Adoption of dynamic spectrum access technologies: a system dynamics approach

Abstract

The introduction of dynamic spectrum access (DSA) technologies in mobile markets faces technical, economic and regulatory challenges. This paper defines industry openness and spectrum centralization as the two key factors that affect the adoption of DSA technologies. The adoption process is analyzed employing a comprehensive System Dynamics model that considers the network and substitution effects. Two possible scenarios, namely operator-centric and user-centric adoption of DSA technologies are explored in the model. The analysis indicates that operator-centric DSA technologies may be adopted in most countries where spectrum is centralized, while end-user centric DSA technologies may be adopted in countries with decentralized spectrum regime and in niche emerging services. The study highlights the role of standards-based design and concludes by citing case studies that show the practicality of this analysis and associated policy prescriptions.

Appendices

Appendices

1.1 Appendix 1: Formulation of network and substitution effects

Under high network effect, path dependence implies that technologies rapidly lock-in to a stable equilibrium after reaching a critical mass. The attractiveness of each product is determined by several elements, one being the effect of compatibility on attractiveness of the technology due to the network effect [79], which can be described by an exponential function¹²:

$$\begin{aligned} \hbox {Eca}\left( \hbox {t} \right) =e^{{{\mathrm{se}}*\mathrm{b} }\,\left( {{\mathrm{t}}-1} \right) /{ \mathrm{th}}}, \end{aligned}$$

where Eca(t)= effect of compatibility on attractiveness at t, se = sensitivity of attractiveness; b(t-1) = installed base of devices at $t-1$, and th = threshold for compatibility effect.

Then, the technology attractiveness is also affected by the investment incentives which are determined by the market structure:

$$\begin{aligned} \hbox {Aud }\left( \hbox {t} \right) =\hbox {Eca }\left( {\hbox {t}-1} \right) \,*\,\hbox {Ii}\left( {\hbox {t}-1} \right) , \end{aligned}$$

where Aud(t) = Attractiveness of devices at t, Eca(t-1) = Effect of compatibility on attractiveness of devices at $t-1$, and Ii(t-1) = incentives to invest at $t-1$.

During the simulation time, the model accumulates the number of adopted devices, which is calculated by the following integral:

$$\begin{aligned} \hbox {Ib}\left( \hbox {t} \right) =Ibo+\int sa\left( t \right) dt, \end{aligned}$$

where Ib(t) = Installed base of devices at t, sa(t) = sales of devices at t; Ibo: initial installed base of devices.

The first formula indicates that the number of devices should reach a threshold value to positively impact the attractiveness of the technology. In addition to this, other compatibility elements may also impact attractiveness. Market share is determined by the attractiveness of the technology divided by the total attractiveness of all competing technologies. This relies on the assumption that these two competing technologies are not complement.

Under substitution effect, a new technology substitutes an older one. The substitution effect can be described through a predator-prey competition model by means of the Lotka-Volterra equations which are shown as follows [48]:

$$\begin{aligned} \frac{dM}{dt}= & {} a_M M-b_M M^{2}\pm c_{ME} EM,\\&a_M >0, b_M >0, c_{ME} >0\\ \frac{dE}{dt}= & {} a_E E-b_E E^{2}\pm c_{EM} ME,\\&a_E >0, b_E >0, c_{EM} >0, \end{aligned}$$

where a is the growth or positive feedback from the adoption, b is the inhibition or saturation coefficient, which describes the loss of potential market due to the growth of a technology, and therefore can be expressed as growth rate/capacity. Finally c is the competition coefficient between two technologies (E and M in this case). If $c_{EM}$ is positive, the technology E influences positively the technology M. If $c_{EM}$ is negative, the technology E influences negatively the technology M. If $c_{EM}$ is zero, the influence is neutral. In a predator-prey scenario, the c coefficient of the prey is positive, while the c coefficient of the predator is negative.

These models are adopted in Figs. 3 and 4 by utilizing causal loop diagrams.

1.2 Appendix 2: Parameter description of system dynamics models

Network effect model
Variable	Value
Spectrum centralization	from 0 to 1
Industry openness	from 0 to 1
Incentives to invest	from 0 to 1
Threshold for spectrum sharing	25 %$^{\mathrm{a}}$
Initial amount of spectrum available for user access	5 %
Initial base of user-centric devices	100
Initial base of operator-centric devices	100

Substitution model
Variable	Value
Spectrum centralization	from 0 to 1
Industry openness	from 0 to 1
Incentives to invest	from 0 to 1
Threshold for user-centric spectrum access	25 %
Initial amount of spectrum available for user access	5 %
Initial base of operator-centric devices	90 %
Initial base of user-centric devices	10 %
Competition effect user-centric devices	$-$0.02
Competition effect operator-centric devices	0.02

1. $^{\mathrm{a}}$ Amongst the OECD countries [96], the average market share of the top four MNOs is 43, 31, 19 and 6 % respectively, yielding an average market share of about 25 %. Using this data, we have considered the minimum threshold for entry of an MNO to be approximately 5 % (the fourth market share). The average of the top four MNOs (25 %) is considered as indicative of the average critical size for sustainable equilibrium, utilized as a threshold value of available spectrum for user-centric adoption

1.3 Appendix 3: Country data

List of selected countries with variables describing spectrum centralization and industry openness¹³:

Countries	Finland	India	Japan	United States
Market concentration (HHI)	0.332	0.186	0.348	0.247
Spectrum concentration (HHI)	0.327	0.131	0.347	0.287
Reselling rights	Yes	No	No	Yes
Mobile monthly ARPU	32	3	84	47
Churn rate (% monthly)	1,60	5,80	0,60	1,80
Cellular investment per capita per year (USD)	34,33	6,05	134,49	77,91
Price (USD per minute)	0,14	0,04	0,63	0,39
Fraction of prepaid subscriptions (%)	10	95	1	22
Separation of network and service operators	Yes	No	No	No
Number of MNOs (per service area or nationwide)	3	10	3	6