Abstract
We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisfied and penalties are incurred otherwise. Within the context of the corresponding fluid model, we investigate the dynamic scheduling of different classes of service under conditions where the workload of certain classes may be overloaded for a transient period of time. Specifically, we consider the case with two fluid classes and a single server whose capacity can be shared arbitrarily among the two classes. We assume that the class 1 arrival rate varies with time and the class 1 fluid can more efficiently reduce the holding cost. Under these assumptions, we characterize the optimal server allocation policy that minimizes the holding cost in the fluid model when the arrival rate function for class 1 is known. Using the insights gained from this deterministic case, we study the stochastic fluid system when the arrival rate function for class 1 is random and develop various policies that are optimal or near optimal under various conditions. In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.
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F. Avram, D. Bertsimas and M. Ricard, Fluid models of sequencing problems in open queueing networks: An optimal control approach, in: Stochastic Networks, eds. F.P. Kelly and R.J. Williams (Springer, New York,1995 pp.199–234.
N. Bansal and M. Harchol-Balter, Scheduling solutions for coping with transient overload, Technical Report, CMU-CS-01-134, Department of Computer Science, Carnegie Mellon University (2001).
N. Bauerle and U. Rieder, Optimal control of single-server fluid networks, Queueing Systems 35 (2000)185–200.
J.X. Chang, H. Ayhan, J. Dai, Z. Liu, M.S. Squillante and C.H. Xia, Optimal dynamic scheduling in a multiclass fluid model of Internet servers with transient overload, in: Proc. of the 42nd IEEE Conf. on Decision and Control (2003) pp.721–727.
J.X. Chang, H. Ayhan, J. Dai and C.H. Xia, Dynamic scheduling of a multiclass fluid model with transient overload, Technical Report, School of ISyE, Georgia Institute of Technology, www.isye.gatech.edu/people/faculty/Hayriye_Ayhan (2003).
H. Chen and P. Mohapatra, Session-based overload control in QoS-aware Web servers, in: Proc. of INFOCOM, Vol. 2 (2002) pp.516–524.
A. Gajrat and A. Hordijk, Fluid approximation of a controlled multiclass tandem network, Queueing Systems 35 (2000)349–380.
T.C. Green and S. Stidham, Sample-path conservation laws, with applications to scheduling queues and fluid systems, Queueing Systems 36 (2000)175–199.
A. Iyengar, E. MacNair and T. Nguyen, An analysis of Web server performance, in: Proc. of IEEE Global Telecommunications Conf., Vol. 3 (1997) pp.1943–1947.
G.P. Klimov, Time sharing service systems I, Theory Probab. Appl. 19(3) (1974)532–551.
Z. Liu, N. Niclausse and C. Jalpa-Villanueva, Traffic model and performance evaluation of Web servers, Performance Evaluation 46 (2001)77–100.
Z. Liu, M.S. Squillante and J.L. Wolf, Optimal control of resource allocation in e-business environments with strict quality-of-service performance guarantees, in: Proc. of the 41st IEEE Conf. on Decision and Control, Vol. 4 (2002) pp.4431–4439.
Z. Liu, M.S. Squillante, C.H. Xia, S.-Z. Yu and L. Zhang, Profile-based traffic characterization of commercial Web sites, in: Proc. of the 18th Internat. Teletraffic Congress (ITC18), Berlin, Germany (2003) pp.231–240.
L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The Mathematical Theory of Optimal Processes (Interscience, New York,1962).
A. Seierstad and K. Sydsater, Sufficient conditions in optimal control theory, Internat. Economic Rev. 18(2) (1977)367–391.
J.G. Shanthikumar and S.H. Xu, Strongly asymptotically optimal design and control of production and service systems, IIE Trans. 32(9) (2000)881–890.
W.E. Smith, Various optimizers for single-stage production, Naval Res. Logist. Quart. 3 (1956)59–66.
G. Weiss, Scheduling and control of manufacturing systems a fluid approach, in: Proc. of the 37th Allerton Conf. (1999) pp.577–586.
C.H. Xia and J.G. Shanthikumar, Asymptotic optimal control of multiclass G/G/1 queues with feedback, in: Stochastic Modeling and Optimization of Manufacturing Systems and Supply Chains, eds. J.G. Shanthikumar, D.D. Yao and W.H.M. Zijm (2003) pp.127–142.
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Chang, J., Ayhan, H., Dai, J. et al. Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload. Queueing Systems 48, 263–307 (2004). https://doi.org/10.1023/B:QUES.0000046579.23036.8a
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DOI: https://doi.org/10.1023/B:QUES.0000046579.23036.8a