This paper investigates the problem of optimal spot pricing of spectrum by a provider in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users, and investigates the design of efficient single pricing policies.
Abstract:
Recent deregulation initiatives enable cellular providers to sell excess spectrum for secondary usage. In this paper, we investigate the problem of optimal spot pricing of spectrum by a provider in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users. We first show that optimal pricing can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. Next, we investigate the design of efficient single pricing policies. We provide numerical and analytical evidences that static pricing policies do not perform well in such settings (in sharp contrast to settings where all the users are elastic). On the other hand, we prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. We characterize the profit regions of static and threshold pricing, as a function of the arrival rate of primary users. Under certain reasonable assumptions on the demand function, we show that the profit region of threshold pricing can be far larger than that of static pricing. Moreover, we also show that these profit regions critically depend on the support of the demand function rather than specific form of it. We prove that the profit function of threshold pricing is unimodal in price and determine a restricted interval in which the optimal threshold lies. These two properties enable very efficient computation of the optimal threshold policy that is far faster than that of the global optimal policy.
TL;DR: TRUST takes as input any reusability-driven spectrum allocation algorithm, and applies a novel winner determination and pricing mechanism to achieve truthfulness and other economic properties while significantly improving spectrum utilization.
TL;DR: This paper provides a unique, complementary analysis of cellular primary usage by analyzing a dataset collected inside a cellular network operator, which reveals several results that are relevant if dynamic spectrum access (DSA) approaches are to be deployed for cellular frequency bands.
TL;DR: Using a unique dataset collected inside a cellular network operator, the usage in cellular bands is analyzed and the implications of the results on enabling DSA in these bands are discussed.
TL;DR: This work proposes a sub-optimal pricing scheme in terms of revenue maximization of the primary service provider, and it is claimed that this scheme is not only fair in Terms of power allocation among secondary users but that it is also efficient.
TL;DR: A cooperative communication-aware spectrum leasing framework is proposed, in which, primary network leverages secondary users as cooperative relays, and decides the optimal strategy on the relay selection and the price for spectrum leasing.
TL;DR: The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.
TL;DR: This paper considers problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, time-varying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
TL;DR: It is shown that the well-known Guard Channel policy is optimal for the MINOBJ problem, while a new Fractional Guard Channelpolicy is optimalFor the MINBLOCK and MINC problems.
TL;DR: It is shown that the well-known guard channel policy is optimal for the MLNOBJ problem, while a new fractional guard channels policy is ideal for the MINBLOCK and MINC problems.
Q1. What contributions have the authors mentioned in the paper "Spot pricing of secondary spectrum usage in wireless cellular networks" ?
In this paper, the authors investigate the problem of optimal spot pricing of spectrum by a provider in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users. The authors first show that optimal pricing can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. Next, the authors investigate the design of efficient single pricing policies. The authors provide numerical and analytical evidences that static pricing policies do not perform well in such settings ( in sharp contrast to settings where all the users are elastic ). On the other hand, the authors prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. Under certain reasonable assumptions on the demand function, the authors show that the profit region of threshold pricing can be far larger than that of static pricing. Moreover, the authors also show that these profit regions critically depend on the support of the demand function rather than specific form of it. The authors prove that the profit function of threshold pricing is unimodal in price and determine a restricted interval in which the optimal threshold lies.
Q2. What is the problem the authors consider of this paper?
The problem the authors consider of this paper is related to two well studied areas in communication networks, namely, pricing and call admission control.
Q3. What is the main contribution of the paper?
Their main contribution with respect to this previous body of work is to go beyond numerical optimizations and attempt to prove general structural properties, applicable to very general demand functions.
Q4. What is the condition for R′T ( s) 0?
(16)Since R′T (λ ∗ s) = 0, the authors obtain from Eq. (15):Q′(λ∗s) Q(λ∗s) + XλpK = B′SU (λ ∗ s, T ) 1 − BSU (λ∗s, T ) (17)From Eq. (16) and Assumption 5.3, a sufficient condition for R′′T (λ ∗ s) < 0 isQ′(λ∗s) Q(λ∗s) + XλpK ≥ −B ′′ SU (λ ∗ s, T ) 2B′SU (λ∗s, T ) , (18)which holds true by Lemma 5.4 and Eq. (17).
Q5. What is the optimal threshold for a PU?
The authors consider PUs and SUs as two different contract user classes for which prices are set to K and u and arrival rates are λp and λs, respectively.
Q6. What is the objective of a single-price policy?
A simple single-price policy is the so-called static pricing where SU calls are always applied the same admission price, unless all the channels are busy.
Q7. What is the optimal threshold for a given price?
By using Lemma 6.2 the authors can claimT ∗(λs, u) ≤ T ∗(λs, u + α) ≤ T ∗(λs − β, u + α) (33) Eq. (33) means if the authors increase u, the corresponding optimal threshold will not decrease.
Q8. What is the optimal price in the infinite capacity case?
Lemma 4.1: In the infinite capacity case (i.e., C → ∞), the optimal price in each state isu∞ = arg max u∈U (λs(u)u),and the corresponding profit isR∞ = λs(u∞)u∞.
Q9. What is the probability of a PU being blocked?
the probability of finding the system in state n, denoted by πn(Λ), can be explicitly written as follows:πn(Λ) = λ0λ1λ2...λn−1 n!1 + λ01! + λ0λ1 2! + . . . + λ0λ1λ2...λC−1 C!. (1)Due to the PASTA (Poisson Arrivals See Time Averages) property, the probability that a PU is blocked is πC(Λ).