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Dynamic admission control for loss systems with batch arrivals

Published online by Cambridge University Press:  01 July 2016

E. L. Örmeci*
Affiliation:
Koç University
A. Burnetas*
Affiliation:
University of Athens
*
Postal address: Department of Industrial Engineering, Koç University, Rumeli Feneri Yolu, 34450 Sarıyer, İstanbul, Turkey. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, University of Athens, Panepistimiopolis, 15784 Athens, Greece. Email address: [email protected]
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Abstract

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We consider the problem of dynamic admission control in a Markovian loss system with two classes. Jobs arrive at the system in batches; each admitted job requires different service rates and brings different revenues depending on its class. We introduce the definition of a ‘preferred class’ for systems receiving mixed and single-class batches separately, and derive sufficient conditions for each system to have a preferred class. We also establish a monotonicity property of the optimal value functions, which reduces the number of possibly optimal actions.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2005 

References

Altman, E. (2002). Applications of Markov decision processes in communication networks. In Handbook of Markov Decision Processes, eds Feinberg, E. A. and Shwartz, A., Kluwer, Boston, MA, pp. 489536.CrossRefGoogle Scholar
Altman, E., Jiménez, T. and Koole, G. M. (2001). On optimal call admission control in a resource-sharing system. IEEE Trans. Commun 49, 16591668.CrossRefGoogle Scholar
Carrizosa, E., Conde, E. and Munoz-Marquez, M. (1998). Admission policies in loss queueing models with heterogeneous arrivals. Manag. Sci. 44, 311320.CrossRefGoogle Scholar
Carrol, W. and Grimes, R. (1995). Evolutionary change in product management. Experiences in the car rental industry. Interfaces 25, 84104.CrossRefGoogle Scholar
Geraghty, M. K. and Johnson, E. (1997). Revenue management saves national car rental. Interfaces 27, 107127.CrossRefGoogle Scholar
Harrison, J. M. (1975). Dynamic scheduling of a multiclass queue. Discount optimality. Operat. Res. 23, 270282.CrossRefGoogle Scholar
Lippman, S. A. (1975). Applying a new device in the optimization of exponential queueing systems. Operat. Res. 23, 687710.CrossRefGoogle Scholar
Lippman, S. A. and Ross, S. M. (1971). The streetwalker's dilemma. A Job shop model. SIAM J. Appl. Math. 20, 336342.CrossRefGoogle Scholar
Lippman, S. A. and Stidham, S. M. (1977). Individual versus social optimization in exponential congestion systems. Operat. Res. 25, 233247.CrossRefGoogle Scholar
Liu, Z., Nain, P. and Towsley, D. (1995). Sample path methods in the control of queues. Queueing Systems 21, 293336.CrossRefGoogle Scholar
Miller, B. (1971). A queuing reward system with several customer classes. Manag. Sci. 16, 234245.CrossRefGoogle Scholar
Naor, P. (1969). On the regulation of queue size by levying tolls. Econometrica 37, 1524.CrossRefGoogle Scholar
Örmeci, E. L. and Burnetas, A. N. (2004). Admission control with batch arrivals. Operat. Res. Lett. 32, 448454.CrossRefGoogle Scholar
Örmeci, E. L., Burnetas, A. N. and Emmons, H. (2002). Dynamic policies of admission to a two-class system based on customer offers. IIE Trans. 34, 813822.CrossRefGoogle Scholar
Örmeci, E. L., Burnetas, A. N. and van der Wal, J. (2001). Admission policies for a two class loss system. Stoch. Models 17, 513540.CrossRefGoogle Scholar
Puhalskii, A. A. and Reiman, M. I. (1998). A critically loaded multirate link with trunk reservation. Queueing Systems 28, 157190.CrossRefGoogle Scholar
Puterman, M. (1994). Markov Decision Processes. John Wiley, New York.CrossRefGoogle Scholar
Righter, R. (1994). Scheduling. In Stochastic Orders and Their Applications, eds Shaked, M. and Shanthikumar, J. G., Academic Press, Boston, MA, pp. 381432.Google Scholar
Ross, K. W. (1995). Multiservice Loss Models for Broadband Telecommunication Networks. Springer, London.CrossRefGoogle Scholar
Ross, S. M. (1970). Applied Probability Models with Optimization Applications. Dover, New York.Google Scholar
Savin, S., Cohen, M., Gans, N. and Katalan, Z. (2000). Capacity management in rental businesses with heterogeneous customer bases. Operat. Res. 53, 617631.CrossRefGoogle Scholar
Walrand, J. (1988). Introduction to Queueing Networks. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Xu, S. H. and Shanthikumar, J. G. (1993). Optimal expulsion control—a dual approach to admission control of an ordered-entry system. Operat. Res. 41, 11371152.CrossRefGoogle Scholar