A proportionate fair scheduling rule with good worst-case performance

Adler, Micah; Berenbrink, Petra; Friedetzky, Tom; Goldberg, Leslie Ann; Goldberg, Paul; Paterson, Mike

doi:10.1145/777429.777430

Cited by 7 publications

(47 citation statements)

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“…possible permutations of the input is equally likely, the average or expected number of comparisons is merely 648. Unfortunately, since the array is given at run-time, assuming that the values in it appear as a random permutation is not necessarily valid 1 . But a randomized version of quicksort, which randomly permutes the array prior to sorting, would indeed have the expected number of comparisons be 648 regardless of the input.…”

Section: Silmentioning

confidence: 99%

“…This is equivalent to determining an upper bound on the maximum backlog that can build up in any buffer. It was shown [1] that the node can guarantee a Θ(log n) bound on the backlog of any flow by employing the greedy strategy of processing, at each step, one unit of flow from the incoming flow with the currently largest backlog (ties broken arbitrarily); it was also shown that this bound is tight in the sense that no (deterministic) algorithm can guarantee a o(log n) backlog. Hence, to guarantee no loss on any flow, we must provision each incoming flow with a buffer that can hold Θ(log n) flow.…”

Section: Buffer Sizingmentioning

confidence: 99%

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The safe and effective application of probabilistic techniques in safety-critical systems

Agrawal

Baruah

Guo

et al. 2020

Proceedings of the 39th International Conference on Computer-Aided Design

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Section: Silmentioning

confidence: 99%

Section: Buffer Sizingmentioning

confidence: 99%

The safe and effective application of probabilistic techniques in safety-critical systems

Agrawal

Baruah

Guo

et al. 2020

Proceedings of the 39th International Conference on Computer-Aided Design

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“…Starting with the seminal paper of Liu [30], work on the p processor cup game has spanned more than five decades [7,20,8,29,27,33,6,23,30,31,16,10,25,1,15,28]. In addition to processor scheduling [7,20,8,29,27,33,6,23,30,31,1,28,16], applications include network-switch buffer management [21,4,35,19], quality of service guarantees [7,1,28], and data structure deamortization [2,16,15,3,34,22,17,24,9]. The game has also been studied in many different forms.…”

Section: Introductionmentioning

confidence: 99%

“…The game has also been studied in many different forms. Researchers have studied the game with a fixed-filling-rate constraint [7,20,8,29,27,33,6,23,30,31], with various forms of resource augmentation [10,25,28,16], with both oblivious and adaptive adversaries [1,7,30,10,25], with smoothed analysis [25,10], with a semi-clairvoyant emptier [28], with competitive analysis [5,18,14], etc.…”

Section: Introductionmentioning

confidence: 99%

“…For the plain form of the p-processor cup game, the greedy emptying algorithm (i.e., always empty from the fullest cups) is known to be asymptotically optimal [1,10,25], achieving backlog O(log n). The optimal backlog for randomized emptying algorithms remains an open question [16,10,25] and is known to be between Ω(log log n) and O(log log n + log p) [25].…”

Section: Introductionmentioning

confidence: 99%

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The Variable-Processor Cup Game

Kuszmaul,

Westover

2020

Preprint

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The problem of scheduling tasks on p processors so that no task ever gets too far behind is often described as a game with cups and water. In the p-processor cup game on n cups, there are two players, a filler and an emptier, that take turns adding and removing water from a set of n cups. In each turn, the filler adds p units of water to the cups, placing at most 1 unit of water in each cup, and then the emptier selects p cups to remove up to 1 unit of water from. The emptier's goal is to minimize the backlog, which is the height of the fullest cup.The p-processor cup game has been studied in many different settings, dating back to the late 1960's. All of the past work shares one common assumption: that p is fixed. This paper initiates the study of what happens when the number of available processors p varies over time, resulting in what we call the variable-processor cup game.Remarkably, the optimal bounds for the variable-processor cup game differ dramatically from its classical counterpart. Whereas the p-processor cup has optimal backlog Θ(log n), the variable-processor game has optimal backlog Θ(n). Moreover, there is an efficient filling strategy that yields backlog Ω(n 1−ε ) in quasi-polynomial time against any deterministic emptying strategy.We additionally show that straightforward uses of randomization cannot be used to help the emptier. In particular, for any positive constant ∆, and any ∆-greedy-like randomized emptying algorithm A, there is a filling strategy that achieves backlog Ω(n 1−ε ) against A in quasi-polynomial time.

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The minimum backlog problem

Bender

Fekete

Kröller

et al. 2015

Theoretical Computer Science

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We study the minimum backlog problem (MBP). This online problem arises, e.g., in the context of sensor networks. We focus on two main variants of MBP.The discrete MBP is a 2-person game played on a graph G = (V, E). The player is initially located at a vertex of the graph. In each time step, the adversary pours a total of one unit of water into cups that are located on the vertices of the graph, arbitrarily distributing the water among the cups. The player then moves from her current vertex to an adjacent vertex and empties the cup at that vertex. The player's objective is to minimize the backlog, i.e., the maximum amount of water in any cup at any time.The geometric MBP is a continuous-time version of the MBP: the cups are points in the two-dimensional plane, the adversary pours water continuously at a constant rate, and the player moves in the plane with unit speed. Again, the player's objective is to minimize the backlog.We show that the competitive ratio of any algorithm for the MBP has a lower bound of Ω(D), where D is the diameter of the graph (for the discrete MBP) or the diameter of the point set (for the geometric MBP). Therefore we focus on determining a strategy for the player that guarantees a uniform upper bound on the absolute value of the backlog.For the absolute value of the backlog there is a trivial lower bound of Ω(D), and the deamortization analysis of Dietz and Sleator gives an upper bound of O(D log N ) for N cups. Our main result is a tight upper bound for the geometric MBP: we show that there is a strategy for the player that guarantees a backlog of O(D), independently of the number of cups.We also study a localized version of the discrete MBP: the adversary has a location within the graph and must act locally (filling cups) with respect to his position, just as the player acts locally (emptying cups) with respect to her position. We prove that deciding the value of this game is PSPACE-hard.

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A proportionate fair scheduling rule with good worst-case performance

Cited by 7 publications

References 0 publications

The safe and effective application of probabilistic techniques in safety-critical systems

The safe and effective application of probabilistic techniques in safety-critical systems

The Variable-Processor Cup Game

The minimum backlog problem

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