A mathematical programming approach to optimal markovian switching of poisson arrival streams to queueing systems

Queueing Systems

Volumn 36, Issue 4, 2000, Pages 443-461

  Hemachandra, N ^a   Narahari, Y ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

^b INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Admission control in queues; Global optimization; Linear and nonlinear programming; Markov modulated poisson process

Indexed keywords

CONVEX OPTIMIZATION; GLOBAL OPTIMIZATION; LINEAR PROGRAMMING; MANUFACTURE; MARKOV CHAINS; PROFITABILITY; QUEUEING NETWORKS;

CONVEX PROGRAMS; FINITE CAPACITY QUEUES; LINEAR AND NONLINEAR PROGRAMMING; MARKOV MODULATED POISSON PROCESS; MARKOVIAN SWITCHING; MEAN QUEUE LENGTHS; OPTIMIZATION PROBLEMS; UTILIZATION FACTOR;

QUEUEING THEORY;

EID: 0034346382     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

1. S. Asmussen, Ladder heights and the Markov-modulated M/G/1 queue, Stochastic Process. Appl. 37 (1991) 313-326.
2. M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd ed. (Wiley, New York, 1993).
3. E.A. van Doom and G.J.K. Regterschot, Conditional PASTA, Oper. Res. Lett. 7(5) (October 1988) 229-232.
4. E.A. Fienberg, A generalization of 'Expectation equals reciprocal of intensity' to non-stationary exponential distributions, J. Appl. Probab. 31 (1994) 262-267.
5. W. Fischer and K. Meier-Hellstern, The Markov-modulated Poisson process (MMPP) cookbook, Performance Evaluation 18 (1993) 149-171.
6. P. Hansen and B. Jaumard, Lipschitz optimization, in: Handbook of Global Optimization, R. Horst and M. Pardalos, eds. (Kluwer Academic, Dordrecht, 1995) pp. 407-494.
7. R. Horst and M. Pardolas (eds.), Handbook of Global Optimization (Kluwer Academic, Dordrecht, 1995).
8. K.G. Murty, Linear Programming (Wiley, New York, 1983).
9. T. Rolski, Queues with non-stationary input stream: Ross's conjecture. Adv. in Appl. Probab. 13 (1981) 603-618.
10. T. Rolski, Upper bounds for single server queues with doubly stochastic Poisson arrivals, Math. Oper. Res. 11 (1986) 442-456.
11. E. Seneta, Non-negative Matrices and Markov Chains, 2nd ed. (Springer-Verlag, New York, 1981).
12. S. Stidham, Jr., Optimal control of admission to aqueueing system, IEEE Trans. Automat. Control 30 (August 1985) 705-713.
13. S. Stidham, Jr., Scheduling, routing, and flow control in stochastic networks, in: Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA, Vol. 10, W. Fleming and P.L. Lions, eds. (Springer-Verlag, Berlin, 1988) pp. 529-561.
14. S. Stidham, Jr. and R. Weber, A survey of Markov decision models for control of networks of queues, Queueing Systems Theory Appl. 13 (1993) 291-314.