Assessing and Modelling Tail Dependencies Between Service Times in Discrete Event Simulation With Minimum Information Copulas for a Better Understanding of Maximum Time in System Risk

Abstract

In Discrete Event Simulation (DES) we can often assume that the distributions of service times are independent of each other. 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. 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. A main modelling challenge for this is the lack of relevant historical data on tail dependencies. Therefore, we present a linear programming-based method to assess minimum information copulas through expert judgements which minimise unspecified parametric assumptions. It offers a structured way to include tail dependencies in DES via copula theory despite lacking historical data. 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. 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.