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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.
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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 

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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