Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T18:53:49.790Z Has data issue: false hasContentIssue false
  • English
  • Français

Further results for dynamic scheduling of multiclass G/G/1 queues

Published online by Cambridge University Press:  14 July 2016

Tetsuji Hirayama ,
Masaaki Kijima  and
Shoichi Nishimura
Tetsuji Hirayama*
Affiliation:
University of Electro-communications
Masaaki Kijima*
Affiliation:
Tokyo Institute of Technology
Shoichi Nishimura*
Affiliation:
University of Tsukuba
*
∗Postal address: Department of Communications and Systems Engineering, University of Electro-communications, Chofugaoka, Chofu-shi, Tokyo 182, Japan.
∗∗Present address: Graduate School of Management, University of Tsukuba, Tokyo, Otsuka, Bunkyoku, Tokyo, Japan.
∗∗∗Postal address: Institute of Socio-Economic Planning, University of Tsukuba, Tsukuba, Ibaraki 305, Japan.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider discrete-time dynamic scheduling problems of the following three types of G/G/1 queue with K different customer classes: (i) a G/DFR/1 queue with K classes under preemptive resume service discipline, (ii) a G/IFR/1 queue with two classes under preemptive resume service discipline, and (iii) a G/G/1 queue with two classes under non-preemptive service discipline. Interchange arguments are used to show that simple index policies of different type minimize the total holding cost of customers in a finite-horizon scheduling period for the three cases. Our results extend the result for a G/M/1 queue by Buyukkoc et al. (1985) to general queues.

Keywords

DFR SERVICE TIMEIFR SERVICE TIMEINTERCHANGE ARGUMENT
Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 595 - 603
Copyright
Copyright © Applied Probability Trust 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.Google Scholar
[2] Buyukkoc, C., Varaiya, P. and Walrand, J. (1985) The cµ rule revisited. Adv. Appl. Prob. 17, 237–238.Google Scholar
[3] Gittins, J. C. (1979) Bandit processes and dynamic allocation indices. J. R. Statist. Soc. 41, 148–177.Google Scholar
[4] Gittins, J. C. (1981) Multiserver scheduling of jobs with increasing completion rates. J. Appl. Prob. 18, 321–324.Google Scholar
[5] Glazebrook, K. D. (1979) Scheduling tasks with exponential service times on parallel processors. J. Appl. Prob. 16, 685–689.Google Scholar
[6] Glazebrook, K. D. (1982) On the evaluation of fixed permuations as strategies in stochastic scheduling. Stoch. Proc. Appl. 13, 171–187.Google Scholar
[7] Glazebrook, K. D. (1987) Evaluating the effects of machine breakdowns in stochastic scheduling problems. Naval Res. Log. 34, 319–335.Google Scholar
[8] Harrison, J. M. (1975) Dynamic scheduling of a multiclass queue: discount optimality. Operat. Res. 23, 270–282.Google Scholar
[9] Hirayama, T. (1987) Nonpreemptive scheduling of a finite-source queue with two customer classes. J. Operat. Res. Soc. Japan 30, 200–217.Google Scholar
[10] Jaiswal, N. K. (1968) Priority Queues. Academic Press, New York.Google Scholar
[11] Klimov, G. P. (1974) Time-sharing service systems I. Theory Prob. Appl. 19, 532–551.CrossRefGoogle Scholar
[12] Nash, P. (1973) Optimal Allocation of Resource between Research Projects. Ph.D. Thesis, Cambridge University.Google Scholar
[13] Shanthikumar, J. G. and Sumita, U. (1987) Convex ordering of sojourn times in singleserver queues: extremal properties of FIFO and LIFO service disciplines. J. Appl. Prob. 24, 737–748.Google Scholar
[14] Varaiya, P., Walrand, J. and Buyukkoc, C. (1985) Extensions of the multiarmed bandit problem: the discounted case. IEEE Trans. Autom. Control 30, 426–439.CrossRefGoogle Scholar
[15] Whittle, P. (1981) Arm-acquiring bandits. Ann. Prob. 9, 284–292.Google Scholar
[16] Wolff, R. W. (1970) Work-conserving priorities. J. Appl. Prob. 7, 327–337.Google Scholar