Entry and Spectrum Sharing Scheme Selection in Femtocell Communications Markets

Abstract

Focusing on a femtocell communications market, we study the entrant network service provider's (NSP's) longterm decision: whether to enter the market and which spectrum sharing technology to select to maximize its profit. This long-term decision is closely related to the entrant's pricing strategy and the users' aggregate demand, which we model as medium-term and short-term decisions, respectively. We consider two markets, one with no incumbent and the other with one incumbent. For both markets, we show the existence and uniqueness of an equilibrium point in the user subscription dynamics, and provide a sufficient condition for the convergence of the dynamics. For the market with no incumbent, we derive upper and lower bounds on the optimal price and market share that maximize the entrant's revenue, based on which the entrant selects an available technology to maximize its long-term profit. For the market with one incumbent, we model competition between the two NSPs as a non-cooperative game, in which the incumbent and the entrant choose their market shares independently, and provide a sufficient condition that guarantees the existence of at least one pure Nash equilibrium. Finally, we formalize the problem of entry and spectrum sharing scheme selection for the entrant and provide numerical results to complement our analysis.

Service provisioning with multiple service providers in 5G ultra-dense small cell networks

“…We denote d y as the fraction of users selected service y and d := (d 1 , d 2 , ..., d Y ) as the user distributions or load profile. Without loss of generality, we assume that Q y (d y ) is continuous, differentiable and monotonous non-increasing non-negative function of d y , which is a common assumption in [5] [8].…”

“…In order to encourage SCs to accommodate macrocell users, a refund mechanism was proposed in [7]. Authors of [8] focused on the SC market and studied entrant NSPŠs long-term decision about whether to enter the market and which spectrum sharing technology to select to maximize considered profit. To study the resource allocation scheme in a SCs underlaid macrocell, the work of [9] concentrated on a Stackelberg game that is formulated to study the joint utility maximization of the macrocell and the SCs subject to an interference power constraint.…”

Optimal Pricing Strategy for Operators in Cognitive Femtocell Networks

“…Therefore, the NE price can be found by calculating the intersection point of those two network operators' best response functions, i.e., (9), (12) and (15), (16). Due to page limit, we omit the derivation details here.…”

“…Note that when there is no intersection, the boundary point is taken as NE, as shown in Case 3) of Theorem 1, since the boundary point p m = w already maximizes the utility of the macrocell operator. Moreover, since all the best response functions are linear as shown in (9), (12) and (15), (16), the intersection of two linear functions can only be unique, which guarantees the uniqueness of the NE price.…”

“…In the literatures, the pricing related issues were discussed in [13] and [14], where Yun et al designed two pricing schemes (flat and partial volume pricing) under the case of monopoly market in [14] and Kang et al analyzed two pricing models (uniform and non-uniform pricing) under two scenarios (sparsely and densely deployed scenarios) in [15]. From the perspective of operators, Ren et al discussed whether the operator should enter the femtocell market in [16], while Duan et al studied whether the operator should provide users with only the macrocell service, only the femtocell service, or both services in [17].…”