Stability of the stochastic matching model
Jean Mairesse,Pascal Moyal +1 more
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The matching model is introduced and it is proved that the model may be stable if and only if the matching graph is nonbipartite.Abstract:
We introduce and study a new model that we call the matching model. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be matched. There is a finite set of classes 𝒱 for the items, and the allowed matchings depend on the classes, according to a matching graph on 𝒱. Upon arrival, an item may find several possible matches in the buffer. This indeterminacy is resolved by a matching policy. When the sequence of classes of the arriving items is independent and identically distributed, the sequence of buffer-content is a Markov chain, whose stability is investigated. In particular, we prove that the model may be stable if and only if the matching graph is nonbipartite.read more
Citations
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FCFS parallel service systems and matching models
TL;DR: Three parallel service models in which customers of several types are served by several types of servers subject to a bipartite compatibility graph are considered, and Burke's theorem is generalized to parallel service systems.
Journal ArticleDOI
On the instability of matching queues
Pascal Moyal,Ohad Perry +1 more
TL;DR: In this article, it was shown that there always exists a matching policy that is strictly smaller than the set of arrival intensities satisfying NCOND, which is not the case in general.
Journal ArticleDOI
Fluid and diffusion approximations of probabilistic matching systems
Burak Büke,Hanyi Chen +1 more
TL;DR: This work proposes approximation methods based on fluid and diffusion limits using different scalings and shows that some performance measures are insensitive to the matching probability, agreeing with the existing results.
Posted Content
Reversibility and further properties of FCFS infinite bipartite matching
TL;DR: In this article, a pathwise Loynes' type construction is proposed to prove the existence of a unique matching for the infinite bipartite matching model defined over all the integers.
Journal ArticleDOI
Reward maximization in general dynamic matching systems
TL;DR: In this article, the authors considered a matching system with random arrivals of items of different types and proposed an optimal matching scheme that asymptotically maximizes the long-term average matching reward, while keeping the queues stable.
References
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Book
Topics in the Constructive Theory of Countable Markov Chains
TL;DR: In this paper, the authors present a history of ergodic Markov chains, including the explicit construction of Lyapunov functions and random walks in two-dimensional complexes.
Journal ArticleDOI
Re-entrant lines
TL;DR: This paper describes several scheduling policies of interest, and provides some results concerning their stability and performance, and several open problems are suggested.
Journal ArticleDOI
Fcfs infinite bipartite matching of servers and customers
TL;DR: In this paper, the problem of infinite bipartite matching is investigated and the authors present a countable state Markov chain to describe the process and prove ergodicity and existence of limiting rates.
Journal ArticleDOI
On the dynamic control of matching queues
Itai Gurvich,Amy R. Ward +1 more
TL;DR: A myopic discrete-review matching control that asymptotically–as the arrival rates become large–achieves the imbalance-based lower bound.
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Exact FCFS Matching Rates for Two Infinite Multitype Sequences
Ivo Adan,Gideon Weiss +1 more
TL;DR: In this paper, a bipartite graph G of allowable matches between the types of items in the two sequences is considered and the matching rate rci, sj is defined as the long-term fraction of (ci,sj) matches in the infinite matching.