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Under a weaker set of assumptions than those commonly established in the literature, we prove that the scaled steady-state queue length at each station converges weakly to a common exponential random variable in heavy traffic. Specifically, our results hold under the assumption of the (2 + \u03b5)th moment for the interarrival and service distributions with some \u03b5 &gt; 0. The proof leverages the Palm version of the basic adjoint relationship (BAR) as a key technique.<\/jats:p>","DOI":"10.1145\/3711703","type":"journal-article","created":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T16:05:24Z","timestamp":1741622724000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Steady-State Convergence of the Continuous-Time Routing System with General Distributions in Heavy Traffic"],"prefix":"10.1145","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-5519-3424","authenticated-orcid":false,"given":"Jin","family":"Guang","sequence":"first","affiliation":[{"name":"The Chinese University of Hong Kong, Shenzhen, Shenzhen, Guangdong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2187-7157","authenticated-orcid":false,"given":"Yaosheng","family":"Xu","sequence":"additional","affiliation":[{"name":"University of Chicago, Chicago, Illinois, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5223-0129","authenticated-orcid":false,"given":"J. 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