Portfolio optimization in secondary spectrum markets

Abstract

In this paper, we address the spectrum portfolio optimization (SPO) question in the context of secondary spectrum markets, where bandwidth (spectrum access rights) can be bought in the form of primary and secondary contracts. While a primary contract on a channel provides guaranteed access to the channel bandwidth (possibly at a higher per-unit price), the bandwidth available to use from a secondary contract (possibly at a discounted price) is typically uncertain/stochastic. The key problem for the buyer (service provider) in this market is to determine the amount of primary and secondary contract units needed to satisfy its uncertain user demand.We formulate single and multi-region spectrum portfolio optimization problems as one of minimizing the cost of the spectrum portfolio subject to constraints on bandwidth shortage. Two different forms of bandwidth shortage constraints are considered, namely, the demand satisfaction rate constraint, and the demand satisfaction probability constraint. While the SPO problem under demand satisfaction rate constraint is shown to be convex for all density functions, the SPO problem under demand satisfaction probability constraint is not convex in general. We derive some sufficient conditions for convexity in this case. We also discuss application of the Bernstein approximation technique to approximate a non-convex demand satisfaction probability constraint by a convex constraint. The SPO problems can therefore be solved efficiently using standard convex optimization techniques. We then consider a discrete version of the SPO problem, in which the primary and secondary contracts can bought/sold in discrete units. We study the submodularity property of the discrete SPO problem and discuss a branch-and-bound algorithm algorithm to solve it efficiently. Finally, we perform a thorough simulation-based study of the single-region and the multiple-region problems for different choices of the problem parameters, and provide key insights regarding the portfolio composition. We provide several insights about the scaling behavior of the unit prices of the secondary contracts, as the stochastic characterization of the bandwidth available from secondary contracts change.

Wireless Network Pricing

“…In [75], Duan et al proposed a time-power screening contract for cooperative spectrum sharing between primary users and secondary users, where the secondary users relay traffic for PUs in exchange for the guaranteed access time on the primary users' licensed spectrums. In [76,77], Kasbekar and Sarkar et al considered the secondary spectrum trading with two types of contracts: the guaranteed-bandwidth contract, which provides guaranteed access to a certain amount of bandwidth for a specified duration of time, and the opportunistic-access contract, which offers restricted (uncertain) access rights on a certain amount of bandwidth at the current time slot. In [78], Gao et al studies the secondary spectrum trading in a hybrid market with both contract users and spot purchasing users.…”

An Iterated Game of Uncoordinated Sharing of Licensed Spectrum Using Zero-Determinant Strategies

“…See for example [1], [21], [22] for studies that involve economic models and pricing techniques for secondary spectrum utilization. Here, we consider a pricing scheme where the license holder charges the service providers on usage basis per unit data transmitted on the downlinks.…”

Combining Spot and Futures Markets: A Hybrid Market Approach to Dynamic Spectrum Access

“…2.1.2. Secondary Spectrum Trading in Hybrid Spectrum Markets Kasbekar et al (2010) and Muthusamy et al (2011) considered the secondary spectrum trading in a hybrid market.…”