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 queues and types of packets. We show that an optimal policy is monotonic.
Mots clés : queues, flow control, dynamic programming, policies, IP network
@article{RO_2002__36_3_191_0, author = {Haqiq, Abdelkrim and Lambadaris, I. and Mikou, N. and Orozco-Barbosa, L.}, title = {Optimal {QoS} control of interacting service stations}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {191--208}, publisher = {EDP-Sciences}, volume = {36}, number = {3}, year = {2002}, doi = {10.1051/ro:2003002}, zbl = {1062.90017}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro:2003002/} }
TY - JOUR AU - Haqiq, Abdelkrim AU - Lambadaris, I. AU - Mikou, N. AU - Orozco-Barbosa, L. TI - Optimal QoS control of interacting service stations JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2002 DA - 2002/// SP - 191 EP - 208 VL - 36 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro:2003002/ UR - https://zbmath.org/?q=an%3A1062.90017 UR - https://doi.org/10.1051/ro:2003002 DO - 10.1051/ro:2003002 LA - en ID - RO_2002__36_3_191_0 ER -
Haqiq, Abdelkrim; Lambadaris, I.; Mikou, N.; Orozco-Barbosa, L. Optimal QoS control of interacting service stations. RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 3, pp. 191-208. doi : 10.1051/ro:2003002. http://www.numdam.org/articles/10.1051/ro:2003002/
[1] Requirements for Internet Hosts Communication Layers. STD 3, RFC 1122 (1989).
,[2] Optimal Control of Arrivals to a Feedback Queueing System, in Proc. of the 27th CDC. Austin, Texas (1988) 663-667.
, and ,[3] 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).
,[4] A Simple Dynamic Routing Problem. IEEE Trans. Automat. Control 25 (1980) 690-693. | MR 583444 | Zbl 0451.90060
, and ,[5] Optimal Switching Policies in a Nonhomogeneous Exponential Queueing System, Ph.D. Dissertation. Graduate School of Management, University of California, Los Angeles (1976).
,[6] Random Early Detection Gateways for Congestion Avoidance. IEEE/ACM Trans. Networking (1993).
and ,[7] 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).
,[8] Optimal Control of Arrivals to Two Queues in Series. Eur. J. Oper. Res. 21 (1985) 399-409. | MR 811095 | Zbl 0569.60091
and ,[9] Optimal Control of Two Interacting Service Stations. IEEE Trans. Automat. Control 29 (1984) 491-499. | MR 745188 | Zbl 0555.90047
,[10] Contrôle Dynamique de Flux dans un Système d'Attente avec Panne. RAIRO: Oper. Res. 33 (1999) 69-86. | Numdam | Zbl 1024.90022
and ,[11] Admission and routing dynamic control in a queueing system with breakdown, in Troisième Conférence Internationale en Recheche Opérationnelle. Marrakech, Maroc (2002).
,[12] Congestion Avoidance and Control. ACM SIGCOMM (1988).
,[13] Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice Hall (1986). | Zbl 0706.93057
and ,[14] Jointly Optimal Admission and Routing Controls at a Network Node. Commun. Statist. Stochastic Models 10 (1994) 223-252. | MR 1259860 | Zbl 0791.60080
and ,[15] 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.
, and ,[16] Optimal Flow Control of a Class of Queueing Networks in Equilibrium. IEEE Trans. Automat. Control 28 (1983) 1001-1007. | MR 722351 | Zbl 0526.90041
,[17] Applying a New Device in the Optimization of Exponential Queueing Systems. Oper. Res. 23 (1975) 687-710. | MR 443125 | Zbl 0312.60048
,[18] On Dynamic Programming with Unbounded Rewards. Management Sci. 21 (1975) 1225-1233. | MR 398535 | Zbl 0309.90017
,[19] Congestion Control in IP/TCP. RFC 896 (1984).
,[20] Optimal Control of Service in Tandem Queues. IEEE Trans. Automat. Control AC-27 (1982) 600-610. | MR 680318 | Zbl 0497.90024
, and ,[21] TCP Slow Start, Congestion Avoidance, Fast Retransmit, and Fast Recovery Algorithms. RFC 2001 (1997).
,[22] Optimal Control of Admission to a Queueing System. IEEE Trans. Automat. Control AC-30 (1985) 705-713. | MR 794203 | Zbl 0563.90044
,[23] Control of Service Rates in Cycles and Series of Queues. Stat. Lab., Univ. Cambridge, Cambridge (1983).
and ,[24] Note on Optimization. Van Nostrand Reinhold, New York (1972). | Zbl 0251.90034
,[25] Optimal Switching of Voice and Data at a Network Node, in Proc. of the 26th CDC, Vol. CA. Los Angeles (1987) 1504-1507.
and ,[26] An Introduction to Queueing Networks. Prentice Hall International Editions, Englwood Cliffs, New Jersey (1988). | Zbl 0854.60090
,[27] On the Optimal Assignment of Customers to Parallel Servers. J. Appl. Probab. 15 (1978) 406-413. | MR 518586 | Zbl 0378.60095
,[28] Optimalily of the Shortest-Processing-Time Discipline. J. Appl. Probab. 14 (1977) 181-189. | MR 428516 | Zbl 0357.60023
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