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Stochastic Scheduling

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Introduction

Models

  Scheduling a Batch of Stochastic Jobs

  Multi-Armed Bandits

  Scheduling Queueing Systems

References

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References

  1. Agrawala AK, Coffman Jr EG, Garey MR, Tripathi SK (1984) A stochastic optimization algorithm minimizing expected flow times on uniform processors. IEEE Trans Comput c‑33:351–356

    Google Scholar 

  2. Ansell PS, Glazebrook KD, Niño-Mora J, O'Keeffe M (2003) Whittle's index policy for a multi-class queueing system with convex holding costs. Math Methods Oper Res 57:21–39

    Article  MathSciNet  MATH  Google Scholar 

  3. Asawa M, Teneketzis D (1996) Multi-armed bandits with switching penalties. IEEE Trans Autom Control 41:328–348

    Article  MathSciNet  MATH  Google Scholar 

  4. Atkins D, Chen H (1995) Performance evaluation and scheduling control of queueing networks: fluid model heuristics. Queueing Sys Theory Appl 21:391–413

    Article  MathSciNet  MATH  Google Scholar 

  5. Banks JS, Sundaram RK (1994) Switching costs and the Gittins index. Econometrica 62:687–694

    Article  MATH  Google Scholar 

  6. Bell SL, and Williams RJ (2001) Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: asymptotic optimality of a threshold policy. Ann Appl Probab 11:608–649

    Article  MathSciNet  MATH  Google Scholar 

  7. Bellman R (1956) A problem in the sequential design of experiments. Sankhyā 16:221–229

    Google Scholar 

  8. Bertsimas D, Niño-Mora J (1996) Conservation laws, extended polymatroids and multiarmed bandit problems; a polyhedral approach to indexable systems. Math Oper Res 21:257–306

    Article  MathSciNet  MATH  Google Scholar 

  9. Bertsimas D, Niño-Mora J (1999) Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part I, the single-station case. Math Oper Res 24:306–330

    Article  MathSciNet  MATH  Google Scholar 

  10. Bertsimas D, Niño-Mora J (1999) Optimization of multiclass queueing networks with changeover times via the achievable region approach: Part II, the multi-station case. Math Oper Res 24:331–361

    Article  MathSciNet  MATH  Google Scholar 

  11. Bertsimas D, Niño-Mora J (2000) Restless bandits, linear programming relaxations and a primal-dual index heuristic. Oper Res 48:80–90

    Article  MathSciNet  MATH  Google Scholar 

  12. Bertsimas D, Paschalidis IC, Tsitsiklis JN (1994) Optimization of multiclass queueing networks: Polyhedral and nonlinear characterizations of achievable performance. Ann Appl Probab 4:43–75

    Article  MathSciNet  MATH  Google Scholar 

  13. Bradt RN, Johnson SM, Karlin S (1956) On sequential designs for maximizing the sum of n observations. Ann Math Statist 27:1060–1074

    Article  MathSciNet  MATH  Google Scholar 

  14. Bramson M (1994) Instability of FIFO queueing networks. Ann Appl Probab 4:414–431

    Article  MathSciNet  MATH  Google Scholar 

  15. Bruno J, Downey P, Frederickson GN (1981) Sequencing tasks with exponential service times to minimize the expected flow time or makespan. J ACM 28:100–113

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen H, Yao DD (1993) Dynamic scheduling of a multiclass fluid network. Oper Res 41:1104–1115

    Article  MathSciNet  MATH  Google Scholar 

  17. Chen YR, Katehakis MN (1986) Linear programming for finite state multi-armed bandit problems. Math Oper Res 11:180–183

    Article  MathSciNet  MATH  Google Scholar 

  18. Coffman Jr EG, Flatto L, Garey MR, Weber RR (1987) Minimizing expected makespans on uniform processor systems. Adv Appl Probab 19:177–201

    Article  MathSciNet  MATH  Google Scholar 

  19. Coffman Jr EG, Hofri M, Weiss G (1989) Scheduling stochastic jobs with a two-point distribution on two parallel machines. Probab Eng Inform Sci 3:89–116

    Article  MATH  Google Scholar 

  20. Coffman Jr EG, Mitrani I (1980) A characterization of waiting time performance realizable by single server queues. Oper Res 28:810–821

    Article  MathSciNet  MATH  Google Scholar 

  21. Cox DR, Smith WL (1961) Queues. Methuen, London

    Google Scholar 

  22. Dacre M, Glazebrook K, Niño-Mora J (1999) The achievable region approach to the optimal control of stochastic systems (with discussion). J Royal Stat Soc Ser B Methodol 61:747–791

    Article  MATH  Google Scholar 

  23. Dai JG, Lin W (2005) Maximum pressure policies in stochastic processing networks. Oper Res 53:197–218

    Article  MathSciNet  MATH  Google Scholar 

  24. Dai JG, Weiss G (1996) Stability and instability of fluid models for reentrant lines. Math Oper Res 21:115–134

    Article  MathSciNet  MATH  Google Scholar 

  25. Federgruen A, Groenevelt H (1988) Characterization and optimization of achievable performance in general queueing systems. Oper Res 36:733–741

    Article  MathSciNet  MATH  Google Scholar 

  26. Gittins JC (1979) Bandit processes and dynamic allocation indices (with discussion). J Royal Stat Soc Ser B Methodol 41:148–177

    MathSciNet  MATH  Google Scholar 

  27. Gittins JC (1989) Multi-Armed Bandit Allocation Indices. Wiley, Chichester

    MATH  Google Scholar 

  28. Gittins JC, Jones DM (1974) A dynamic allocation index for the sequential design of experiments. In: Gani J, Sarkadi K, Vincze I (eds) Progress in Statistics (European Meeting of Statisticians, Budapest, 1972). North-Holland, Amsterdam, pp 241–266

    Google Scholar 

  29. Glazebrook KD (1979) Scheduling tasks with exponential service times on parallel processors. J Appl Probab 16:685–689

    Article  MathSciNet  MATH  Google Scholar 

  30. Glazebrook KD, Niño-Mora J (1999) A linear programming approach to stability, optimisation and performance analysis for Markovian multiclass queueing networks. Ann Oper Res 92:1–18

    Article  MathSciNet  MATH  Google Scholar 

  31. Glazebrook KD, Niño-Mora J (2001) Parallel scheduling of multiclass \( M/M/m \) queues: approximate and heavy-traffic optimization of achievable performance. Oper Res 49:609–623

    Article  MathSciNet  MATH  Google Scholar 

  32. Harrison JM (1988) Brownian models of queueing networks with heterogeneous customer populations. In: Fleming W, Lions PL (eds) Stochastic Differential Systems, Stochastic Control Theory and Their Applications, vol 10. IMA Volumes in Mathematics and Its Applications. Springer, New York, pp 147–186

    Google Scholar 

  33. Harrison JM, Zeevi A (2004) Dynamic scheduling of a multiclass queue in the Halfin-Whitt heavy traffic regime. Oper Res 52:243–257

    Article  MathSciNet  MATH  Google Scholar 

  34. Jun T (2004) A survey on the bandit problem with switching costs. Economist 152:513–541

    Article  Google Scholar 

  35. Kallenberg LCM (1986) A note on M. N. Katehakis' and Y.‑R. Chen's computation of the Gittins index. Math Oper Res 11:184–186

    Article  MathSciNet  MATH  Google Scholar 

  36. Kämpke T (1987) On the optimality of static priority policies in stochastic scheduling on parallel machines. J Appl Probab 24:430–448

    Article  MathSciNet  MATH  Google Scholar 

  37. Kämpke T (1989) Optimal scheduling of jobs with exponential service times on identical parallel processors. Oper Res 37:126–133

    Article  MathSciNet  MATH  Google Scholar 

  38. Klimov GP (1974) Time-sharing service systems. I. Theory Probab Appl 19:532–551

    Article  MathSciNet  MATH  Google Scholar 

  39. Levy H, Sidi M (1990) Polling systems: applications, modeling, and optimization. IEEE Trans Commun 38:1750–1760

    Article  Google Scholar 

  40. Möhring RH, Schulz AS, Uetz M (1999) Approximations in stochastic scheduling: The power of LP-based priority policies. J ACM 46:924–942

    Article  MathSciNet  MATH  Google Scholar 

  41. Nain P, Tsoucas P, Walrand J (1989) Interchange arguments in stochastic scheduling. J Appl Probab 27:815–826

    Article  MathSciNet  Google Scholar 

  42. Niño-Mora J (2001) Restless bandits, partial conservation laws and indexability. Adv Appl Probab 33:77–98

    Google Scholar 

  43. Niño-Mora J (2002) Dynamic allocation indices for restless projects and queueing admission control: a polyhedral approach. Math Program Ser A 93:361–413

    Article  MATH  Google Scholar 

  44. Niño-Mora J (2006) Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue. Queueing Syst 54:281–312

    Article  MathSciNet  MATH  Google Scholar 

  45. Niño-Mora J (2006) Restless bandit marginal productivity indices, diminishing returns and optimal control of make-to-order/make-to-stock \( M/G/1 \) queues. Math Oper Res 31:50–84

    Article  MathSciNet  MATH  Google Scholar 

  46. Niño-Mora J (2007) A \( (2/3)n^3 \) fast-pivoting algorithm for the Gittins index and optimal stopping of a Markov chain. INFORMS J Comput 19:596–606

    Article  MathSciNet  Google Scholar 

  47. Niño-Mora J (2007) Dynamic priority allocation via restless bandit marginal productivity indices (with discussion). Top 15:161–198

    Article  MathSciNet  MATH  Google Scholar 

  48. Niño-Mora J (2007) Marginal productivity index policies for admission control and routing to parallel multi-server loss queues with reneging. In: Network Control and Optimization: Proceedings of the First EuroFGI International Conference (NET-COOP 2007, Avignon, France), vol 4465. Lecture Notes in Computer Science. Springer, Berlin, pp 138–149

    Google Scholar 

  49. Niño-Mora J (2008) A faster index algorithm and a computational study for bandits with switching costs. INFORMS J Comput 20: in press

    Google Scholar 

  50. Papadimitriou CH (1985) Games against nature. J Comput Syst Sci 31:288–301

    Article  MathSciNet  MATH  Google Scholar 

  51. Papadimitriou CH, Tsitsiklis JN (1987) On stochastic scheduling with in-tree precedence constraints. SIAM J Comput 16:1–6

    Article  MathSciNet  MATH  Google Scholar 

  52. Papadimitriou CH, Tsitsiklis JN (1999) The complexity of optimal queuing network control. Math Oper Res 24:293–305

    Article  MathSciNet  MATH  Google Scholar 

  53. Pinedo M (1983) Stochastic scheduling with release dates and due dates. Oper Res 31:559–572

    Article  MATH  Google Scholar 

  54. Reiman MI, Wein LM (1998) Dynamic scheduling of a two-class queue with setups. Oper Res 4:532–547

    Article  MathSciNet  Google Scholar 

  55. Righter R (1988) Job scheduling to minimize expected weighted flowtime on uniform processors. Syst Control Lett 10:211–216

    Article  MathSciNet  MATH  Google Scholar 

  56. Robbins H (1952) Some aspects of the sequential design of experiments. Bull Am Math Soc 58:527–535

    Article  MathSciNet  MATH  Google Scholar 

  57. Rothkopf MH (1966) Scheduling with random service times. Manag Sci 12:707–713

    Article  MathSciNet  Google Scholar 

  58. Sevcik KC (1974) Scheduling for minimum total loss using service time distributions. J ACM 21:66–75

    Article  MathSciNet  Google Scholar 

  59. Shanthikumar JG, Yao DD (1992) Multiclass queueing systems: Polymatroidal structure and optimal scheduling control. Oper Res 40:S293–S299

    Article  MathSciNet  Google Scholar 

  60. Smith WE (1956) Various optimizers for single-stage production. Nav Res Logist Quart 3:59–66

    Article  Google Scholar 

  61. Tcha DW, Pliska SR (1977) Optimal control of single-server queueing networks and multiclass \( M/G/1 \) queues with feedback. Oper Res 25:248–258

    Article  MathSciNet  MATH  Google Scholar 

  62. Thompson WR (1933) On the likelihood that one unknown probability exceeds another in view of the evidence of two samples. Biometrika 25:285–294

    MATH  Google Scholar 

  63. Tsitsiklis JN (1994) A short proof of the Gittins index theorem. Ann Appl Probab 4:194–199

    Article  MathSciNet  MATH  Google Scholar 

  64. Varaiya PP, Walrand JC, Buyukkoc C (1985) Extensions of the multiarmed bandit problem: the discounted case. IEEE Trans Autom Control 30:426–439

    Article  MathSciNet  MATH  Google Scholar 

  65. Weber RR (1992) Scheduling jobs with stochastic processing requirements on parallel machines to minimize makespan or flowtime. J Appl Probab 19:167–182

    Article  Google Scholar 

  66. Weber RR (1992) On the Gittins index for multiarmed bandits. Ann Appl Probab 2:1024–1033

    Article  MathSciNet  MATH  Google Scholar 

  67. Weber RR, Varaiya P, Walrand J (1986) Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime. J Appl Probab 23:841–847

    Article  MathSciNet  MATH  Google Scholar 

  68. Weber RR, Weiss G (1990) On an index policy for restless bandits. J Appl Probab 27:637–648

    Article  MathSciNet  MATH  Google Scholar 

  69. Wein LM (1992) Dynamic scheduling of a multiclass make-to-stock queue. Oper Res 40:724–735

    Article  MathSciNet  MATH  Google Scholar 

  70. Weiss G (1988) Branching bandit processes. Probab Eng Inf Sci 2:269–278

    Article  MATH  Google Scholar 

  71. Weiss G (1992) Turnpike optimality of Smith's rule in parallel machines stochastic scheduling. Math Oper Res 17:255–270

    Article  MathSciNet  MATH  Google Scholar 

  72. Weiss G, Pinedo M (1980) Scheduling tasks with exponential service times on non-identical processors to minimize various cost functions. J Appl Probab 17:197–202

    Article  MathSciNet  Google Scholar 

  73. Whittle P (1980) Multiarmed bandits and the Gittins index. J Royal Stat Soc Ser B Method 42:143–149

    MathSciNet  MATH  Google Scholar 

  74. Whittle P (1988) Restless bandits: Activity allocation in a changing world. In: Gani J (ed) A celebration of applied probability, spec vol 25A. Appl Probab Trust, Sheffield, pp 287–298

    Google Scholar 

  75. Wie SH, Pinedo M (1986) On minimizing the expected makespan and flow time in stochastic flow shops with blocking. Math Oper Res 11:336–342

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Statistics, Universidad Carlos III de Madrid, Getafe, Spain

    José Niño-Mora

Authors
  1. José Niño-Mora
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Niño-Mora, J. (2008). Stochastic Scheduling . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_665

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