linear dynamics (Section \[sec:policies\]).

We characterize the stationary solutions in terms of the policies of the Petri net. This allows us to set up a correspondence between the (ultimately affine) stationary solutions of the discrete dynamics that were described in [@allamigeon2015performance] and the stationary solutions of the continuous dynamics (Section \[sec:4\]). We also relate the continuous stationary solutions to the initial marking of the Petri net. This relies on restrictive assumptions, in particular the semi-simplicity of a 0 eigenvalue of a matrix associated with a policy.

We finally provide some numerical simulations of the continuous dynamics. We consider a model of emergency call center with two hierarchical levels for handling calls, originating from a real case study (17-18-112 call center in the Paris area) [@allamigeon2015performance]. On this Petri net, numerical experiments illustrate the convergence of the trajectory towards the stationary solution. This exhibits an advantage of the continuous setting in comparison to the discrete one, in which, for certain values of the parameters, the asymptotic throughputs computed by simulations differ from the stationary solutions (Section \[sec:numerical experiments\]).

Related work {#related-work .unnumbered}
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The motivation of this work stems from our previous study [@allamigeon2015performance], in which we addressed the same class 