One-dimensional transport equations with discontinuous coefficients
Nonlinear Analysis: Theory, Methods & Applications
Studying Balanced Allocations with Differential Equations
Combinatorics, Probability and Computing
Stochastic Approximations and Differential Inclusions
SIAM Journal on Control and Optimization
Stability of Parallel Queueing Systems with Coupled Service Rates
Discrete Event Dynamic Systems
A class of mean field interaction models for computer and communication systems
Performance Evaluation
A mean field model of work stealing in large-scale systems
Proceedings of the ACM SIGMETRICS international conference on Measurement and modeling of computer systems
On the power of (even a little) centralization in distributed processing
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Performance analysis of the IEEE 802.11 distributed coordination function
IEEE Journal on Selected Areas in Communications
MPTCP is not pareto-optimal: performance issues and a possible solution
Proceedings of the 8th international conference on Emerging networking experiments and technologies
Continuous approximation of collective system behaviour: A tutorial
Performance Evaluation
MPTCP is not pareto-optimal: performance issues and a possible solution
IEEE/ACM Transactions on Networking (TON)
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In this paper, we study deterministic limits of Markov processes having discontinuous drifts. While most results assume that the limiting dynamics is continuous, we show that these conditions are not necessary to prove convergence to a deterministic system. More precisely, we show that under mild assumptions, the stochastic system is a stochastic approximation algorithm with constant step size that converges to a differential inclusion. This differential inclusion is obtained by convexifying the rescaled drift of the Markov chain. This generic convergence result is used to compute stability conditions of stochastic systems, via their fluid limits. It is also used to analyze systems where discontinuous dynamics arise naturally, such as queuing systems with boundary conditions or with threshold control policies, via mean field approximations.