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First, it results in frequent handoffs, thus leading to long delay and low service availability. Second, the available AP sets and their channel quality change dynamically, making the AP selection problem even harder. Therefore, there is a strong need to develop an efficient association control mechanism that provides efficient vehicular Wi-Fi access. In this paper, we present a theoretical framework to formulate the optimal association problem through <jats:italic>non-linear integer programming<\/jats:italic>, whose objective function is to maximize the throughput or to minimize the handoff overhead. We show that this problem holds the <jats:italic>totally unimodular<\/jats:italic> (TU) property and is thus solvable in polynomial time. Then, we study the optimality of association control by comparing existing online algorithms through real trace-based simulations. The results show that there exists a large performance gap between the performance of existing online algorithms and the optimal one. We also observe that the association control algorithm can be further improved if it has access to future knowledge. Particularly, the offline optimal with future AP information improves the performance of the local optimal by up to 10%.<\/jats:p>","DOI":"10.1186\/1687-1499-2014-192","type":"journal-article","created":{"date-parts":[[2014,11,17]],"date-time":"2014-11-17T18:05:05Z","timestamp":1416247505000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A theoretical approach to optimal association control in vehicular Wi-Fi networks"],"prefix":"10.1186","volume":"2014","author":[{"given":"Jaeryong","family":"Hwang","sequence":"first","affiliation":[]},{"given":"Jaehyuk","family":"Choi","sequence":"additional","affiliation":[]},{"given":"Joon","family":"Yoo","sequence":"additional","affiliation":[]},{"given":"Chong-kwon","family":"Kim","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,11,17]]},"reference":[{"key":"1069_CR1","unstructured":"Ott J, Kutscher D: Drive-thru Internet: IEEE 802.11b for 'automobile\u2019 user. 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