computer software. Probability in the Engineering and Informational Sciences 4(2): 243255.CrossRefGoogle Scholar
Xie, M. & Yang, B. (2003). A study of the effect of imperfect debugging on software development cost. IEEE Transactions on Software Engineering 29(5): 471473.Google Scholar
Yamada, S. & Osaki, S. (1985). Cost-reliability optimal release policies for software systems. IEEE Transactions on Reliability R-34(5): 422424.10.1109/TR.1985.5222222CrossRefGoogle Scholar
Yang, B., Hu, H., & Jia, L. (2008). A study on uncertainty in software cost and its impact on optimal software release time. IEEE Transactions on Software Engineering 34(6): 813835.CrossRefGoogle Scholar
Yang, J., Liu, Y., Xie, M., & Zhao, M. (2016). Modeling and analysis of reliability of multi-release open source software incorporating both fault detection and correction processes. Journal of Systems and Software 115: 102110.10.1016/j.jss.2016.01.025CrossRefGoogle Scholar
Zeephongsekul, P. & Chiera, C. (1995). Optimal software release policy based on a two-person game of timing. Journal of Applied Probability 32: 470481.CrossRefGoogle Scholar
Zheng, S. (2002). Dynamic release policies for software systems with a reliability constraint. IIE Transactions 34: 253262.CrossRefGoogle Scholar
Zhu, M. & Pham, H. (2018). A multi-release software reliability modeling for open source software incorporating dependent fault detection process. Annals of Operations Research 269: 773790.CrossRefGoogle Scholar