@preamble{ "\newcommand{\noopsort}[1]{} " # "\newcommand{\printfirst}[2]{#1} " # "\newcommand{\singleletter}[1]{#1} " # "\newcommand{\switchargs}[2]{#2#1} " } @string{rrw="R.R. Weber"} @string{gw="G. Weiss"} @string{kg="Glazebrook, K.D."} @string{aap="Adv. Appl. Prob."} @string{jap="J. Appl. Prob."} @string{mor="Mathematics of Operations Research"} @string{ms="Management Science"} @string{om="Omega"} @string{or="Operations Research"} @string{naval="Naval Research Logistics Quarterly"} @string{peis="Probability in the Engineering and Informational Sciences"} @string{auto="IEEE Trans. Auto. Control"} @article{Agr84, author = {Agrawala, A.K. and {Coffman Jr}, E.G. and Garey, M.R. and Tripathi, S.K.}, title = {A Stochastic Optimization Algorithm Minimizing Expected Flow Times on Uniform Processors}, journal = {IEEE Trans. on Computers}, year = 1984, volume = {{\bf 33}}, pages = {351--356} } @article{Bag70, author = {Bagga, P.C.}, title = {{$N$}-Job, 2 Machine Sequencing Problem with Stochastic Service Times}, journal = {Opsearch}, year = 1970, volume = {{\bf 7}}, pages = {184--199} } @techreport{Bru77a, author = {Bruno, J.}, title = {Sequencing Tasks with Exponential Service Times on Parallel Machines}, institution = {Department of Computer Science, University of California at Santa Barbara}, year = 1977 } @techreport{Bru77b, author = {Bruno, J. and Downey, P.}, title = {Sequencing Tasks with Exponential Service Times on Parallel Machines}, institution = {Department of Computer Science, University of California at Santa Barbara}, year = 1977 } @article{Bru81, author = {Bruno, J. and Downey, P. and Fredrickson, G.N.}, title = {Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan}, journal = jacm, year = 1981, volume = {{\bf 28}}, pages = {100--113} } @inproceedings{Cha75, author = {Chandy, K.M. and Reynolds, P.F.}, title = {Scheduling Partially Ordered Tasks with Probabilistic Execution Times}, booktitle = {Fifth Symposium on Operating System Principles}, year = 1975, pages = {169--177} } @article{Cha91b, author = {Chang, C-S. and Nelson, R. and Pinedo, M.}, title = {Scheduling Two Classes of Exponential Jobs on Parallel Processors: Structural Results and Worst Case Analysis}, journal = jap , year = 1991 } @article{Cha91c, author = {Chang, C-S. and Hordijk, A. and Righter, R.}, title = {Note on the Stochastic Optimality of {SEPT} and {LEPT} in Parallel Machine Scheduling}, journal = { }, year = 1991, pages = { } } @article{Cha92, author = {Chang, C-S. and Chao, X. and Pinedo, M. and Weber, R.R.}, title = {On the Optimality of the {LEPT} rule and the $c\mu$ Rule for Machines in Parallel}, journal = jap, year = 1992, volume = {{\bf 29}}, pages = {667--681} } @article{Cha94, author = {Chang, C-S. and Righter, R.}, title = {The Optimality of {LEPT} in Parallel Machine Scheduling}, journal = jap, year = 1994, volume = {{\bf 31}}, pages = {788--796} } @inproceedings{Cof82, author = {{Coffman Jr}, E.G. and Fredrickson, G.N. and Lueker, G.S.}, title = {Probabilistic Analysis of the {LPT} Processor Scheduling Heuristic}, booktitle = {Deterministic and Stochastic Scheduling}, year = 1982, editor = {M.A.H. 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Ott}, publisher = {Birkhauser, Boston, MA} } @article{Web82b, author = rrw, title = {Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime}, journal = jap, year = 1982, volume = {{\bf 19}}, pages = {167--182} } @article{Web86b, author = rrw # {and Varaiya, P. and Walrand, J.}, title = {Scheduling jobs with stochastically ordered processing requirements to minimize expected flowtime}, journal = jap, year = 1986, volume = {{\bf 23}}, pages = {841--847} } @incollection{Web88a, author = rrw, title = {Stochastic scheduling on parallel processors and minimization of concave functions of completion times}, booktitle = {Stochastic Differential Systems, Stochastic Control Theory and Applications}, year = 1988, editor = {W. Fleming and P.L. Lions}, publisher = {Springer-Verlag, New York}, pages = {601--609}, volume = {{\bf 10}} } @article{Wei80, author = {Weiss, G. and Pinedo, M.}, title = {Scheduling Tasks with Exponential Service Times on Non-Identical Processors to Minimize Various Cost Functions}, journal = jap, year = 1980, volume = {{\bf 17}}, pages = {187--202} } @inproceedings{Wei82, author = {Weiss, G.}, title = {Multiserver Stochastic Scheduling}, booktitle = {Deterministic and Stochastic Scheduling}, year = 1982, editor = {M.A.H. Dempster and J.K. Lenstra and A.H.G. 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Queyranne}}, year = 1990, volume = {{\bf 26}}, pages = {299--303} } @article{Wei91, author = {Weiss, G.}, title = {Approximation results in Parallel Machines Stochastic Scheduling}, journal = { }, year = 1991 , pages = { } } @article{Wei92, author = {Weiss, G.}, title = {Turnpike Optimality of {S}mith's Rule in Parallel Machines Stochastic Scheduling}, journal = or, year = 1988 } @article{Xu88, author = {Xu, S.H.}, title = {Scheduling Stochastic Jobs on Uniform Processors to Minimize Flowtime in Distribution}, journal = { }, year = 1988 } @article{Xu89a, author = {Xu, S.H.}, title = {On {K}umar and {W}alrand's Conjecture for Job Routing in Parallel Processors Systems}, journal = { }, year = 1989 , pages = { } } @article{Xu90, author = {Xu, S.H. and Mirchandani, P.B. and Kumar, S.P.R. and} # rrw , title = {Stochastic dispatching of multi-priority jobs to heterogeneous processors}, journal = jap, year = 1990, volume = {{\bf 27}}, pages = {852--861} } @article{Xu91a, author = {Xu, S.H. and Shanthikumar, J.G.}, title = {Optimal Expulsion Control --- a Dual Approach to Admission Control of Ordered-Entry System}, journal = { }, year = 1991 , pages = { } } @article{Xu91b, author = {Xu, S.H.}, title = {Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines}, journal = peis, year = 1991, volume = {{\bf 5}}, pages = {333--348} } @article{Xu91c, author = {Xu, S.H.}, title = {Minimizing Expected Makespans of Multi-Priority Classes of Jobs on Uniform Processors}, journal = {Op. 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