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Common applications simulate manufacturing, healthcare and call-center processes for which main events are i.a. Between these events no changes to the system’s state occur. It is applicable whenever a system can be represented by events occurring over time and thereby changing the system’s state. In the mathematical modelling literature and practice, Discrete Event Simulation (DES) is a well-established method for analysing dynamic, stochastic and complex real-world problems. Lastly, we apply the assessment method and model tail dependencies in a simulation of an emergency ambulance service as here the maximum time in system is often critical. Additionally, we provide a classification of the possible sources of tail dependencies in DES problems to better understand their impact on commonly used results in simulation studies, such as the maximum time in system. It offers a structured way to include tail dependencies in DES via copula theory despite lacking historical data. Therefore, we present a linear programming-based method to assess minimum information copulas through expert judgements which minimise unspecified parametric assumptions. A main modelling challenge for this is the lack of relevant historical data on tail dependencies. Given that the impact of potential tail dependencies on simulation results has only sparsely been addressed in the simulation literature, in this paper we present a novel framework to model tail dependencies between service time distributions in DES through copulas. However, in some simulation problems this might lead to underestimating the potential risk of certain simulation results, such as the maximum time in system, exceeding some critical threshold, especially when tail dependencies are present. In Discrete Event Simulation (DES) we can often assume that the distributions of service times are independent of each other.