Performance Evaluation of Stochastic Bipartite Matching Models

Comte, Céline; Dorsman, Jan-Pieter

doi:10.1007/978-3-030-91825-5_26

Cited by 3 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first example of a stochastic matching model in the literature, which predated the model that we consider, is the bipartite matching model introduced in [12] and studied in [1,2,3,8,9,10,15]. In this model, the compatibility graph is bipartite, with two parts that correspond to supply and demand items, respectively.…”

Section: Bipartite Stochastic Matchingmentioning

confidence: 99%

Stochastic dynamic matching: A mixed graph-theory and linear-algebra approach

Comte¹,

Mathieu²,

Bušíć³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The stochastic dynamic matching problem has recently drawn attention in the stochastic-modeling community due to its numerous applications, ranging from supply-chain management to kidney exchange programs. In this paper, we consider a matching problem in which items of different classes arrive according to independent Poisson processes. Unmatched items are stored in a queue, and compatibility constraints are described by a simple graph on the classes, so that two items can be matched if their classes are neighbors in the graph. We analyze the efficiency of matching policies, not only in terms of system stability, but also in terms of matching rates between different classes.Our results rely on the observation that, under any stable policy, the matching rates satisfy a conservation equation that equates the arrival and departure rates of each item class. Our main contributions are threefold. We first introduce a mapping between the dimension of the solution set of this conservation equation, the structure of the compatibility graph, and the existence of a stable policy. In particular, this allows us to derive a necessary and sufficient stability condition that is verifiable in polynomial time. Secondly, we describe the convex polytope of non-negative solutions of the conservation equation. When this polytope is reduced to a single point, we give a closed-form expression of the solution; in general, we characterize the vertices of this polytope using again the graph structure. Lastly, we show that greedy policies cannot, in general, achieve every point in the polytope. In contrast, non-greedy policies can reach any point of the interior of this polytope, and we give a condition for these policies to also reach the boundary of the polytope. ACM Subject ClassificationMathematics of computing → Queueing theory; Mathematics of computing → Markov processes; Mathematics of computing → Matchings and factors

show abstract

Section: Bipartite Stochastic Matchingmentioning

confidence: 99%

Stochastic dynamic matching: A mixed graph-theory and linear-algebra approach

Comte¹,

Mathieu²,

Bušíć³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Stability regions of systems with compatibilities and ubiquitous measures on graphs

2023

View full text Add to dashboard Cite

New directions in pass-and-swap queues

Dorsman,

Gardner

2024

Queueing Syst

View full text Add to dashboard Cite

Recently, driven by redundancy systems and matching systems, there has been renewed interest in models with product form stationary distributions. By a “product form,” we mean that the stationary distribution can be expressed as a product of terms, each of which corresponds to a job in the system. Given the recent discovery of many such systems, it is natural to ask: how broad is this class of systems? In this paper, we consider extensions and generalizations of the recently-proposed pass-and-swap queue, which has a product-form stationary distribution. We make three main contributions. First, we identify sufficient conditions under which pass-and-swap queues can be connected in a closed network, while still preserving the product form. Second, we identify dimensions along which the pass-and-swap system can be extended while preserving the product-form stationary distribution. At the same time, we also identify cases in which generalizing the pass-and-swap queue causes the product-form nature of the stationary distribution to break. Finally, we identify questions that remain open and present a road map for future study.

show abstract

Performance Evaluation of Stochastic Bipartite Matching Models

Cited by 3 publications

References 21 publications

Stochastic dynamic matching: A mixed graph-theory and linear-algebra approach

Stochastic dynamic matching: A mixed graph-theory and linear-algebra approach

Stability regions of systems with compatibilities and ubiquitous measures on graphs

New directions in pass-and-swap queues

Contact Info

Product

Resources

About