arXiv subjects

Arnaud Cadas

Publications and source records attributed to Arnaud Cadas.

3 recordsLinked to original sources

arXiv2020

Flexibility can hurt dynamic matching system performance

We study the performance of general dynamic matching models. This model is defined by a connected graph, where nodes represent the class of items and the edges the compatibilities between items. Items of different classes arrive one by one to the system according to a given probability distribution. Upon arrival, an item is matched with a compatible item according to the First Come First Served discipline and leave the system immediately, whereas it is enqueued with other items of the same class, if any. We show that such a model may exhibit a non intuitive behavior: increasing the services ability by adding new edges in the matching graph may lead to a larger average population. This is similar to a Braess paradox. We first consider a quasicomplete graph with four nodes and we provide values of the probability distribution of the arrivals such that when we add an edge the mean number of items is larger. Then, we consider an arbitrary matching graph and we show sufficient conditions for the existence or non-existence of this paradox. We conclude that the analog to the Braess paradox in matching models is given when specific independent sets are in saturation, i.e., the system is close to the stability condition.

cs.GT↗

arXiv2020

Optimal Control of Dynamic Bipartite Matching Models

A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a stochastic process. Matched pairs leave the system and the others wait in the queues, which induces a holding cost. We model this problem as a Markov Decision Process and study the discounted cost and the average cost problem. We fully characterize the optimal matching policy for complete matching graphs and for the N -shaped matching graph. In the former case, the optimal policy consists of matching everything and, in the latter case, it prioritizes the matchings in the extreme edges and is of threshold type for the diagonal edge. In addition, for the average cost problem, we compute the optimal threshold value. For more general graphs, we need to consider some assumptions on the cost of the nodes. For complete graphs minus one edge, we provide conditions on the cost of the nodes such that the optimal policy of the N-shaped matching graph extends to this case. For acyclic graphs, we show that, when the cost of the extreme edges is large, the optimal matching policy prioritizes the matchings in the extreme edges. We also study the W-shaped matching graph and, using simulations, we show that there are cases where it is not optimal to prioritize to matchings in the extreme edges.

cs.DM↗

arXiv2019

The power disaggregation algorithms and their applications to demand dispatch

We were interested in solving a power disaggregation problem which comes down to estimating the power consumption of each device given the total power consumption of the whole house. We started by looking at the Factorial Hierarchical Dirichlet Process - Hidden Semi-Markov Model. However, the inference method had a complexity which scales withthe number of observations. Thus, we developed an online algorithm based on particle filters. We applied the method to data from Pecan Street https://dataport.cloud/ using Python. We applied the disaggregation algorithm to the control techniques used in Demand Dispatch.

stat.AP↗