In this paper, we study the link between difficulty and player's motivation in two games developed by Ubisoft®: Rayman®Legends and Tom Clancy's The Division®. We describe a method to estimate players' difficulty over time and link it's time varying effect with players retention. Results confirm flow and self-efficacy theory. Also, for the first hours of playtime, results differ between the two games. We explain that discrepancy with regard to attribution theory : in Rayman Legends, failure can be mainly attributed to the player skills, while in Tom Clancy's The Division, avatar's strength plays a fundamental role and can always be relatively quickly improved.

Probabilistic validation is an approach for the validation of highly dependable and complex systems. It relies on a partial analysis on a system model and tries to prove that the failed event occurrences has a sufficiently low probability. We define a probabilistic validation method using worst event driven and an importance sampling simulation. The system which must be validated is modeled by a stochastic Petri net. An efficient simulation of the net must be able to sample complex and improbable trajectories which eventually reach critical markings. Two problems have to be solved. The sequence of transition firings which may lead to critical markings must be characterized ad the Petri net level. The second problem is to sample these sequences and to build an accurate estimate of the incorrect behavior probability. We discuss several simulation algorithms in the Markovian and non-Markovian cases. We show the effectiveness of these techniques on the validation of several examples.>

A method to estimate the value of remote clocks in distributed systems is proposed. The method is able to deal with isotropic and anisotropic networks and includes a way to detect performance failures on single exchanges. It uses a statistical approach to estimate the relative drift of clocks and a round trip clock reading protocol to compute the offset. A good precision can be attained and maintained without exchanging too many specific extra messages. Numerical results obtained from a discrete event simulation are presented.>

A new solution is given for the steady-state probability computation of closed synchronized queuing networks. A closed synchronized queuing network is a particular Markov stochastic Petri net (a bounded and monovaluated Petri net with a strongly connected reachability graph and constant firing rates independent of markings). It is shown that the steady-state probability distribution can be expressed using matrix products. The results generalize the Gordon-Newell theorem. The solution is similar to the Gordon-Newell product form using matrix and vectors instead of scalars. A prototype solver developed from this result is presented.>

A necessary and sufficient ergodicity condition for complex open queueing systems is given. The queueing networks considered belong to a particular class of unbounded Markov stochastic Petri nets. These systems can include synchronization features like fork and join arrivals and departures, and feedback between behavior of different queues. Grouped and correlated arrivals and departures are also allowed. An example and a proof of the ergodicity results are presented.>