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Wireless Networks

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16-03-2020

Beyond the VCG mechanism: truthful reverse auctions for relay selection with high data rates, high base station utility and low interference in D2D networks

Authors: M. V. S. Aditya, Harsh Pancholi, P. Priyanka, Gaurav S. Kasbekar

Published in: Wireless Networks | Issue 5/2020

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Abstract

Device-to-device communication allows a cellular user (relay node) to relay data between the base station (BS) and another cellular user (destination node). We address the problem of designing reverse auctions to assign a relay node to each destination node, when there are multiple potential relay nodes and multiple destination nodes, in the scenarios where the transmission powers of the relay nodes are: (1) fixed, (2) selected to achieve the data rates desired by destination nodes, and (3) selected so as to approximately maximize the BS’s utility. We show that auctions based on the widely used Vickrey–Clarke–Groves (VCG) mechanism have several limitations in scenarios (1) and (2); also, in scenario (3), the VCG mechanism is not applicable. Hence, we propose novel reverse auctions for relay selection in each of the above three scenarios. We prove that all the proposed reverse auctions can be truthfully implemented as well as satisfy the individual rationality property. Using numerical computations, we show that in scenarios (1) and (2), our proposed auctions significantly outperform the auctions based on the VCG mechanism in terms of the data rates achieved by destination nodes, utility of the BS and/or the interference cost incurred to the BS.

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Note that some overhead is incurred during the process of estimating the channel gains.

All our results readily generalize to the case when \(E_{i,j}=\alpha _{i} (P_{i,j}+P_{c,i}) + P_0\) where \(P_0\) is a constant.

For example, in the context of an auction mechanism, an allocation may be a vector \(Y=(Y_1,\ldots , Y_n)\), where \(Y_i\) is 1 if the good is allocated to bidder i and 0 else.

A bipartite graph \(G=(V_1,V_2,E)\) is said to be complete if there is an edge between every \(v_1\in V_1\) and every \(v_2\in V_2\).

The neighbourhood of a vertex v under the matching m is the set of all vertices which are connected by an edge in m with the vertex v. The neighbourhood of a set of vertices C under the matching m is the set \(\{v:v \text { is in the neighbourhood of a vertex }c\in C\text { under }m\}\).

\(P_{i,j}=0\) if relay node i is not assigned to destination node j.

When \(P_{i,j}^*<0\), we set \(P_{i,j}^*=0\) and when \(P_{i,j}^*>P_m\), we set \(P_{i,j}^*=P_m\). This process is followed for all the relaying schemes.

The transmission power is 0 if both roots are negative.

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Title: Beyond the VCG mechanism: truthful reverse auctions for relay selection with high data rates, high base station utility and low interference in D2D networks
Authors: M. V. S. Aditya
Harsh Pancholi
P. Priyanka
Gaurav S. Kasbekar
Publication date: 16-03-2020
Publisher: Springer US
Published in: Wireless Networks / Issue 5/2020
Print ISSN: 1022-0038
Electronic ISSN: 1572-8196
DOI: https://doi.org/10.1007/s11276-020-02304-4

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