Stochastic Matching Networks: Theory and Applications to Matching Markets
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Varma, Sushil Mahavir
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Abstract
Traditional service-based marketplaces have now moved online with the emergence of platform economies. Examples include ride-hailing systems, meal and grocery delivery platforms, and EV-based transportation systems. Such systems share the common operational challenge of dynamically matching customers and servers with each other. In addition to such software-based platforms, recent technological breakthroughs are leading to networked matching platforms that match various virtual or physical entities—for example, matching payments in peer-to-peer payment channel networks. The focus of this thesis is on studying such matching platforms.
While matching is a classical problem with rich literature in Economics and CS theory, throughput and delay in matching platforms with dynamic matching is not fully understood. Such objectives in service systems are usually studied using queueing models. Consequently, we take the stochastic network viewpoint to model them as stochastic matching networks composed of matching queues. In contrast to classical queues with dedicated servers, both customers and servers arrive and depart in matching queues. An example is an airport taxi stand, where both riders (customers) and drivers (servers) arrive, and are queued separately. Once a rider and driver are matched, they immediately depart from the system. It is a lot harder to analytically study such two-sided behavior, and classical queueing theory cannot be directly applied. In this thesis, we develop a theory of stochastic matching networks, providing a comprehensive understanding of throughput and delay in matching platforms. Hence, allowing us to design optimal control, e.g., matching decisions, that optimizes these objectives.
This thesis is divided into three parts. The first part, comprising three chapters, sets up the stage by developing the fundamentals of stochastic matching networks. After setting up the preliminary and background, we start by developing a heavy-traffic theory of matching queues. Then, we introduce several models of stochastic matching networks composed of interacting matching queues. These networks are shown to model matching platforms like online marketplaces. We then present a thorough survey of different stochastic matching network models in the literature to put our work in a broader context. This part of the thesis highlights our fundamental contributions, both theoretical and modeling, to stochastic matching networks.
The second part, comprising four chapters, develops optimal control for matching platforms by analyzing the models introduced in the previous part. Specifically, we consider applications to online marketplaces, EV-based transportation systems, and payment channel networks. We model online marketplaces as a bipartite matching network and develop profit-maximizing joint pricing and matching policies with delay-sensitive agents. We further consider the more challenging setting when the agents are strategic and tailor our policies to account for such strategic behavior. Next, we model an EV-based transportation system as a spatial matching network and provide an infrastructure planning prescription, i.e., the number of EVs and chargers needed to ensure a given throughput. Our result throws light on the effects of pickup times and downtimes due to charging on the infrastructure planning. Lastly, we model a payment channel network as a connected network of matching queues and provide a throughput optimal routing policy to route transaction requests on the network. In the process of developing these results, we unravel fundamental trade-offs, providing key insights into the operations of these matching platforms.
The third part of the thesis shifts the focus to analyzing classical queueing analogs of the proposed stochastic matching networks. In particular, some of the novel aspects of stochastic matching networks motivated us to investigate new facets of their classical equivalents. We first generalize the heavy traffic theory of a single server queue by considering state-dependent arrival rates. Then, we consider the classical load balancing model and provide the queue length distribution for the power-of-$d$ choices policy in the sub-Halfin-Whitt regime. Lastly, we consider the parallel server queueing model and develop sparse flexibility graphs while ensuring that the customers experience low delays. These results contribute to and build upon the fundamentals of queueing theory.
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2024-06-13
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Dissertation