Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-03T19:19:09.042Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Scheduling of a Four-Station Queueing Network

Published online by Cambridge University Press:  27 July 2009

C. N. Laws  and
G. M. Louth
C. N. Laws
Affiliation:
University of Cambridge Statistical Laboratory, 16 Mill Lane Cambridge CB2 1SB
G. M. Louth
Affiliation:
University of Cambridge Statistical Laboratory, 16 Mill Lane Cambridge CB2 1SB
Get access Rights & Permissions [Opens in a new window]

Extract

This paper is concerned with the problem of optimally scheduling a multiclass open queueing network with four single-server stations in which dynamic control policies are permitted. Under the assumption that the system is heavily loaded, the original scheduling problem can be approximated by a dynamic control problem involving Brownian motion. We reformulate and solve this problem and, from the interpretation of the solution, we obtain two dynamic scheduling policies for our queueing network. We compare the performance of these policies with two static scheduling policies and a lower bound via simulation. Our results suggest that under either dynamic policy the system, at least when heavily loaded, exhibits the form of resource pooling given by the solution to the approximating control problem. Furthermore, even when lightly loaded the system performs better under the dynamic policies than under either static policy.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 1 , January 1990 , pp. 131 - 156
Copyright
Copyright © Cambridge University Press 1990

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

Ephremides, A., Varaiya, P., & Walrand, J. (1980). A simple dynamic routing problem. IEEE Transact ions on Automatic Control 25: 690–693.Google Scholar
Foschini, G. J. (1977). On heavy-traffic diffusion analysis and dynamic routing in packet switched networks. In Chandy, K. M. & Reiser, M. (eds.), Computer performance. Amsterdam: North Holland, pp. 499–513.Google Scholar
Foschini, G. J. & Salz, J. (1978). A basic dynamic routing problem and diffusion. IEEE Transactions on Communications 26: 320–327.Google Scholar
Gallager, R.G. (1977). A minimum delay routing algorithm using distributed computation. IEEE: Transactions on Communicatirins 25: 73–85.Google Scholar
Gibbens, R.J. (1988). Dynamic routing in circuit-switched networks: the dynamic alternative routing strategy. Ph.D. Thesis, Statistical Laboratory, University of Cambridge.Google Scholar
Hajek, B. (1983). The proof of a folk theorem on queueing delay with applications to routing in networks. Journal of the Association for Computing Machinery 30: 834–851.CrossRefGoogle Scholar
Hajek, B. (1985). Extremal splittings of point processes. Mathematics of Operations Research 10: 543–556.CrossRefGoogle Scholar
Harrison, J.M. (1988). Brownian models of queueing networks with heterogeneous customer populations. In Fleming, W. & Lions, P.L. (eds.), Stochastic differential systems, stochastic control theory and applications, IMA Volume 10. New York: Springer-Verlag, pp. 147–186.CrossRefGoogle Scholar
Harrison, J.M. & Wein, L.M. (1987). Scheduling networks of queues: heavy traffic analysis of two-station closed network. Submitted to Operations Research.Google Scholar
Houck, D.J. (1987). Comparison of policies for routing customers to parallel queueing systems. Operations Research 35: 306–310.CrossRefGoogle Scholar
Johnson, D.P. (1983). Diffusion approximations for optimal filtering of jump processes and for queueing networks. Ph.D. Thesis, Department of Mathematics, University of Wisconsin, Madison.Google Scholar
Laws, C.N. (1989). Dynamic routing and sequencing in queueing networks. Rayleigh Prize Essay, University of Cambridge.Google Scholar
Peterson, W.P. (1985). Djffusion approximations for networks of queues with multiple customer types. Ph.D. Thesis, Department of Operations Research, Stanford University.Google Scholar
Reiman, M.I. (1983). Some diffusion approximations with state-space collapse. In Baccelli, F. & Fayolle, G. (eds.), Lecture notes in control and information sciences 60. Proceedings of the international seminar on modelling and performance evaluation methodology. Berlin: Springer- Verlag, pp. 209–240.Google Scholar
Weber, R.R. (1978). On the optimal assignment of customers to parallel servers. Journal of Applied Probability 15: 406–413.Google Scholar
Wein, L.M. (1987). Asymptotically optimal scheduling of a two-station multiclass queueing network. Ph.D. Thesis, Department of Operations Research, Stanford University.Google Scholar
Wein, L.M. (1988). Brownian networks with discretionary routing. Submitted to Operations Research.Google Scholar
Whitt, W. (1971). Weak convergence theorems for priority queues: preemptive-resume discipline. Journal of Applied Probability 8: 74–94.CrossRefGoogle Scholar
Whitt, W. (1986). Deciding which queue to join: some counterexamples. Operations Research 34: 55–62.CrossRefGoogle Scholar
Winston, W. (1977). Optimality of the shortest line discipline. Journal of Applied Probability 14: 181–189.Google Scholar