Emergency response time in traffic accidents is one of the key determinants of the quality of pre-hospital emergency medical services. Predicting this time enables decision-makers to improve the efficiency of emergency services and reduce response time. The data related to emergency response time are a type of time-to-event data, whose main characteristic is their dependency on duration. To account for this feature, baseline hazard models are commonly used; however, the performance of these models may be limited due to their underlying assumptions. In contrast, machine learning models serve as an alternative approach for modeling emergency response time. Their main advantage is that they are not constrained by the restrictive assumptions of baseline hazard models and can capture nonlinear and interactive relationships among variables. In this study, a survival-based neural network model was employed to simultaneously estimate the survival function and predict emergency response time. By utilizing the concept of multi-task learning, this model can account for duration dependence while predicting response time through the concurrent estimation of the survival function. Using 28,505 traffic accident reports recorded by the Mashhad Emergency Medical Services, the performance of the proposed model was evaluated and compared with statistical models and other machine learning methods. The results indicate that the proposed model can serve as an effective alternative to traditional approaches for predicting emergency response time.