1,216 research outputs found

    A Single Server Queue with Random Arrivals and Balking: Confidence Interval Estimation

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    35 pages, 1 article*A Single Server Queue with Random Arrivals and Balking: Confidence Interval Estimation* (Rubin, Gail; Robson, Douglas S.) 35 page

    Dynamic Auctions: A Survey

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    We survey the recent literature on designing auctions and mechanisms for dynamic settings. Two settings are considered: those with a dynamic population of agents or buyers whose private information remains fixed throughout time; and those with a fixed population of agents or buyers whose private information changes across time. Within each of these settings, we discuss both efficient (welfare-maximizing) and optimal (revenue-maximizing) mechanisms.Dynamic auctions and mechanisms, Random arrivals and departures, Changing private information, Incentive compatibility

    Posted Price Mechanisms and Optimal Threshold Strategies for Random Arrivals

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    The classic prophet inequality states that, when faced with a finite sequence of non-negative independent random variables, a gambler who knows their distribution and is allowed to stop the sequence at any time, can obtain, in expectation, at least half as much reward as a prophet who knows the values of each random variable and can choose the largest one. In this work we consider the situation in which the sequence comes in random order. We look at both a non-adaptive and an adaptive version of the problem. In the former case the gambler sets a threshold for every random variable a priori, while in the latter case the thresholds are set when a random variable arrives. For the non-adaptive case, we obtain an algorithm achieving an expected reward within at least a 1-1/e fraction of the expected maximum and prove this constant is optimal. For the adaptive case with i.i.d. random variables, we obtain a tight 0.745-approximation, solving a problem posed by Hill and Kertz in 1982. We also apply these prophet inequalities to posted price mechanisms, and prove the same tight bounds for both a non-adaptive and an adaptive posted price mechanism when buyers arrive in random order

    Online Vertex-Weighted Bipartite Matching: Beating 1-1/e with Random Arrivals

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    We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the randomized primal-dual framework by Devanur et al. (SODA 2013) and design a two dimensional gain sharing function, which depends not only on the rank of the offline vertex, but also on the arrival time of the online vertex. To our knowledge, this is the first competitive ratio strictly larger than 1-1/e for an online bipartite matching problem achieved under the randomized primal-dual framework. Our algorithm has a natural interpretation that offline vertices offer a larger portion of their weights to the online vertices as time goes by, and each online vertex matches the neighbor with the highest offer at its arrival