Skip to main content
SpringerLink
Log in

Task allocation in multiserver systems — A survey of results

  • Queueing Models For Performance Analysis Of Computer And Communication Systems
  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

Jobs consisting of one or more tasks arrive to a system comprising several servers, each with its own queue. Each task requires a single service at any of the servers, and a job completes service when all its constituent tasks have been serviced. Such models arise in the performance modelling of distributed computing systems, computer communication networks, and manufacturing systems. We survey the literature on this class of models.

We classify jobs as being of one of three types: single tasks, multitask with precedence constraints, and multitask stream jobs. After surveying the optimal allocation problem for single task jobs, we discuss the results on the performance analysis and optimal allocation of tasks for the other two job types.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Agrawala A, Tripathi S 1981 On the optimality of semidynamic routing schemes.Inf. Process. Lett. 13: 20–22

    Article  MATH  Google Scholar 

  • Baccelli F, Makowski A M 1990 Synchronization in queuing systems: Instochastic analysis of computer and communication system (ed.) H Takagi (Amsterdam: North Holland/Elsevier Science Publishers)

    Google Scholar 

  • Baccelli F, Makowski A M, Schwartz A 1985 Simple computable bounds and approximations for the fork-join queue.Proc. Int. Seminar on Computer Networking and Performance Evaluation

  • Baccelli F, Massey W A, Towsley D 1989 Acyclic fork-join queuing networks.J. Assoc. Comput. Mach. 36: 615–642

    MATH  MathSciNet  Google Scholar 

  • Barlow R E, Proschan F 1975Statistical theory of reliability and life testing: Probability models (New York: Holt, Rinehart and Winston)

    Google Scholar 

  • Bonomi F, Kumar A 1990 Adaptive optimal load balancing in a non-homogeneous multiserver system with a central job scheduler.IEEE Trans. Comput. 39: 1232–1250

    Article  Google Scholar 

  • Chow Y C, Kohler W 1979 Models of dynamic load balancing in a heterogeneous multiple processor system.IEEE Trans. Comput. 28: 354–361

    Article  MATH  MathSciNet  Google Scholar 

  • de Souza e Silva E, Gerla M 1984 Load balancing in distributed systems, with multiple classes and site constraints.Performance 84 17–33

    Google Scholar 

  • Eager D L, Lazowska E D, Zahorjan J 1986 Adaptive load sharing in homogeneous distributed systemsIEEE Trans. Software Eng. 12: 662–675

    Google Scholar 

  • Ephremides A, Varaiya P, Walrand J 1980 A simple dynamic routing problem:IEEE Trans. Autom. Control. 25: 690–693

    Article  MATH  MathSciNet  Google Scholar 

  • Flatto L, Hahn S 1984 Two parallel queues created by arrivals with two demands I:SIAM J. Appl. Math. 44: 1041–1053

    Article  MATH  MathSciNet  Google Scholar 

  • Flatto L, McKean H P 1977 Two queues in parallel.Commun. Pure Appl. Math. 30: 255–263

    Article  MATH  MathSciNet  Google Scholar 

  • Flores C 1990 Diffusion approximations for computer communications networks: InStochastic analysis of computer and communication systems (ed.) H Takagi (Amsterdam: North Holland/Elsevier Science)

    Google Scholar 

  • Foschini G J 1977 On heavy traffic diffusion analysis and dynamic routing in packet switched networks. InComputer performance (eds) K M Chandy, M Reiser (Amsterdam: North Holland)

    Google Scholar 

  • Foschini G J, Salz J 1978 A basic dynamic routing problem and diffusion.IEEE Trans. Commun. 26: 320–327

    Article  MATH  Google Scholar 

  • Gün L, Jean-Marie A 1990 Resequencing in parallel M/G/1 queues with Bernoulli loading.Oper. Res. (submitted)

  • Hajek B 1984 Optimal control of two interacting service stations.IEEE Trans. Autom. Control. 29: 491–499

    Article  MATH  MathSciNet  Google Scholar 

  • Hajek B 1985 Extremal splitting of point processes.Math. Oper. Res. 10: 543–556

    Article  MATH  MathSciNet  Google Scholar 

  • Jean-Marie A 1988 Load balancing in a system of two queues with resequencing.Performance ’87 75–88

  • Jean-Marie A, Gün L 1990 Asymptotic results for parallel queues with resequencing.J. Assoc. Comput. Mach. (submitted)

  • Kemae T, Krengel U, O’Brien G L 1977 Stochastic inequalities on partially ordered spaces.Ann. Probab. 5: 899–912

    Article  Google Scholar 

  • Kuri J 1990Comparative performance evaluation of routing strategies in connection-oriented and connectionless data networks. M E thesis, Electrical Communication Engineering Department, Indian Institute of Science, Bangalore

    Google Scholar 

  • Kuri J, Kumar A 1991 On the optimal allocation of customers that must depart in sequence.Oper. Res. Lett. (submitted)

  • Lin W, Kumar P R 1987 Optimal control of a queuing system with two heterogeneous servers.IEEE Trans. Autom. Control. 29: 696–703

    Article  MathSciNet  Google Scholar 

  • Mirchandaney R, Towsley D, Stankovic J A 1989 Analysis of the effects of delays on load sharing.IEEE Trans. Comput. 38: 1513–1525

    Article  Google Scholar 

  • Nelson R D, Philips T K 1990 An approximation for the mean response time for shortest queue routing with general interarrival and service times. IBM Research Report, RC-15429 (# 68659)

  • Nelson R, Tantawi A N 1988 Approximate analysis of fork join synchronisation in parallel queues.IEEE Trans. Comput. 37: 739–743

    Article  Google Scholar 

  • Ni L M, Hwang K 1985 Optimal load balancing in a multiple processor system with multiple job classes.IEEE Trans. Software Eng. 11: 491–496

    Article  MathSciNet  Google Scholar 

  • Reiman M I 1983 Some diffusion approximation with state space collapse.Modelling and performance evaluation methodology (eds) F Baccelli, G Fayolle (Lecture Notes in Control and Inf. Science) Vol. 60. (Berlin: Springer Verlag)

    Google Scholar 

  • Ross S 1983Stochastic processes (New York: John Wiley)

    MATH  Google Scholar 

  • Shorey R 1990Performance analysis and scheduling of stochastif fork-join jobs in a multicomputer system. M Sc (Eng). thesis, Electrical Communication Engineering Department, Indian Institute of Science, Bangalore

    Google Scholar 

  • Smith D R, Whitt W 1981 On the efficiency of shared resources in queuing systems.Bell Syst. Tech. J. 60: 39–56

    MATH  MathSciNet  Google Scholar 

  • Stoyan D 1983Comparison methods for queues and other stochastic models (New York: John Wiley)

    MATH  Google Scholar 

  • Tanenbaum A 1988Computer networks, 2nd edn (Englewood Cliffs,NJ: Prentice Hall)

    Google Scholar 

  • Tantawi A N, Towsley D 1984 Optimal load balancing in distributed computer systems. Tech. Rep.rc-10346,ibm T J Watson Research Center

  • Varma S 1987Some problems in queuing systems with resequencing, M S thesis, Electrical Engineering Dept., Univ. of Maryland, College Park, Maryland; Also Tech. Rep.TR-87-192, Systems Res. Center, Univ. of Maryland, College Park.

    Google Scholar 

  • Walrand J 1988An introduction to queuing networks (Englewood Cliffs,NJ: Prentice Hall)

    Google Scholar 

  • Weber R R 1978 On the optimal assignment of customers to parallel queues.J. Appl. Probab. 15: 406–413

    Article  MATH  Google Scholar 

  • Whitt W 1986 Deciding which queue to join: Some counterexamples.Oper. Res. 34: 55–62

    MATH  MathSciNet  Google Scholar 

  • Winston W 1977 Optimality of the shortest line discipline.J. Appl. Probab. 14: 181–189

    Article  MATH  MathSciNet  Google Scholar 

  • Wolff R W 1977 An upper bound for multi-channel queues.J. Appl. Probab. 14: 884–888

    Article  MATH  MathSciNet  Google Scholar 

  • Wolff R W 1989Stochastic modelling and the theory of queues (Englewood Cliffs,NJ: Prentice Hall)

    Google Scholar 

  • Yum T S 1981 The design and analysis of a semidynamic deterministic routing rule:IEEE Trans. Commun. 29: 498–504

    Article  Google Scholar 

  • Yum T S, Schwartz M 1981 The join-biased queue rule and its application to routing in computer communication networks.IEEE Trans. Commun. 29: 505–511

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Communication Engineering, Indian Institute of Science, 560012, Bangalore, India

    Anurag Kumar

Authors
  1. Anurag Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, A. Task allocation in multiserver systems — A survey of results. Sadhana 15, 381–395 (1990). https://doi.org/10.1007/BF02811333

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02811333

Keywords

Search

Navigation