Queueing Systems

, Volume 2, Issue 2, pp 115–145 | Cite as

Polling and greedy servers on a line

  • E. G. CoffmanJr.
  • E. N. Gilbert
Contributed Paper

Abstract

A single server moves with speed υ on a line interval (or a circle) of length (circumference)L. Customers, requiring service of constant durationb, arrive on the interval (or circle) at random at mean rate λ customers per unit length per unit time. A customer's mean wait for service depends partly on the rules governing the server's motion. We compare two different servers: thepolling server and thegreedy server. Without knowing the locations of waiting customers, a polling server scans endlessly back and forth across the interval (or clockwise around the circle), stopping only where it encounters a waiting customer. Knowing where customers are waiting, a greedy server always travels toward the current nearest one. Except for certain extreme values of υ,L, b, andλ, the polling and greedy servers are roughly equally effective. Indeed, the simpler polling server is often the better. Theoretical results show, in most cases, that the polling server has a high probability of moving toward the nearest customer, i.e. moving as a greedy server would. The greedy server is difficult to analyze, but was simulated on a computer.

Keywords

Polling systems disk systems disk SCAN policy shortest-seek-time-first disk scheduling moving-server systems 

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References

  1. [1]
    E.G. Coffman, Jr. and E.N. Gilbert, A continuous polling system, IEEE Trans. Inf. Th., IT-3 2(1986)5 84.Google Scholar
  2. [2]
    E.G. Coffman, Jr. and M. Hofri, On the expected performance of scanning disks, SIAM J. Comput. 11(1982)60.Google Scholar
  3. [3]
    E.G. Coffman, Jr. and M. Hofri, Queueing analyses of secondary storage devices, Queueing Systems 1(1986)129.Google Scholar
  4. [4]
    R. Geist and S. Daniel, A continuum of disk scheduling algorithms, Tech. Rep., Computer Science Dept., Clemson University, Clemson, NC (1985); see also S. Daniel and R. Geist, V-SCAN: An adaptive disk scheduling algorithm,Proc. IEEE Int. Symp. on Comp. Sys. Org., New Orleans (1983).Google Scholar
  5. [5]
    M. Hofri, Disk scheduling: FCFS vs. SSTF revisited, Comm. ACM 23(1980)645.Google Scholar
  6. [6]
    L.B.W. Jolley,Summation of Series (Dover Publications, 1961).Google Scholar
  7. [7]
    D.E. Knuth,The Art of Computer Programming: Sorting and Searching, Vol. III (Addison-Wesley, Reading, MA, 1973) (see pp. 254–255, 259–264).Google Scholar
  8. [8]
    T. Teorey and T. Pinkerton, A comparative analysis of disk scheduling policies, Comm. ACM 15(1972)177.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1987

Authors and Affiliations

  • E. G. CoffmanJr.
    • 1
  • E. N. Gilbert
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA

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