Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-30T17:28:42.365Z Has data issue: false hasContentIssue false
  • English
  • Français

Throughput properties of a queueing network with distributed dynamic routing and flow control

Part of: Control systems Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Leandros Tassiulas  and
Anthony Ephremides
Leandros Tassiulas*
Affiliation:
University of Maryland
Anthony Ephremides*
Affiliation:
University of Maryland
*
* Postal address: Department of Electrical Engineering and Institute for Systems Research, University of Maryland, College Park, MD20742, USA.
* Postal address: Department of Electrical Engineering and Institute for Systems Research, University of Maryland, College Park, MD20742, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A queueing network with arbitrary topology, state dependent routing and flow control is considered. Customers may enter the network at any queue and they are routed through it until they reach certain queues from which they may leave the system. The routing is based on local state information. The service rate of a server is controlled based on local state information as well. A distributed policy for routing and service rate control is identified that achieves maximum throughput. The policy can be implemented without knowledge of the arrival and service rates. The importance of flow control is demonstrated by showing that, in certain networks, if the servers cannot be forced to idle, then no maximum throughput policy exists when the arrival rates are not known. Also a model for exchange of state information among neighboring nodes is presented and the network is studied when the routing is based on delayed state information. A distributed policy is shown to achieve maximum throughput in the case of delayed state information. Finally, some implications for deterministic flow networks are discussed.

Keywords

QUEUEING NETWORK CONTROLDISTRIBUTED ROUTINGSTABILITYFLOW CONTROL

MSC classification

Primary: 93C05: Linear systems
Secondary: 90B22: Queues and service

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 285 - 307
Copyright
Copyright © Applied Probability Trust 1996 

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.)

Article purchase

Temporarily unavailable

References

[1] Cohen, J. W. (1982) The Single Server Queue. North Holland, Amsterdam.Google Scholar
[2] Ephremides, A., Varaiya, P. and Walrand, J. (1980) A simple dynamic routing problem. IEEE Trans. Aut. Control AC25.Google Scholar
[3] Fayolle, G., Malyshev, V. A., Menshikov, M. V. and Sidorenko, A. F. (1991) Lyapunov functions for Jackson networks. INRIA Rapports de Recherche No 1380.Google Scholar
[4] Hajek, B. (1984) Optimal control of two interacting service stations, IEEE Trans. Aut. Control, AC25, p. 491–499.Google Scholar
[5] Jackson, J. R. (1957) Networks of waiting lines. Operat. Res. 5, 518–521.Google Scholar
[6] Kelly, F. P. (1976) Networks of queues. Adv. Appl. Prob. 8, 416–432.CrossRefGoogle Scholar
[7] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[8] Lin, W. and Kumar, P. R. (1984) Optimal control of a queueing systems with two heterogeneous servers. IEEE Trans. Aut. Control AC25, 296–705.Google Scholar
[9] Massey, W. (1984) An operator analytic approach to Jackson network. J. Appl. Prob. 21, 379–393.Google Scholar
[10] Melamed, B. (1979) Characterization of Poisson traffic streams in Jackson queueing networks. Adv. Appl. Prob. 11, 422–438.Google Scholar
[11] Papadimitriou, C. H. and Steiglitz, K. (1982) Combinatorial Optimization Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
[12] Tassiulas, L. and Ephremides, A. (1990) Ergodicity of a queueing network and an alternative proof of the maxflow-mincut theorem. Proc. 28th Annual Allerton Conference on Communication, Control and Computing. Illinois.Google Scholar
[13] Tassiulas, L. and Ephremides, A. (1990) Stability properties of constrained queueing systems and scheduling for maximum throughput in multihop radio networks. Proc. 29th CDC, Honolulu, Hawaii.CrossRefGoogle Scholar
[14] Walrand, J. (1983) A probabilistic look at networks of quasi-reversible queues. IEEE Trans. Info. Theory IT29, 825–831.CrossRefGoogle Scholar
[15] Walrand, J. (1988) Queueing Networks. Prentice Hall, New York.Google Scholar