Optimization in Internet Networks Using Data Envelopment Analysis Model with Undesirable Outputs

Document Type : Research Paper


1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Science and Research Branch, IAU, Hesarak, poonak

3 Department of mathematics, Science and Research Branch, Islamic Azad University, , Tehran, Iran


The purpose of this paper is to use the decision making techniques of Data Envelopment Analysis (DEA) in order to evaluate the existing Internet networks to select the most desirable networks.To achieve this goal, we first begin by simulating a specific Internet network called Differentiated Service (DS) network that provides the quality of service to the user through the mechanism of Call Admission Control (CAC). We then evaluate and rank the networks by proposing a novel DEA model in the literature of undesirable outputs. Finally, by using the results of DEA model, we select the optimal Internet network.


  1. E. Alipour Chavari and M. Rostamy-Malkhalifeh, Internet network design for qual[1]ity of service guarantee using Data Envelopment Analysis (DEA), international data envelopment analysis, 7, 1–14 (2019).
  2. R. J. Banker, A. Charnes and W. W. Cooper, Some models for estimating technicaland scale inefficiencies in data envelopment analysis, Management Science, 30, 1078–1092 (1984).
  3. A. Barzegarinegad, G. Jahanshahloo and M. Rostamy-Malkhalifeh, A full ranking forde[1]cision making units using ideal and anti-ideal points in DEA, The Scientific World Journal, (2014).
  4. V. Belton and SP. Vickers, Demystifying DEA-A visual interactive Approach based on multiple criteria analysis, J. Opl. Res. Soc., 44, 883–896 (1993).
  5. A. Charnes, W. W. Cooper and E. Rhodes, Measuring efficiency of n decision making unit, Eur. J. Opl. Res., 2, 429–444 (1978).
  6. Y-W. Chen, M. Larbani and Y-P. Chang, Multiobjective data envelopment analysis, J. Opl. Res. Soc., 60, 1556–1566 (2009).
  7. W. Cooper, L. Seiford and T. Kaoru, Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software. Springer, (2000).
  8. J. Doyle and R. Green, Efficiency and cross efficiency in DEA: Derivations, meanings and uses, J. Opl. Res. Soc., 45, 567–578 (1994).
  9. M. Ehrgott, Multicriteria Optimization, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 491, (2000).
  10. R. Fare, S. Grosskopf, C. A. K. Lovell and S. Yaiswarng, Deviation of shadow prices for undesirable outputs: a distance function approach, The Review of Economics and Statistics, 75, 374–380 (1993).
  11. R. Fare, S. Grosskopf, C. A. K. Lovell, Multilateral productivity comparisons when some outputs are undesirable :a nonparametric approach, The Review of Economics and Statistics, 71, 90–98 (1989).
  12. B. Golany and G. Yu, A goal programming-discriminantfunction approach to the estimation of an empirical productionfunction based on DEA results, J. Prod. Anal., 6, 171–186 (1995).
  13. A. Hailu and T. Veeman, Non-parametric productivity analysis with undesirable outputs: an application to Canadian pulp and paper industry, American Journal of Agri[1]cultural Economics, 83, 605–616 (2001).
  14. S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang and W. Weiss, Rfc2475: An archi[1]tecture for differentiated service, RFC Editor, (1998).
  15. G. Jahanshahloo, F. H. Lotfi, M. Rostamy-Malkhalifeh, R. Maddahi and A. Ebrahim[1]nejad, Ranking non-extreme efficient units based on super efficiency method in the presence of undesirable outputs: a DEA approach, International Journal of Applied Decision Sciences, 6, 83–95 (2013).
  16. C. Kao and CT. Hung, Data envelopment analysis with common weight: The compro[1]mise solution approach, J. Opl. Res. Soc., 56, 1196–1203 (2005).
  17. M. Karimi and B. Karimi, Linear and conic scalarizations for obtaining properly efficient solutions in multiobjective optimization, Mathematical Sciences, 11, 319–325 (2017).
  18. E. E. Karsak and N. Goker, Improved common weight DEA-based decision approach for economic and financial performance assessment, Technological and Economic Development of Economy, 26, 430–448 (2020).
  19. X-B Li and GR. Reevese, A multiple criteria approach to data envelopment analysis, Eur. J. Opl. Res., 115, 507–517 (1999).
  20. F. L. Lugayizi, B. M. Esiefarienrhe and A. Warren, Comparative evaluation of QoS routing in VANET, International Conference on Advances in Computing and Communication Engineering (ICACCE), Durban, 183–188 (2016).
  21. M. Moeini, B. Karimi and E. Khorram, A Cross-Efficiency Approach for Evaluating Decision Making Units in Presence of Undesirable Outputs, Modelling, Computation and Optimization in Information Systems and Management Sciences, Springer, 487–498 (2015).
  22. J. Rexford, Route Optimization in IP Networks. In: Resende M.G.C., Pardalos P.M. (eds) Handbook of Optimization in Telecommunications, Springer, Boston, (2006).
  23. Y. Roll and B. Golany, Alternative methods of treating factor weights in DEA, Omega, 21, 99–103 (1993).
  24. S. Sadri, M. Rostamy-Malkhalifeh and N. Shoja, A New Method for Optimization of Inefficient Cost units in the Presence of Undesirable Outputs, International Journal Industrial Mathematics, 10, 331–338 (2018).
  25. L.M. Seiford and J. Zhu, Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, 142, 16–20 (2002).
  26. N. N. Srinidhi, S. M. Dilip Kumar and K. R. Venugopal, Network optimizations in the 2333 Internet of Things: A review. Engineering Science and Technology, 22, 1–21 (2019).
  27. T. Sueyoshi and M. Goto, Returns to scale vs. damages to scale in data envelopment analysis: An impact of U.S. clean air act on coal-fired power plants, Omega, 41, 164–175 (2013).
  28. K. Tone, Dealing with undesirable outputs in DEA: a slacks-based measure (SBM) approach, Presentation at NAPW III, Toronto, (2004).
  29. Wu, Chong, Y. Li, Q. Liu and K. Wang, A stochastic DEA model considering undesirable outputs with weak disposability, Mathematical and Computer Modelling, 58, 980–989 (2013).
  30. A.P. Yekta, S. Kordrostami, A. Amirteimoori and R. K. Matin, Data envelopment analysis with common weights: The weight restriction approach, Math. Sci., 12, 197–203 (2018).
  31. S. O. Yese, A. Abdulhakeem and M. Aminu, Performance Evaluation of Dynamic QoS[1]Aware CAC (DQA-CAC) Algorithm for Broadband Networks, European Journal of Electrical Engineering and Computer Science, 3, (2019).
  32. H. Zare-Haghighi, M. Rostamy-Malkhalifeh, G. R. Jahanshahloo, Measurement of con[1]gestion in the simultaneous presence of desirable and undesirable outputs, Journal of Applied Mathematics, 2014, (2014).
  33. M. Zohrehbandian A. Makui and A. Alinezhad, A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung’s approach, J. Opl. Res. Soc., 61, 604–610 (2010).