Skip to main content
Log in

The optimal macro control strategies of service providers and micro service selection of users: quantification model based on synergetics

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

Multiple wireless technologies, possibly administered by same or different service providers (SPs), are expected to coexist in the rapidly-expanding heterogeneous networks. It is also economically beneficial for all SPs to cooperate with each other. In such model, one SP temporally shares a portion of its spectrum with other SPs at a certain price to allow better utilization of the available spectrum . To this end, users can make service selection decisions dynamically at micro level according to the performance satisfaction level and cost, depending on the pricing plans and spectrum sharing strategies of SPs at macro level. On the other hand, the users’ service selection population states in turn influence the control strategies of SPs. To model this dynamic interactive decision making problem, a novel approach based on synergetics is presented in this paper. The motion equations of population state decided by pricing and spectrum sharing are derived . Then, by taking into account the population state, an optimization problem is formulated to determine the optimal dynamic pricing and open access ratio for the SPs in order to maximize their respective benefits. A closed-loop feedback equilibrium is obtained as the solution of the formed optimization problem. Numerical results demonstrate the effectiveness and advantages of the proposed model in terms of dynamic control of the spectrum sharing and pricing as well as dynamic analysis of service selection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. FCC. (2003). Promoting efficient use of spectrum through elimination of barriers to the development of secondary markets, Technical Report FCC:03-113.

  2. Ofcom. (2011). Simplifying spectrum trading, spectrum leasing and other market enhancements, Final Statement Report, June 2011.

  3. New Zealand Government. (2016). Radio spectrum management. Available: http://www.rsm.govt.nz/cms.

  4. Australia Government. (2014). ACMA. Available: http://www.acma.gov.au/web/homepage/pc=home.

  5. Wang, L., & Kuo, G. S. (2013). Mathematical modeling for network selection in heterogeneous wireless networks—a tutoria. IEEE Communications Surveys & Tutorials, 15(1), 271–292. First quarter.

    Article  Google Scholar 

  6. Bari, F., & Leung, V. C. M. (2007). Multi-attribute network selection by iterative TOPSIS for heterogeneous wireless access. In Proceedings of IEEE Consumer Communications and Networking Conference (CCNC), (pp. 808–812).

  7. Song, Q., & Jamalipour, A. (2005). Network selection in an integrated wireless LAN and UMTS environment using mathematical modeling and computing techniques. IEEE Wireless Communication, 12(3), 42–48.

    Article  Google Scholar 

  8. Kassar, M., Kervella, B., & Pujolle, G. (2008). An overview of vertical handover decision strategies in heterogeneous wireless networks. Computer Communications, 31(10), 2607–2620.

    Article  Google Scholar 

  9. Trestian, R., Ormond, O., & Muntean, G. M. (2012). Game theory-based network selection: Solutions and challenges. IEEE Communications Surveys Tutorials, 14(4), 1212–1231. Fourth quarter.

    Article  Google Scholar 

  10. Stevens-Navarro, E., Lin, Y., & Wong, V. W. S. (2008). An MDP-based vertical handoff decision algorithm for heterogeneous wireless networks. IEEE Transactions on Vehicular Technology, 57(2), 1243–1254.

    Article  Google Scholar 

  11. Song, Q., & Jamalipour, A. (2008). A quality of service negotiation-based vertical handoff decision scheme in heterogeneous wireless systems. European Journal of Operational Research, 191(3), 1059–1074.

    Article  MathSciNet  MATH  Google Scholar 

  12. Chang, H. B., & Chen, K. C. (2011). Cooperative spectrum sharing economy for heterogeneous wireless networks. In IEEE GLOBECOM Workshops (pp. 458–463). Dec 2011.

  13. Bennis, M., Lasaulce, S., & Debbah, M. (2009). Inter-operator spectrum sharing from a game theoretical perspective. EURASIP Journal of Signal Processing, 2009, 295739. doi:10.1155/2009/295739.

  14. Singh, C., Sarkar, S., Aram, A., & Kumar, A. (2012). Cooperative profit sharing in coalition-based resource allocation in wireless networks. IEEE/ACM Transactions on Networking, 20(1), 69–83.

    Article  Google Scholar 

  15. Zhu, K., Hossain, E., & Niyato, D. (2014). Pricing, spectrum sharing, and service selection in two-tier small cell networks: A hierarchical dynamic game approach. IEEE Transaction on Mobile Computing, 13(8), 1843–1856.

    Article  Google Scholar 

  16. Zhu, X., Dianati, M., & Zhu, H. (2014). Analysis of cooperative and competitive spectrum sharing for heterogeneous networks based on differential dynamics model. International Journal of Communication Systems, 27, 4564–4574.

    Article  Google Scholar 

  17. Guerrero-Iban, A., Flores-Corte, C., Barba, A., & Reyes, A. (2010). A quality of service-enabled pricing approach for heterogeneous wireless access networks. In 2010 Sixth International Conference on Intelligent Environments (IE), (pp. 231–236).

  18. Niyato, D., & Hossain, E. (2008). Market-equilibrium, competitive, and cooperative pricing for spectrum sharing in cognitive radio networks: Analysis and comparison. IEEE Transactions on Wireless Communications, 7(11), 4273–4283.

    Article  Google Scholar 

  19. Yang, L., Kim, H., et al. (2013). Pricing-based decentralized spectrum access control in cognitive radio networks. IEEE/ACM Transaction on Networking, 21(2), 522–535.

    Article  Google Scholar 

  20. Krishnaswamy, D. (2010). Network economics considerations for incremental data services in heterogeneous wireless wide area networks. In VehicularTechnology Conference Fall (VTC 2010-Fall), (pp. 1–5).

  21. Chun, S. H., & La, R. J. (2014). Secondary spectrum trading: auction-based framework for spectrum allocation and profit sharing. IEEE/ACM Transactions on Networking, 21(1), 176–189.

    Article  Google Scholar 

  22. Shy, O. (2011). A short survey of network economics. Review of Industrial Organization, 38, 119–149.

    Article  Google Scholar 

  23. Chen, Y., Zhang, J., & Zhang, Q. (2012). Utility-aware refunding framework for hybrid access femtocell network. IEEE Transactions on Wireless Communications, 11(5), 1688–1697.

    Article  Google Scholar 

  24. Haken, H. (2006). Information and self-organization, a macroscopic approach to complex systems. New York: Springer.

    MATH  Google Scholar 

  25. Haken, H. (1983). Synergetics, an introduction: Nonequilibrium phase transitions and self-organization in physics, chemistry, and biology (3rd ed.). New York: Springer.

    Book  MATH  Google Scholar 

  26. Haken, H. (1993). Advanced synergetics: Instability hierarchies of self-organizing systems and devices. New York: Springer.

    MATH  Google Scholar 

  27. Badia, L., Lindstrom, M., Zander & J., Zorzi, M. (2003). Demand and pricing effects on the radio resource allocation of multimedia communication systems. In IEEE GLOBECOM, (vol. 7, pp. 4116–4121).

Download references

Acknowledgements

This work was supported by Natural Science Foundation of China (61372125), 973 project (2013CB329104), and the open research fund of National Mobile Communications Research Laboratory, Southeast University (2013D01).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaorong Zhu.

Appendix A

Appendix A

Proof

Here, we introduce the drift factor K(x) and fluctuation factor Q(x) as follows

$$\begin{aligned} K(x) = (1 - x)\lambda _{12} (Nx) - (1 + x)\lambda _{21} (Nx) \end{aligned}$$
(34)

and

$$\begin{aligned} Q(x) = (1 - x)\lambda _{12} (Nx) + (1 + x)\lambda _{21} (Nx) \end{aligned}$$
(35)

Then, (19) is changed into the standard form of the Fokker-Planck equation [25] as follows

$$\begin{aligned} \frac{{dP(x,t)}}{{dt}} = - \frac{\partial }{{\partial x}}[K(x)P(x,t)] + \frac{1}{2}\varepsilon \frac{{\partial ^2 }}{{\partial x^2 }}[Q(x)P(x,t)] \end{aligned}$$
(36)

The solution of (36) not only yields the evolution of the most probable population configuration but also the width and form of the probabilistic fluctuations around them. There are many kinds of user choice configuration. According to (36), it is reasonable to get the dynamic equations of the mean value \(\bar{x}\) of the variables x as follows

$$\begin{aligned} \frac{{d\bar{x}}}{{dt}} = \left. {\overline{K(x)} - \frac{\varepsilon }{2}[Q(x)P(x,t)]} \right| _{x = - 1}^{x = 1} \end{aligned}$$
(37)

and

$$\begin{aligned} \frac{{d\overline{x^2 } }}{{dt}} = 2\left. {\overline{xK(x)} + \varepsilon \overline{Q(x)} - \varepsilon [xQ(x)P(x,t)]} \right| _{x\,= \,- 1}^{x\,=\,1} \end{aligned}$$
(38)

When \(x =\pm 1\), the value of P(xt) is so small that the second term in the right-hand side of (37) and the third term of the right-hand side of (38) can be ignored. Hence, (37) and (38) can be changed to

$$\begin{aligned} \frac{{d\bar{x}}}{{dt}} = \overline{K(x)} \end{aligned}$$
(39)

and

$$\begin{aligned} \frac{{d\overline{x^2 } }}{{dt}} = 2\overline{xK(x)} + \varepsilon \overline{Q(x)} \end{aligned}$$
(40)

We introduce the bias \(\sigma (t)\) of the variable x(t) as

$$\begin{aligned} \sigma (t)= \overline{(x-\overline{x} )^2 }= \overline{x^2 }-(\overline{x} )^2 \ge 0 \end{aligned}$$
(41)

The first derivative of this parameter can be deduced as

$$\begin{aligned} \frac{{d\sigma (t)}}{{dt}} = 2[\overline{xK(x)} - \overline{x} \overline{K(x)} ] + \varepsilon \overline{Q(x)} \end{aligned}$$
(42)

The exact solutions can be obtained in the special case that K(x) is a linear function of x and Q is a constant. But in the case that P(xt) has one peak, K(x) can be expressed by Taylor series expansion at \(\bar{x}\) as follows:

$$\begin{aligned} K(x) = K(\bar{x})+K^\prime (\bar{x} )(x-{\bar{x}})+\frac{1}{2}K^{\prime \prime }(\bar{x})(x-{\bar{x}})^2+\cdots \end{aligned}$$
(43)

Hence, we have

$$\begin{aligned} \overline{xK(x)}= & {} {\bar{x} }K(\bar{x})+K^\prime (\bar{x})\sigma (t)+\cdots \end{aligned}$$
(44)
$$\begin{aligned} \overline{K(x)}= & {} K(\bar{x} ) +\frac{1}{2}K^{\prime \prime }(\bar{x} )\sigma (t) + \cdots \end{aligned}$$
(45)

If \(\varepsilon =\frac{1}{N}\ll 1\), \(\varepsilon Q(x)\) only needs to keep the first order term, i.e.,

$$\begin{aligned} \varepsilon \overline{Q(x)} = \varepsilon (\bar{x} ) +\cdots \end{aligned}$$
(46)

Then (39) and (42) can be approximately expressed by

$$\begin{aligned} \frac{{d\bar{x}}}{{dt}} = K(\bar{x} ) \end{aligned}$$
(47)

and

$$\begin{aligned} \frac{{d\sigma (t)}}{{dt}} = 2K^\prime (\bar{x} )\sigma (t) + \varepsilon Q(\bar{x} ) \end{aligned}$$
(48)

Since \(\left| {K(\bar{x} )} \right| \gg \frac{1}{2}\left| {K^{\prime \prime }(\bar{x} )\sigma (x)} \right| \), the term \(\frac{1}{2}\left| {K^{\prime \prime }(\bar{x} )\sigma (x)} \right| \) is neglected in (45).

If we further assume its track average \(\bar{x}\) equals to its actual track x(t), (47) can be changed into

$$\begin{aligned} \frac{{dx}}{{dt}} = K(x(t)) \end{aligned}$$
(49)

From (34), (49) can also be expressed by

$$\begin{aligned} \frac{{dx}}{{dt}} = (1 - x)\lambda _{12} (Nx) - (1 + x)\lambda _{21} (Nx) \end{aligned}$$
(50)

Taking (9) into (50), we get

$$\begin{aligned} \frac{{dx}}{{dt}}= & {} \theta (1 - x)\exp \left[ \frac{{B_1 \eta _1 + B_2 \eta _2 r}}{{N(1 + x)m_1 }} - \frac{{B_2 (1 - r)\eta _2 }}{{N(1 - x)m_2 }}\right] \nonumber \\&- \theta (1 + x)\exp \left[ \frac{{B_2 (1 - r)\eta _2 }}{{N(1 - x)m_2 }} - \frac{{B_1 \eta _1 + B_2 \eta _2 r}}{{N(1 + x)m_1 }}\right] \end{aligned}$$
(51)

Thus, we prove the correctness of (20). \(\square \)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, X., Gong, X. & Tsang, D.H.K. The optimal macro control strategies of service providers and micro service selection of users: quantification model based on synergetics. Wireless Netw 24, 1991–2004 (2018). https://doi.org/10.1007/s11276-016-1436-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-016-1436-3

Keywords

Navigation