Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-01T00:13:29.112Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal QoS control of interacting service stations

Published online by Cambridge University Press:  15 April 2003

Abdelkrim Haqiq ,
I. Lambadaris ,
N. Mikou  and
L. Orozco–Barbosa
Abdelkrim Haqiq
Affiliation:
Faculté des Sciences et Techniques, Département de Mathématiques et Informatique, route de Casablanca, BP. 577, Settat, Maroc; [email protected].
I. Lambadaris
Affiliation:
Carleton University, Department of Systems and Computer Engineering, 1125 Colonel By Drive, Ottawa, Ontario, K1 S5 B6, Canada
N. Mikou
Affiliation:
Faculté des Sciences Mirande, Laboratoire Informatique de Recherche sur les Systèmes Intelligents et leurs Applications, BP. 47870, 21078 Dijon Cedex, France
L. Orozco–Barbosa
Affiliation:
University of Ottawa, School of Information, Technology and Engineering, 161 Louis Pasteur, Ottawa, Ontario, K1 N6 N5, Canada
Get access

Abstract

We consider a system of three queues and two types of packets. Each packet arriving at this system finds in front of it a controller who either sends it in the first queue or rejects it according to a QoS criterion. When the packet finishes its service in the first queue, it is probabilistically routed to one of two other parallel queues. The objective is to minimize a QoS discounted cost over an infinite horizon. The cost function is composed of a waiting cost per packet in each queue and a rejection cost in the first queue. Subsequently, we generalize this problem by considering a system of (m+1) queues and n types of packets. We show that an optimal policy is monotonic.

Keywords

Queuesflow controldynamic programmingPoliciesIP network.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 3 , July 2002 , pp. 191 - 208
Copyright
© EDP Sciences, 2002

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

R. Braden, Requirements for Internet Hosts Communication Layers. STD 3, RFC 1122 (1989).
I. Christidou, I. Lambadaris and R. Mazumdar, Optimal Control of Arrivals to a Feedback Queueing System, in Proc. of the 27th CDC. Austin, Texas (1988) 663-667.
E. Davis, Optimal Control of Arrivals to a Two-server Queueing System with Separate Queues, Ph.D. Dissertation, Program in Operations Research. N.Y. State University, Raleigh (1977).
Ephremides, A., Varaiya, P. and Walrand, J., Simple Dynamic Routing Problem, A. IEEE Trans. Automat. Control 25 (1980) 690-693. CrossRef
W. Farrell, Optimal Switching Policies in a Nonhomogeneous Exponential Queueing System, Ph.D. Dissertation. Graduate School of Management, University of California, Los Angeles (1976).
S. Floyd and V. Jacobson, Random Early Detection Gateways for Congestion Avoidance. IEEE/ACM Trans. Networking (1993).
H. Ghoneim, Optimal Control of Arrivals to a Network of Two Queues in Series, Ph.D. Dissertation, Program in Operations Research. North Carolina State University, Raleigh (1980).
Ghoneim, H. and Stidham, S., Optimal Control of Arrivals to Two Queues in Series. Eur. J. Oper. Res. 21 (1985) 399-409. CrossRef
Hajek, B., Optimal Control of Two Interacting Service Stations. IEEE Trans. Automat. Control 29 (1984) 491-499. CrossRef
Haqiq, A. and Mikou, N., Contrôle Dynamique de Flux dans un Système d'Attente avec Panne. RAIRO: Oper. Res. 33 (1999) 69-86. CrossRef
A. Haqiq, Admission and routing dynamic control in a queueing system with breakdown, in Troisième Conférence Internationale en Recheche Opérationnelle. Marrakech, Maroc (2002).
V. Jacobson, Congestion Avoidance and Control. ACM SIGCOMM (1988).
P.R. Kumar and P. Varaiya, Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice Hall (1986).
Lambadaris, I. and Narayan, P., Jointly Optimal Admission and Routing Controls at a Network Node. Commun. Statist. Stochastic Models 10 (1994) 223-252.
I. Lambadaris, P. Narayan and I. Viniotis, Optimal Service Allocation among Two Heterogeneous Traffic Types at a Network Node with no Queueing, in Proc. of the 26th CDC. Los Angeles, Vol. CA (1987) 1496-1498.
Lazar, A., Optimal Flow Control of a Class of Queueing Networks in Equilibrium. IEEE Trans. Automat. Control 28 (1983) 1001-1007. CrossRef
Lippman, S., Applying a New Device in the Optimization of Exponential Queueing Systems. Oper. Res. 23 (1975) 687-710. CrossRef
Lippman, S., Dynamic Programming, On with Unbounded Rewards. Management Sci. 21 (1975) 1225-1233. CrossRef
J. Nagle, Congestion Control in IP/TCP. RFC 896 (1984).
Z. Rosberg, P. Varaiya and J. Walrand, Optimal Control of Service in Tandem Queues. IEEE Trans. Automat. Control AC-27 (1982) 600-610.
W. Stevens, TCP Slow Start, Congestion Avoidance, Fast Retransmit, and Fast Recovery Algorithms. RFC 2001 (1997).
S. Stidham, Optimal Control of Admission to a Queueing System. IEEE Trans. Automat. Control AC-30 (1985) 705-713.
S. Stidham and R. Weber, Control of Service Rates in Cycles and Series of Queues. Stat. Lab., Univ. Cambridge, Cambridge (1983).
P. Varaiya, Note on Optimization. Van Nostrand Reinhold, New York (1972).
I. Viniotis and A. Ephremides, Optimal Switching of Voice and Data at a Network Node, in Proc. of the 26th CDC, Vol. CA. Los Angeles (1987) 1504-1507.
J. Walrand, An Introduction to Queueing Networks. Prentice Hall International Editions, Englwood Cliffs, New Jersey (1988).
Weber, R., On the Optimal Assignment of Customers to Parallel Servers. J. Appl. Probab. 15 (1978) 406-413. CrossRef
Winston, W., Optimalily of the Shortest-Processing-Time Discipline. J. Appl. Probab. 14 (1977) 181-189. CrossRef