Optimal Parametrization of the Gale-Shapley Preallocation Method for Combinatorial Auction-based Channel Assignment

TL;DR

The paper tackles efficient channel assignment in multi-connectivity networks by using a preallocation-based combinatorial auction and optimizing the many-to-many Gale-Shapley preallocation quotas. It formulates a utility-based objective with a connectivity function and capacity bounds, and analyzes how the quotas $q_T$ and $q_{ch}$ shape the CA search space, total utility, and computation time. Through extensive simulations across small, medium, and large scenarios, it shows that high tenant quotas $q_T$ together with low channel quotas $q_{ch}$ yield better utility and lower computation, while excessive preallocation can lead to channel starvation and wasted resources. The work provides practical guidelines for parameter selection to enable scalable CA-based channel allocation in beyond-5G networks, highlighting the balance between search space constriction and allocation efficiency.

Abstract

Algorithms based on combinatorial auctions show significant potential regarding their application for channel assignment problems in multi-connectivity ultra-reliable wireless networks. However the computational effort required by such algorithms grows fast with the number of users and resources. Therefore, preallocation-based combinatorial auction represents a promising approach for these setups. The aim of the preallocation is to constrain the number of bids submitted by participants in the combinatorial auction process, thus reducing computational demands and enabling numerical feasibility of the auction problem. Reduction of bid number is achieved via limiting the number of items (channels) considered by auction participants (tenants) in their bids. Thus the aim of preallocation is to non-exclusively assign channels to tenants. This assignment serves as a basis for the later bid generation in the auction procedure. In this paper we analyze the optimal parametrization of the many-to-many Gale-Shapley preallocation method and formulate recommendations for optimal performance. Numerical assessments illustrate that the appropriate preallocation has significant impact on the performance and computational demand.

Figures (5)

• Figure 1: The relation of channel sets after the preallocation and the final allocation in the case of two tenants.
• Figure 2: Overview of the CA-based allocation process.
• Figure 3: Resulting total utility ($\sum U_k$) values, in the case of various $q_T$ and $q_{ch}$ values. Average values of 200 simulation runs.
• Figure 4: Mean number of not preallocated channels ($N_{npc}$), in the case of various $q_T$ and $q_{ch}$ values. Average values of 200 simulation runs.
• Figure 5: Average value of computational time required for the preallocation process [s], for various $q_T$ and $q_{ch}$ values in the case of the LS setup (200 simulation runs).