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Title: IMPROVED RESULTS FOR STACKLEBERG SCHEDULING STRATEGIES

Abstract

No abstract prepared.

Authors:
;
Publication Date:
Research Org.:
Los Alamos National Lab., NM (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
789008
Report Number(s):
LA-UR-01-6406
TRN: US200306%%53
DOE Contract Number:
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: Conference title not supplied, Conference location not supplied, Conference dates not supplied; Other Information: PBD: 1 Nov 2001
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COMPUTERS; SCHEDULES; OPTIMIZATION

Citation Formats

V. S. A. KUMAR, and M. V. MARATHE. IMPROVED RESULTS FOR STACKLEBERG SCHEDULING STRATEGIES. United States: N. p., 2001. Web.
V. S. A. KUMAR, & M. V. MARATHE. IMPROVED RESULTS FOR STACKLEBERG SCHEDULING STRATEGIES. United States.
V. S. A. KUMAR, and M. V. MARATHE. Thu . "IMPROVED RESULTS FOR STACKLEBERG SCHEDULING STRATEGIES". United States. doi:. https://www.osti.gov/servlets/purl/789008.
@article{osti_789008,
title = {IMPROVED RESULTS FOR STACKLEBERG SCHEDULING STRATEGIES},
author = {V. S. A. KUMAR and M. V. MARATHE},
abstractNote = {No abstract prepared.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Nov 01 00:00:00 EST 2001},
month = {Thu Nov 01 00:00:00 EST 2001}
}

Conference:
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  • We continue the study initiated in [Ro01] on Stackelberg Scheduling Strategies. We are given a set of n independent parallel machines or equivalently a set of n parallel edges on which certain flow has to be sent. Each edge e is endowed with a latency function l{sub e}({center_dot}). The setting is that of a non-cooperative game: players choose edges so as minimize their individual latencies. Additionally, there is a single player who control as fraction ?? of the total flow. The goal is to find a strategy for the leader (i.e. an assignment of flow to indivual links) such thatmore » the selfish users react so as to minimize the total latency of the system. Building on the recent results in [Ro01, RT00], we show the following: 1. We devise a fully polynomial approximate scheme for the problem of finding the cheapest Stackelberg Strategy: given a performance requirement, our algorithm runs in time polynomial in n and {var_epsilon} and produces a Stackelberg strategy s, whose associated cost is within a 1 + {var_epsilon} factor of the optimum stackelberg strategy s*. The result is extended to obtain a polynomial-approximation scheme when instances are restricted to layered directed graphs in which each layer has a bounded number of vertices. 2. We then consider a two round Stackelberg strategy (denoted 2SS). In this strategy, the game consists of three rounds: a move by the leader followed by the moves of all the followers folowed again by a move by the leader who possibly reassigns some of the flows. We show that 2SS always dominates the one round scheme, and for some classes of latency functions, is guaranteed to be closer to the global social optimum. We also consider the variant where the leader plays after the selfish users have routed themselves, and observe that this dominates the one-round scheme. Extensions of the results to the special case when all the latency functions are linear are also presented. Our results extend the earlier results and answer an open question posed by Roughgarden [Ro01].« less
  • The paper introduces different types of Fuzzy tuning methods for the controller parameters of the firing and extinction angle controller of an HVDC link. The test system, a point to point DC link has been subjected to various small and large disturbances to examine the effectiveness of the proposed schemes. The current error and its derivative in case of rectifier and the gamma error and its derivative in case of the inverter are taken as the two principal signals to generate the change in the proportional and the integral gains according to a definite rule base. The results obtained havemore » been compared graphically to prove the superiority of the proposed controllers.« less
  • We consider the scheduling problem of minimizing a weighted sum of completion times under release dates. We present a simple randomized 2-approximation algorithm for the problem running in O(n log n) time. The algorithm applies to both the off-line and on-line settings with no difference in performance guarantees. In the off-line setting, the algorithm can be derandomized in two different ways, leading either to a deterministic 2-approximation algorithm running in O(n{sup 2}) time, or to a 2+1/{kappa}-approximation algorithm IC running in O(n log n + kn) time. In the on-line setting, a specific random choice gives a deterministic 1 +more » {radical}2-competitive algorithm. These bounds improve upon a bound of 2.45 in the off-line setting or in the randomized on-line setting, and upon a bound of 3 + {epsilon} in the deterministic on-line setting, it is based on comparing the weight of the schedule produced to the value of a linear programming (LP) relaxation. However, the algorithm and analysis differ from the approach developed in several respects. First, we simultaneously consider two equivalent LP relaxations for the problem: one involving completion time variables, the other preemptive time-indexed variables. The design of the algorithm is essentially based on the time-indexed relaxation; its analysis is based on the completion time relaxation. Moreover, we exploit properties of the optimum solutions to these LP relaxations, and not just of any feasible solution. Another important difference is that we do not relate directly the completion time of job j with its fractional completion time, but only in an amortized sense. Finally, we use randomization to avoid adversarial situations; this last step can also be seen as constructing n different schedules and keeping the best of them.« less
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