We explore whether bilateral and transit quotas applied by EU countries on Turkey have a negative impact on Turkey's international trade by road transport. Therefore, Turkey's exports by road transport to selected European countries are analyzed in a panel-data framework for the period 2005-2014. We estimate the aggregate effect of different quota types on trade between Turkey and European countries by using an approach that integrates the max-flow and gravity models. In the gravity model, for each country, a single value representing the aggregate restricting effect of different quota types is needed. The single values are obtained by solving multiple max-flow problems, where constraining effects of different quota types are modeled as arc capacities. The results of the gravity model suggest a loss in Turkish exports by road transport because of the quotas imposed by other countries. Most of the negative impact results from bilateral quotas rather than from transit quotas, whose effect is rather marginal. (c) 2017 Elsevier Ltd. All rights reserved.