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By a \u201cproduct form,\u201d 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.\n<\/jats:p>","DOI":"10.1007\/s11134-024-09914-1","type":"journal-article","created":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T12:01:41Z","timestamp":1721131301000},"page":"205-256","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New directions in pass-and-swap queues"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6403-6377","authenticated-orcid":false,"given":"Jan-Pieter","family":"Dorsman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kristen","family":"Gardner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,16]]},"reference":[{"key":"9914_CR1","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/j.peva.2018.10.005","volume":"127","author":"I Adan","year":"2018","unstructured":"Adan, I., Kleiner, I., Righter, R., Weiss, G.: FCFS parallel service systems and matching models. 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