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We show that when a robot swarm can be modeled as a linear birth-death process, well-established results can be used to compute the expected value and\/or the distribution of important swarm performance measures, such as the swarm activity time or the swarm energy consumption. We also show how the linear birth-death model can be used to estimate the long-term value of such performance measures and design robot controllers that satisfy constraints on these measures.<\/jats:p>","DOI":"10.1145\/2870637","type":"journal-article","created":{"date-parts":[[2016,6,10]],"date-time":"2016-06-10T13:00:33Z","timestamp":1465563633000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Modeling Robot Swarms Using Integrals of Birth-Death Processes"],"prefix":"10.1145","volume":"11","author":[{"given":"Yara","family":"Khaluf","sequence":"first","affiliation":[{"name":"University of Paderborn, Paderborn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Dorigo","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Libre de Bruxelles and University of Paderborn, Paderborn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,6,6]]},"reference":[{"volume-title":"The Elements of Stochastic Processes With Applications to the Natural Sciences","author":"Bailey N.","key":"e_1_2_1_1_1","unstructured":"N. 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