Abstract
In conventional mobile telephone networks, users communicate directly with a base station, via which their call is transferred to the recipient. In an ad hoc mobile network, there is no base-station infrastructure and users need to communicate between themselves, either directly if they are close enough, or via transit nodes if they are not.
A number of interesting questions immediately arise in the modeling of ad hoc mobile networks. One that has received attention in the literature concerns how to encourage users to act as transit nodes for calls that they are not partaking in. Solutions to this problem have involved each user maintaining a ‘credit balance’ which is increased by forwarding transit calls and decreased by transmitting one’s own calls.
A second question concerns the ‘amount of resource’ that a network needs in order to be able to operate with a reasonable quality of service. We shall consider this question by modeling each user’s battery energy and credit balance as fluids, the rate of increase or decrease of which is modulated by the network occupancy. This results in a network of stochastic fluid models, each modulated by the same background process.
In this paper, we shall assume that there is no bound on the energy or the credit that a user’s handset can accumulate. Using this model, we can calculate the critical rates of recharge that are necessary and sufficient to guarantee that no calls are lost. For recharge rates less than the critical values, we propose a reduced-load approach to the analysis of the network.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahn, S., Ramaswami, V.: Fluid flow models and queues: A connection by stochastic coupling. Stoch. Models 19, 325–348 (2003)
Asmussen, S.: Stationary distributions for fluid flow models with or without Brownian noise. Stoch. Models 11, 21–49 (1995)
Bean, N.G., O’Reilly, M.M.: Performance measures of a multi-layer Markovian fluid model. Ann. Oper. Res. 160, 99–120 (2008)
Bean, N.G., O’Reilly, M.M., Taylor, P.G.: Hitting probabilities and hitting times for stochastic fluid flows. Stoch. Process. Appl. 115, 1530–1556 (2005)
Bean, N.G., O’Reilly, M.M., Taylor, P.G.: Algorithms for the Laplace–Stieltjes transforms of first return times for stochastic fluid flows. Methodol. Comput. Appl. Probab. 10, 381–408 (2008)
Bean, N.G., O’Reilly, M.M., Taylor, P.G.: Hitting probabilities and hitting times for stochastic fluid flows: The bounded model. Probab. Eng. Inf. Sci. 23, 121–147 (2009)
Buttyán, L., Hubaux, J.-P.: Stimulating cooperation in self-organizing mobile ad hoc networks. In: Mobile Networks and Applications, vol. 8, pp. 579–592 (2003)
Çinlar, E.: Introduction to Stochastic Processes. Prentice-Hall, Englewood Cliffs (1975)
Corson, S., Freebersyser, J., Sastry, A. (eds.): Mobile Networks and Applications. In: Special Issue on Mobile Ad Hoc Networking, vol. 4, pp. 137–241 (1999)
Crowcroft, J., Gibbens, R., Kelly, F., Östring, S.: Modelling incentives for collaboration in mobile ad hoc networks. Perform. Eval. 57, 427–439 (2004)
da Silva Soares, A., Latouche, G.: Level-phase independence for fluid queues. Stoch. Models 21, 327–341 (2005)
da Silva Soares, A., Latouche, G.: A matrix-analytic approach to fluid queues with feedback control. Int. J. Simul. 6, 4–12 (2005). Also published in Al-Begain, K., Bolch, G. (eds.). In: Proceedings of the 11th International Conference on Analytical and Stochastic Modelling Techniques and Applications, pp. 190–198. SCS-Publishing House (2004)
da Silva Soares, A., Latouche, G.: Fluid queues with level dependent evolution. Eur. J. Oper. Res. 196, 1041–1048 (2009)
Kelly, F.P.: Blocking probabilities in large circuit switched networks. Adv. Appl. Probab. 18, 473–505 (1986)
Kelly, F.P.: Loss networks. Ann. Appl. Probab. 1, 319–378 (1991)
On-line Encyclopedia of integer sequences. http://www.research.att.com/njas/sequences/
Perkins, C.: Ad Hoc Networking. Addison-Wesley, Reading (2001)
Ramaswami, V.: Matrix analytic methods for stochastic fluid flows. In: Proceedings of the 16th International Teletraffic Congress, pp. 1019–1030, Edinburgh, 7–11 June 1999
Rogers, L.C.: Fluid models in queueing theory and Wiener–Hopf factorization of Markov chains. Ann. Appl. Probab. 4, 390–413 (1994)
Van Lierde, S., da Silva Soares, A., Latouche, G.: Invariant measures for fluid queues. Stoch. Models 24, 133–151 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Latouche, G., Taylor, P.G. A stochastic fluid model for an ad hoc mobile network. Queueing Syst 63, 109 (2009). https://doi.org/10.1007/s11134-009-9153-6
Received:
Revised:
Published:
DOI: https://doi.org/10.1007/s11134-009-9153-6