Abstract
This paper investigates theoretical properties of throughput and cost in linear loss networks. The maximum throughput of the network with exponential service times is derived and the arrival process that maximizes throughput, given a fixed arrival rate, is established. For general service times, an asymptotically critical loading regime is identified such that the probability of an arbitrary customer being lost is strictly within (0,1) as the network size increases. This regime delivers throughput comparable to the maximum at a relatively low network cost. The paper establishes the asymptotic throughput and network cost under this critical loading.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arratia, R.: Limiting point processes for rescalings of coalescing and annihilating random walks on Zd. Ann. Probab. 9(6), 909–936 (1981)
Bertsekas, D., Gallager, R.: Data Networks, 2nd edn. Prentice-Hall, Englewood Cliffs (1992)
Bramson, M., Griffeath, D.: Clustering and dispersion rates for some interacting particle systems on Z1. Ann. Probab. 8(2), 183–213 (1980)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Feller, W.: An Introduction to Probability Theory and Its Applications, vol. I. Wiley, New York (1968)
Feller, W.: An Introduction to Probability Theory and Its Applications, 2nd edn., vol. II. Wiley, New York (1971)
Gupta, P., Kumar, P.R.: The capacity of wireless networks. IEEE Trans. Inf. Theory 46(2), 388–404 (2000)
Jelenković, P., Momčilović, P., Squillante, M.: Scalability of wireless networks. IEEE/ACM Trans. Netw. 15(2), 295–308 (2007)
Karatzas, I., Shreve, S.: Brownian Motion and Stochastic Calculus, 2nd edn. Springer, New York (1991)
Krapivsky, P., Redner, S., Ben-Naim, E.: A Kinetic View of Statistical Physics. Cambridge University Press, Cambridge (2010)
Latouche, G., Ramaswami, V.: Introduction to Matrix Analytic Methods in Stochastic Modeling. ASA-SIAM, Philadelphia (1999)
Liggett, T.: Interacting Particle Systems. Springer, New York (1985)
Liggett, T.: Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin, (1999)
Martin, J.: Large tandem queueing networks with blocking. Queueing Syst. Theory Appl. 41(1–2), 45–72 (2002)
Saleh, A., Simmons, J.: Evolution toward the next-generation core optical network. J. Lightwave Technol. 24(9), 3303–3321 (2006)
Whitt, W.: Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues. Springer, New York (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Momčilović, P., Squillante, M.S. Linear loss networks. Queueing Syst 68, 111–131 (2011). https://doi.org/10.1007/s11134-011-9230-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11134-011-9230-5