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Predictive process monitoring is concerned with predicting measures of interest for a running case (e.g., a business outcome or the remaining time) based on historical event logs. Most of the current predictive process monitoring approaches only consider intra-case information that comes from the case whose measures of interest one wishes to predict. However, in many systems, the outcome of a running case depends on the interplay of all cases that are being executed concurrently. For example, in many situations, running cases compete over scarce resources. In this paper, following standard predictive process monitoring approaches, we employ supervised machine learning for prediction. In particular, we present a method for feature encoding of process cases that relies on a bi-dimensional state space representation: the first dimension corresponds to intra-case dependencies, while the second …