Monotone control of queueing systems with heterogeneous servers

Queueing Systems

Volumn 37, Issue 4, 2001, Pages 391-403

  Rykov, V V ^a  

^a GUBKIN RUSSIAN STATE UNIVERSITY OF OIL AND GAS   (Russian Federation)

Author keywords

Controllable queueing systems; Markov decision processes; Monotonicity of optimal policies

Indexed keywords

MARKOV PROCESSES; QUEUEING THEORY;

HETEROGENEOUS SERVERS; MARKOV DECISION PROCESSES; MONOTONICITY PROPERTY; MULTI-SERVER; OPTIMAL POLICIES; QUEUEING SYSTEM;

QUEUEING NETWORKS;

EID: 0035534190     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/A:1010893501581     Document Type: Article

References (15)

1. E. Altman and G. Koole, On submodular functions of dynamic programming, Technical Report 2658, INRIA, Sophia Antipolis (1995).
2. P. Glasserman and D.D. Yao, Monotone Structure in Discrete Event Systems (Wiley, New York, 1994).
3. B. Hajek, Optimal control of two interacting service stations, IEEE Trans. Automat. Control 29 (1984) 491-499.
4. R.A. Howard, Dynamic Programming and Markov Processes (Wiley, 1960).
5. M.Yu. Kitaev and V.V. Rykov, Controlled Queueing Systems (CRC Press, New York, 1995).
6. G. Koole, A simple proof of the optimality of a threshold policy in two-server queueing system, Systems and Control Lett. 26 (1995) 301-303.
7. P. Langrock and W.W. Rykow, Methoden und Modelle zur Steurung von Bedienungssystemen, in: Handbuch der Bedienungstheorie, B. 2 (Berlin, Akademie-Verlag, 1984) pp. 422-486.
8. W. Lin and P.R. Kumar, Optimal control of a queueing system with two heterogeneous servers, IEEE Trans. Automat. Control 29 (1984) 696-703.
9. Sh. Ross, Applied Probability Models with Optimization Applications (Holden Day, San Francisco, 1970).
10. V.V. Rykov, Markov decision processes with finite state and decision spaces, Probab. Theory Appl. 11(2) (1966) 302-311.
11. V.V. Rykov, Controllable queueing systems, In: Itogi Nauki i Techniki. Teoria Verojatn. Matem. Statist. Teoretich. Kibern. 12 (1975) 45-152 (in Russian) (English translation in J. Soviet Math.).
12. Sh. Stidham Jr., Optimal control of admission to a queueing system, IEEE Trans. Automat. Control 30 (1985) 705-713.
13. Sh. Stidham Jr. and R. Weber, A survey of Markov decision models for control of networks of queues, Queueing Systems 13 (1993) 291-314.
14. D. Topkis, Minimizing a submodular function on a lattice, Oper. Res. 26(2) (1978) 305-321.
15. R. Weber, On a conjecture about assigning jobs to processors of different speeds, IEEE Trans. Automat. Control 38(1) (1993) 166-170.