A Survey on Solution Methods for Task Graph Models

We give in this paper a survey on models developed in the literature using the concept of task graphs, focusing on solution techniques. Diierent types of task graphs are considered, from PERTS networks to random task graphs. Reviewed solution methods include exact computations and bounds.

[1]  Paul R. Kleindorfer,et al.  Bounding Distributions for Stochastic Logic Networks , 1974 .

[2]  Charles M. Newman,et al.  Chain Lengths in Certain Random Directed Graphs , 1992, Random Struct. Algorithms.

[3]  F. B. Cowell,et al.  The Completion Time of PERT Networks , 1983 .

[4]  Clifford George Bigelow.  Letter to the Editor—Bibliography on Project Planning and Control by Network Analysis: 1959–1961 , 1962 .

[5]  P. Konstantopoulos,et al.  Estimates of cycle times in stochastic petri nets , 1992 .

[6]  Bajis Dodin.  Reducibility of stochastic networks , 1985 .

[7]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[8]  Vidyadhar G. Kulkarni,et al.  A classified bibliography of research on stochastic PERT networks: 1966-1987 , 1989 .

[9]  Harry Kesten.  Bounds for the Distribution of # W , 1982 .

[10]  Józef Łukaszewicz,et al.  Letter to the Editor-On the Estimation of Errors Introduced by Standard Assumptions Concerning the Distribution of Activity Duration in PERT Calculations , 1965 .

[11]  Jerzy Kamburowski.  Two-point approximations for activity times in PERT networks , 1985 .

[12]  Sergio Lerda-Olberg.  Letter to the Editor - Bibliography on Network-Based Project Planning and Control Techniques: 1962-1965 , 1966, Oper. Res..

[13]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[14]  Zhen. Liu.  Modèles d'exécutions parallèles sur des systèmes multiprocesseurs : analyse et optimisation , 1989 .

[15]  Peter J. B. King,et al.  On the Execution of Programs by Many Processors , 1983, Performance.

[16]  A. W. Wortham,et al.  A Statistical Theory for PERT Critical Path Analysis , 1966 .

[17]  J. J. Martin.  Distribution of the Time Through a Directed, Acyclic Network , 1965 .

[18]  George B. Kleindorfer,et al.  Bounding Distributions for a Stochastic Acyclic Network , 1971, Oper. Res..

[19]  Pierre Cubaud.  Modeles et outils pour la prediction de performance des systemes informatiques paralleles , 1992 .

[20]  F. Baccelli,et al.  Comparison properties of stochastic decision free Petri nets , 1992 .

[21]  Bajis M. Dodin,et al.  Bounding the Project Completion Time Distribution in PERT Networks , 1985, Oper. Res..

[22]  Jean-Marc Vincent,et al.  Stochastic Bounds on Execution Times of Parallel Programs , 1991, IEEE Trans. Software Eng..

[23]  P. C. Roberts,et al.  Stochastic-network Reduction and Sensitivity Techniques in a Cost Effectiveness Study of a Military Communications System , 1970 .

[24]  K. MacCrimmon,et al.  An Analytical Study of the PERT Assumptions , 1964 .

[25]  F. Baccelli,et al.  On a Class of Stochastic Recursive Sequences Arising in Queueing Theory , 1992 .

[26]  H. Robbins,et al.  A class of dependent random variables and their maxima , 1978 .

[27]  Vidyadhar G. Kulkarni,et al.  Markov and Markov-Regenerative pert Networks , 1986, Oper. Res..

[28]  François Baccelli,et al.  Parallel simulation of stochastic Petri nets using recurrence equations , 1993, TOMC.

[29]  L. Ringer.  Numerical Operators for Statistical PERT Critical Path Analysis , 1969 .

[30]  H. Frank,et al.  Shortest Paths in Probabilistic Graphs , 1969, Oper. Res..

[31]  Kishor S. Trivedi,et al.  Performance and Reliability Analysis Using Directed Acyclic Graphs , 1987, IEEE Transactions on Software Engineering.

[32]  D. J. A. Welsh.  Letter to the Editor-Errors Introduced by a PERT Assumption , 1965 .

[33]  Erol Gelenbe,et al.  A performance model of block structured parallel programs , 1986 .

[34]  Marcel F. Neuts,et al.  Matrix-Geometric Solutions in Stochastic Models , 1981 .

[35]  Albert G. Greenberg,et al.  Algorithms for unboundedly parallel simulations , 1991, TOCS.

[36]  Luc Devroye.  Inequalities for the Completion Times of Stochastic PERT Networks , 1979, Math. Oper. Res..

[37]  Pierre N. Robillard,et al.  Technical Note - Expected Completion Time in Pert Networks , 1976, Oper. Res..

[38]  R. J. Joenk,et al.  IBM journal of research and development: information for authors , 1978 .

[39]  A. Alan B. Pritsker,et al.  GERT - Graphical Evaluation and Review Technique , 1966 .

[40]  N. L. Lawrie,et al.  Comparison Methods for Queues and Other Stochastic Models , 1984 .

[41]  Marco Ajmone Marsan,et al.  Performance models of multiprocessor systems , 1987, MIT Press series in computer systems.

[42]  Salah E. Elmaghraby,et al.  Activity networks: Project planning and control by network models , 1977 .