Multiserver loss systems with subscribers

Mathematics of Operations Research

Volumn 34, Issue 1, 2009, Pages 142-179

  Randhawa, Ramandeep S ^a   Kumar, Sunil ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Loss systems; On off hold request model; Subscribers with retrials

Indexed keywords

ARRIVAL RATES; ASYMPTOTIC REGIMES; DIFFUSION LIMITS; INVARIANT DISTRIBUTION; LOSS SYSTEM; LOSS SYSTEMS; MARKOVIAN; MULTI-SERVER; NUMBER OF SUBSCRIBERS; ON-OFF-HOLD REQUEST MODEL; POISSON PROCESS; POISSON STREAM; SUBSCRIBERS WITH RETRIALS;

NONLINEAR CONTROL SYSTEMS; POISSON EQUATION;

POISSON DISTRIBUTION;

EID: 67649922834     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1080.0350     Document Type: Article

References (38)

1. Atar, R., A. Budhiraja, P. Dupuis. 2001. On positive recurrence of constrained diffusion processes. Ann. Probab. 29(2) 979-1000.
2. Billingsley, P. 1986. Probability and Measure. John Wiley and Sons, New York.
3. Billingsley, P. 1995. Convergence of Probability Measures, 2nd ed. John Wiley and Sons, New York.
4. Chen, H., H. Zhang. 2000. Diffusion approximations for some multiclass queueing networks with FIFOservice disciplines. Math. Oper. Res. 25(4) 679-707.
5. Coddington, E. A. 1961. An Introduction to Ordinary Differential Equations. Prentice-Hall, Englewood Cliffs, NJ.
6. Coddington, E. A., N. Levinson. 1955. Theory of Ordinary Differential Equations. McGraw-Hill, New York.
7. Cohen, J. W. 1957. The generalized engset formulae. Philips Telecomm. Rev. 18(4) 158-170.
8. Dai, J. G., B. Prabhakar. 2000. The throughput of data switches with and without speedup. IEEE INFOCOM 2 556-564.
9. Dai, J. G., R. J. Williams. 1995. Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theory Probab. Appl. 50 3-53.
10. Das, A., R. Srikant. 2000. Diffusion approximations for a single node accessed by congestion controlled sources. IEEE Trans. Automatic Control 45(10) 1783-1799.
11. de Véricourt, F., O. B. Jennings. 2008. Dimensioning large-scale membership services. Oper. Res. 56(1) 173-187.
12. Durrett, R. 1996. Stochastic Calculus: APractical Introduction. CRC Press, Boca Raton, FL.
13. Erlang, A. K. 1917. Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. Electroteknikeren 13 5-13.
14. Ethier, S. N., T. G. Kurtz. 1986. Markov Processes: Characterization and Convergence. John Wiley and Sons, New York.
15. Gamarnik, D., A. Zeevi. 2006. Validity of heavy traffic steady-state approximations in generalized Jackson networks. Ann. Appl. Probab. 16 56-90.
16. Gross, D., C. Harris. 1998. Fundamentals of Queueing Theory. John Wiley and Sons, New York.
17. Halfin, S., W. Whitt. 1981. Heavy-traffic limits for queues with many exponential servers. Oper. Res. 29 567-588.
18. Harrison, J. M., R. J. Williams. 1996. A multiclass closed queueing network with unconventional heavy traffic behavior. Ann. Appl. Probab. 6(1) 1-47.
19. Hunt, P. J., F. P. Kelly. 1989. On critically loaded loss networks. Adv. Appl. Probab. 21 831-841.
20. Kelly, F. P. 1979. Reversibility and Stochastic Networks. John Wiley and Sons, New York.
21. Kleinrock, L. 1975. Queueing Systems, Vol. I: Theory. John Wiley and Sons, New York.
22. Kogan, Y. A., R. S. Lipster, A. V. Smorodinskii. 1986. Gaussian diffusion approximations of closed Markov models of computer networks. Problems Inform. Transmission 22 38-51.
23. Krichagina, E. V., A. A. Puhalskii. 1997. A heavy-traffic analysis of a closed queueing system with a GI/∞ service center. Queueing Systems: Theory Appl. 25 235-280.
24. Kumar, S. 2000. Two-server closed networks in heavy traffic: Diffusion limits and asymptotic optimality. Ann. Appl. Probab. 10(3) 930-961.
25. Kurtz, T. 1978. Strong approximation theorems for density dependent Markov chains. Stochastic Processes Appl. 6 223-240.
26. Maglaras, C., A. Zeevi. 2003. Pricing and capacity sizing for systems with shared resources: Approximate solutions and scaling relations. Management Sci. 49 1018-1038.
27. Mandelbaum, A., G. Pats. 1998. State-dependent stochastic networks. Part I: Approximations and applications with continuous diffusion limits. Ann. Appl. Probab. 8(2) 569-646.
28. Mandelbaum, A., W. A. Massey, M. I. Reiman. 1998. Strong approximations for Markovian service networks. Queueing Systems 30 149-201.
29. McKean, H. P. J. 1969. Stochastic Integrals. Academic Press, London.
30. Meyn, S. P., R. L. Tweedie. 1993. Markov Chains and Stochastic Stability. Springer-Verlag, London.
31. Miyazawa, M. 1993. Insensitivity and product form decomposability of reallocatable GSMP. Adv. Appl. Probab. 25 415-437.
32. Puhalskii, A. A., M. I. Reiman. 1998. A critically loaded multirate link with trunk reservation. Queueing Systems: Theory Appl. 28 157-190.
33. Randhawa, R. S. 2006. Operations with subscribers. Ph.D. thesis, Stanford University, Palo Alto, CA.
34. Randhawa, R. S., S. Kumar. 2008. Usage restriction and subscription services: Operational benefits with rational users. Manufacturing Service Oper. Management 10(3) 429-447.
35. Reiman, M. I. 1991. A critically loaded multiclass Erlang loss system. Queueing Systems 9 65-82.
36. Rogers, L. C. G., D. Williams. 2000. Diffusions, Markov Processes and Martingales, Vol. 2, 2nd ed. Cambridge University Press, New York.
37. Royden, H. L. 1988. Real Analysis. Prentice Hall, Englewood Cliffs, NJ.
38. Savin, S. V., M. A. Cohen, N. Gans, Z. Katalan. 2005. Capacity management in rental businesses with two customer bases. Oper. Res. 53(4) 617-631.