Communication Dans Un Congrès Année : 2026

Performance paradox in matching systems

Résumé

In stochastic matching systems operated under first-come–first-matched (FCFM) discipline, adding an edge to the compatibility graph may worsen the steady state performance of the system; we refer to this phenomenon as a performance paradox. We study such paradoxes on simple graphs, multigraphs with self-loops, and systems with abandonment. We consider a stochastic matching model [7] with a single global buffer. Each arriving item belongs to a class represented by a vertex of a compatibility graph. Items arrive over time according to independent Poisson processes, and wait in the buffer until they are matched or leave the system. Two items can be matched if and only if their classes are connected by an edge in the graph. Let G = (V, E) be a simple graph, where vertices represent item classes and edges represent compatibility. Under FCFM, when an item arrives, if at least one compatible item is present in the buffer, it is matched with the oldest compatible item. The two items then depart immediately. If no compatible item is available, the arrival is stored in the buffer. Assuming positive recurrence, we measure performance by the total expected backlog. On connected, nonbipartite graphs, the buffer-content process admits a closed-form stationary distribution, enabling explicit finite independent set expansions of performance metrics; see. A performance paradox occurs if, for a graph G and an added edge e under the same arrival rates μ, E[G+e,μ] > E[G,μ]. This extended abstract surveys three extensions: (i) paradoxes occur on star-free graphs; (ii) the same evaluation machinery extends to multigraphs and yields paradox instances; and (iii) we show that performance paradox can also occur in systems with abandonments, for which there is no known product form solution.

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hal-05534848 , version 1 (05-03-2026)

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  • HAL Id : hal-05534848 , version 1

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Shu Li, Ana Bušić, Jean-Michel Fourneau. Performance paradox in matching systems. ROADEF 2026 - Congrès de la Société Française de Recherche Opérationnelle et d'Aide à la Décision, Université de Tours [UT], Feb 2026, Tours, France. ⟨hal-05534848⟩
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