Skip to main content
SpringerLink
Log in

Queueing models of secondary storage devices

  • Invited Paper
  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

Queueing theory has occupied an important role in the analysis of computer storage structures and algorithms. In this survey we focus on secondary or auxiliary storage devices, which often comprise the principal bottleneck in the overall performance of computer systems. We begin with descriptions of the more important devices, such as disks and drums, and a general discussion of related queueing models. Server motion and dependent successive services are salient features of these models. Widely used, generic results are presented and then applied to specific devices. The paper concludes with a discussion of open problems.

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

  1. Y. Bard, A simple approach to system modeling, Performance Evaluation1(1981)225.

    Google Scholar 

  2. S.C. Bruell and G. Balbo,Computational Algorithms for Closed Queueing Networks (Elsevier North-Holland, New York, 1980).

    Google Scholar 

  3. A.R. Calderbank, E.G. Coffman, Jr., and L. Flatto, Optimum head separation in a disk with two read/write heads, J. Assoc. Comput. Mach. 31(1984)826.

    Google Scholar 

  4. A.R. Calderbank, E.G. Coffman, Jr., and L. Flatto, Two-server sequencing problems, Math. Oper. Res. 10(1985)585.

    Google Scholar 

  5. A.R. Calderbank, E.G. Coffman Jr., and L. Flatto, Optimal placement of directories on a computer disk, AT&T Bell Laboratories, Murray Hill, NJ 07974 (1985), to appear.

    Google Scholar 

  6. E.G. Coffman, Jr., Analysis of a drum input/output queue under scheduled operation in a paged computer system, J. Assoc. Comput. Mach. 16(1969)73; Corrigendum: 16(1969)646.

    Google Scholar 

  7. E.G. Coffman, Jr. and E.N. Gilbert, A continuous polling system with constant service, IEEE Trans. Infor. Theory (1985), to appear.

  8. E.G. Coffman, Jr., and E.N. Gilbert, Analysis of a moving server on the line, AT&T Bell Laboratories, Murray Hill, NJ 07974 (1986), to appear.

    Google Scholar 

  9. E.G. Coffman, Jr., and M. Hofri, A class of FIFO queues arising in computer systems, Oper. Res. 25, 5(1978)864.

    Google Scholar 

  10. E.G. Coffman, Jr., and M. Hofri, On the expected performance of scanning disks, SIAM J. Comput. 11, 1(1982)60.

    Google Scholar 

  11. S. Daniel and R. Geist, V-SCAN: An adapative disk scheduling algorithm,Proc. IEEE Int. Symp. on Comp. Sys. Org., New Orleans (1983).

  12. P.J. Denning, Effects ofscheduling on file memory operations.iVoc.AFIPS, SJCC31(1961)9.

  13. B.T. Doshi, An M/G/1 queue with variable vacations,Proc. Int. Conf. on Modelling Techniques and Tools for Perf. Analaysis, CERAM, France (1985).

    Google Scholar 

  14. B.T. Doshi, Queueing systems with vacations, Queueing Systems 1(1986)29.

    Google Scholar 

  15. M. Eisenberg, Queues with periodic service and changeover time, Oper. Res. 20(1972)440.

    Google Scholar 

  16. S.W. Fuhrmann and R.B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacations, Oper. Res. 33(1985)1117.

    Google Scholar 

  17. S.H. Fuller and F. Baskett, An analysis of drum storage units, J. Assoc. Comput. Mach. 22, 1 (1975)83.

    Google Scholar 

  18. E. Gelenbe and I. Mitrani,Analysis and Synthesis of Computer Systems (Academic Press, London, 1980).

    Google Scholar 

  19. M. Hofri, Disk scheduling: FCFS versus SSTF revisited, Comm. ACM 23, 11(1980)645. Corrigendum: 24,11(1981)772.

    Google Scholar 

  20. M. Hofri, Should the two-headed disk be greedy? -Yes, it should, Inform. Process. Lett. 16(1983)83.

    Google Scholar 

  21. M. Hofri, Analysis of interleaved storage via a constant-service queueing system with Markov-chain driven input, J. Assoc. Comput. Mach. 31, 3(1984)628.

    Google Scholar 

  22. M. Hofri, An M/G/1 queue with vacations and a threshold, Technical Report No. 375, Computer Science Dept., Technion, Haifa, Israel (1985).

    Google Scholar 

  23. M. Hofri, Queueing systems with a procrastinating server, Perf. Eval. Review 14(1986)1.

    Google Scholar 

  24. M. Hofri and Z. Rosberg, Optimally controlled CCD shift registers (optimal interception on a recurrent trajectory), Stochastic Models (1985), to appear.

  25. J.J. Hunter, On the moments of Markov renewal processes, Adv. in Appl. Prob. 1(1969)188.

    Google Scholar 

  26. F.P. Kelly,Reversibility and Stochastic Networks (Wiley, Chichester, 1979).

    Google Scholar 

  27. G.F. Klimov, Time sharing service systems I, Theory Prob. Appl. 19(1974)532.

    Google Scholar 

  28. W.A. Massey, Open networks of queue: their algebraic structure and estimating their transient behaviour, Ann. Appl. Prob. (1984).

  29. R.E. Matick,Computer Storage Systems and Technology (Wiley, New York, 1977).

    Google Scholar 

  30. I. Meilijson and G. Weiss, Multiple feedback at a single-server station, Stochastic Process. Appl. 5(1977)195.

    Google Scholar 

  31. J. McKenna and D. Mitra, Asymptotic expansions and integral representations of moments of queue lengths in closed Markovian networks, J. Assoc. Comput. Mach. 31, 2(1984)346.

    Google Scholar 

  32. M.F. Neuts, Moment formulas for the Markov renewal branching process, Adv. in Appl. Prob. 8(1976)690.

    Google Scholar 

  33. M.F. Neuts, Some explicit formulas for the steady-state behaviour of the queue with semi-Markovian service times, Adv. in Appl. Prob. 9(1977)141.

    Google Scholar 

  34. M.F. Neuts,Matrix-Geometric Solutions in Stochastic Models, an Algorithmic Approach (The Johns Hopkins University Press, Baltimore, (1981).

    Google Scholar 

  35. I.P. Page and R.T. Wood, Empirical analysis of a moving head disc model with two heads separated by a fixed number of tracks, Comput. J. 24(1981)339.

    Google Scholar 

  36. K. Ross, personal communication, 1985 (Dept. of System Eng., University of Pennsylvania).

  37. S.M. Ross,Introduction to Stochastic Dynamic Programming (Academic Press, New York, 1983).

    Google Scholar 

  38. C.H. Sauer, K.M. Chandy,Computer Systems Performance Modeling (Prentice-Hall, Englewood Cliffs, NJ, 1981).

    Google Scholar 

  39. C.E. Skinner, A priority queueing system with server walking time, Oper. Res. 15(1967)278.

    Google Scholar 

  40. P.M. Snyder and W.J. Stewart, A comparison of two numerical methods for solving queueing phenomena, Technical Report, Dept. of Computer Science, North Carolina State University, Raleigh (1983).

    Google Scholar 

  41. P.D. Welch, On a generalized M/G/1 queueing process in which the first customer in each busy period receives exceptional service, Oper. Res. 12(1966)736.

    Google Scholar 

  42. C.K. Wong,Algorithmic Studies in Mass Storage Systems (Computer Science Press Inc., 1982)

  43. J. Zahorjan, J.N.P. Hume and K.C. Sevcik, A queueing model of a rotational position sensing disk system, INFOR -Can. J. Oper. Res. Inform. Process. 16(1978) 199.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, 07974, Murray Hill, New Jersey, USA

    E. G. Coffman Jr.

  2. Department of Computer Science, The Technion, 32000, Haifa, Israel

    M. Hofri

Authors
  1. E. G. Coffman Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Hofri
    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

Coffman, E.G., Hofri, M. Queueing models of secondary storage devices. Queueing Syst 1, 129–168 (1986). https://doi.org/10.1007/BF01536186

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01536186

Keywords and phrases

Search

Navigation