Minimum initial marking in timed marked graphs

This paper addresses the minimum initial marking (MIM) in timed marked graphs. In this problem both the net and the cycle time are fixed, so the problem consists in finding out a minimum initial marking M₀ such that the cycle time of the TMG will be less or equal to the required one. The main result of this work is the heuristic algorithm MIM Solver to solve the MIM problem. It computes a subset of p-semiflows and adds tokens to places in two steps. First it adds the minimum number of tokens needed to reduce the difference between the required cycle time π^d and the cycle time π_i of each p-semiflow belonging to the computed subset. The difference π ^d-π_i>0 must be minimum. In this step a heuristic based on the places belonging to the maximum number of p-semiflows is used. Afterwards, the algorithm adds the largest number of tokens in p-semiflows to fulfil cycle time constraints. In this step a heuristic based on the places belonging to the shortest number of p-semiflows is used