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In this paper, in order to minimize the expect charge, we focus on the problem of how to offload the computation-intensive task from the resource-scarce UE to access point\u2019s (AP) and the cloud, and the density allocation of APs\u2019 at mobile edge. We consider three offloading computing modes and focus on the coverage probability of each mode and corresponding ergodic rates. The resulting optimization problem is a mixed-integer and non-convex problem in the objective function and constraints. We propose a low-complexity suboptimal algorithm called Iteration of Convex Optimization and Nonlinear Programming (ICONP) to solve it. Numerical results verify the better performance of our proposed algorithm. Optimal computing ratios and APs\u2019 density allocation contribute to the charge saving.<\/jats:p>","DOI":"10.1186\/s13638-021-01891-w","type":"journal-article","created":{"date-parts":[[2021,1,25]],"date-time":"2021-01-25T12:06:05Z","timestamp":1611576365000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Joint optimization of computing ratio and access points\u2019 density for mixed mobile edge\/cloud computing"],"prefix":"10.1186","volume":"2021","author":[{"given":"Tianqi","family":"Jing","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0549-4970","authenticated-orcid":false,"given":"Shiwen","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fei","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongming","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luxi","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ju","family":"Ren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,1,25]]},"reference":[{"key":"1891_CR1","unstructured":"Cisco visual networking index: mobile data traffic forecast update 2017-2022. 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