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Validity of heavy traffic steady-state approximations in generalized Jackson networks
We consider a single class open queueing network, also known as a generalized Jackson network (GJN). A classical result in heavy-traffic theory asserts that the sequence of normalized queue lengthExpand
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Join the Shortest Queue with Many Servers. The Heavy-Traffic Asymptotics
tl;dr
We use the martingale method to prove that a scaled process counting the number of idle servers and queues of length exactly two weakly converges to a two-dimensional reflected Ornstein-Uhlenbeck process and a deterministic system decaying to zero in constant time. Expand
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Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
tl;dr
We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erdos-Renyi (ER) graph G(N,c/N) and random r-regular graphs, including independent sets, MAX-CUT, Coloring and K-SAT, by extending and simplifying the interpolation method of Guerra and Toninelli. Expand
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Stability of adaptive and non-adaptive packet routing policies in adversarial queueing networks
tl;dr
We investigate the stability of packet routing policies in adversarial queueing networks. Expand
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The Need for (Long) Chains in Kidney Exchange
It has been previously shown that for sufficiently large pools of patient-donor pairs, (almost) efficient kidney exchange can be achieved by using at most 3-way cycles, i.e. by using cycles among noExpand
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Simple deterministic approximation algorithms for counting matchings
tl;dr
We construct a deterministic fully polynomial time approximationscheme (FPTAS) for computing the total number of matchings in abounded degree graph. Expand
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Belief Propagation for Min-Cost Network Flow: Convergence and Correctness
tl;dr
We study the performance of BP in the context of the capacitated minimum-cost network flow problem---a cornerstone in the development of the theory of polynomial-time optimization problems and widely used in the practice of operations research. Expand
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Finding long chains in kidney exchange using the traveling salesman problem
Significance There are currently more than 100,000 patients on the waiting list in the United States for a kidney transplant from a deceased donor. To address this shortage, kidney exchange programsExpand
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The diameter of a long range percolation graph
One can model a social network as a long-range percolation model on a graph {0, 1, …, N}2. The edges (x, y) of this graph are selected with probability ≈ β/||x - ys if ||x - y|| > 1, and withExpand
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Steady-state $GI/G/n$ queue in the Halfin–Whitt regime
12, is tight. We derive an upper bound on the large deviation exponent of the limiting steady-state queue length matching that conjectured by Gamarnik and Momcilovic in [14]. We also prove a matchingExpand
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