Skip to main content
SpringerLink
Log in

Depletable channels: dynamics, behaviour, and efficiency in network design

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

We present a simple model, called depleatable channels, of multi-hop communication in ad hoc networks. We introduce a model for channel energy consumption, and we propose a notion of channel equivalence based on the communication service they provide, regardless of specific routing protocols. In particular, we consider equivalent two channels with identical maximum and minimum inhibiting flow, and prove that this notion of equivalence, and variants of it, coincide with standard equivalences borrowed from the theory of concurrency. Unfortunately, while the maximum flow can be computed in polynomial time, calculating the value of a minimum inhibiting flow is NP-hard. Thus, we propose a characterization of those graphs, called weak, which admit charge assignments for which the minimum inhibiting flow is strictly less than the maximum flow and show that weakness can be checked efficiently by providing an algorithm that does so in polynomial time.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. Notation \(G|_U\), for every \(U \subseteq V(G)\), denotes the subgraph of G with nodes U and edges \(E(G) \cap (U \times U)\).

References

  1. Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handobook of Process Algebra, pp. 197–292. North-Holland, Amsterdam (2001)

    Chapter  Google Scholar 

  2. Ahuja, R., Magnanti, T., Orlin, J.: Network Flows, Theory, Algorithms, and Applications. Prentice-Hall, Upper Saddle River, NJ (1993)

    MATH  Google Scholar 

  3. Akkaya, K., Younis, M.F.: A survey on routing protocols for wireless sensor networks. Ad Hoc Netw. 3(3), 325–349 (2005)

    Article  Google Scholar 

  4. Akyildiz, I., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor networks. IEEE Commun. Mag. 40(8), 102–116 (2002)

    Article  Google Scholar 

  5. Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven, CT (1956)

    Google Scholar 

  6. Borgström, J., Nestmann, U., Alima, L.O., Gurov, D.: Verifying a structured peer-to-peer overlay network: the static case. In: Global Computing, volume 3267 of LNCS, pp. 250–265. Springer (2005)

  7. Boukerche, A. (ed.): Algorithms and Protocols for Wireless Sensor Networks. Wiley, New York (2009)

    Google Scholar 

  8. Bourke, T., van Glabbeek, R.J., Höfner, P.: Mechanizing a process algebra for network protocols. J. Autom. Reason. 56(3), 309–341 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. Braess, D.: Über ein paradoxon aus der verkehrsplannung. Unternehmensforschung 12, 258–268 (1968)

    MathSciNet  MATH  Google Scholar 

  10. Bres, E., van Glabbeek, R. J., Höfner, P.: A timed process algebra for wireless networks with an application in routing—(extended abstract). In: Proceedings of ESOP, volume 9632 of LNCS, pp. 95–122. Springer (2016)

  11. Cenciarelli, P., Gorla, D., Salvo, I.: A polynomial-time algorithm for detecting the possibility of braess paradox in directed graphs. Algorithmica. A preliminary version is available at arXiv:1610.09320 (in press)

  12. Cenciarelli, P., Gorla, D., Salvo, I.: Depletable channels: dynamics and behaviour. In: Proceedings of FCT09, volume 5690 of LNCS, pp. 50–61. Springer (2009)

  13. Cenciarelli, P., Gorla, D., Salvo, I.: Inefficiencies in network models: a graph-theoretic perspective. Inf. Process. Lett. 131, 44–50 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cenciarelli, P., Gorla, D., Tuosto, E.: Network applications of graph bisimulation. In: Proceedings of ICGT08, volume 5214 of LNCS, pp. 131–146. Springer (2008)

  15. Cerone, A., Hennessy, M.: Modelling probabilistic wireless networks. Log. Methods Comput. Sci. 9(3) (2013)

  16. Cerone, A., Hennessy, M.: Characterising testing preorders for broadcasting distributed systems. In: Proceedings of Trustworthy Global Computing, volume 8902 of LNCS, pp. 67–81. Springer (2014)

  17. Cerone, A., Hennessy, M., Merro, M.: Modelling mac-layer communications in wireless systems. Log. Methods Comput. Sci. 11(1) (2015)

  18. Chen, X., Diao, Z., Hu, X.: Excluding braess paradox in nonatomic selfish routing. In: Proceedings of SAGT15, volume 9347 of LNCS, pp. 219–230. Springer (2015)

  19. Chen, X., Diao, Z., Hu, X.: Network characterizations for excluding braess’s paradox. Theory Comput. Syst. 1–34 (2016)

  20. Cormen, T., Leiserson, C., Rivest, R.: Introduction to Algorithms. MIT Press, Cambridge (1990)

    MATH  Google Scholar 

  21. De Nicola, R.: Behavioral equivalences. In: Encyclopedia of Parallel Computing, pp. 120–127. Springer (2011)

  22. De Nicola, R., Hennessy, M.: Testing equivalences for processes. Theor. Comput. Sci. 34, 83–133 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  23. Ene, C., Muntean, T.: Testing theories for broadcasting processes. Sci. Ann. Cuza Univ. 11, 214–230 (2002)

    MathSciNet  MATH  Google Scholar 

  24. Escalante, F.: Schnittverbände in graphen. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 38(1), 199–220 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  25. Fehnker, A., McIver, A.: Formal techniques for the analysis of wireless networks. In: Proceedings of IEEE-ISOLA. IEEE (2006)

  26. Ford, L.R., Fulkerson, D.R.: Maximal flow through a network. Can. J. Math. 8, 399–404 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  27. Ganjali, Y., Keshavarzian, A.: Load balancing in ad hoc networks: single-path routing versus multi-path routing. In: INFOCOM04, vol. 2, pp. 1120–1125 (2004)

  28. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of np-Completeness (1979)

  29. Ghassemi, F., Fokkink, W., Movaghar, A.: Verification of mobile ad hoc networks: an algebraic approach. Theor. Comput. Sci. 412(28), 3262–3282 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Godskesen, J.C.: A calculus for mobile ad hoc networks. In: Proceedings of Coordination, volume 4467 of LNCS, pp. 132–150. Springer (2007)

  31. Golumbic, J.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, London (1980)

    MATH  Google Scholar 

  32. Helen, D., Arivazhagan, D.: Applications, advantages and challenges of ad hoc networks. J. Acad. Ind. Res. 2(8), 453–457 (2014)

    Google Scholar 

  33. Iri, M.: Theory of uncontrollable flows—a new type of network-flow theory as a model for the twenty-first century of multiple values. Comput. Math. Appl. 35(10), 107–123 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  34. Jhaveri, D.R.: Mobile ad-hoc networking with AODV: a review. 6, 165–191 (2015)

  35. Kanellakis, P., Smolka, S.: CCS expressions, finite state processes and three problems of equivalence. Inf. Comput. 86(1), 43–68 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  36. Kloks, T., Kratsch, D.: Listing all minimal separators of a graph. SIAM J. Comput. 27(3), 605–613 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  37. Lanese, I., Sangiorgi, D.: An operational semantics for a calculus for wireless systems. Theor. Comput. Sci. 411(19), 1928–1948 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  38. Lanotte, R., Merro, M.: Semantic analysis of gossip protocols for wireless sensor networks. In: Proceedings of CONCUR, volume 6901 of LNCS, pp. 156–170. Springer (2011)

  39. Macedonio, D., Merro, M.: A semantic analysis of key management protocols for wireless sensor networks. Sci. Comput. Program. 81, 53–78 (2014)

    Article  Google Scholar 

  40. Merro, M.: An observational theory for mobile ad hoc networks (full version). Inf. Comput. 207(2), 194–208 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  41. Merro, M., Ballardin, F., Sibilio, E.: A timed calculus for wireless systems. Theor. Comput. Sci. 412(47), 6585–6611 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  42. Merro, M., Sibilio, E.: A calculus of trustworthy ad hoc networks. Form. Asp. Comput. 25(5), 801–832 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  43. Mezzetti, N., Sangiorgi, D.: Towards a calculus for wireless systems. In: Proceedings of MFPS, volume 158 of ENTCS, pp. 331–353 (2006)

  44. Miao, G., Song, G.: Energy and Spectrum Efficient Wireless Network Design. Cambridge University Press, Cambridge (2014)

    Google Scholar 

  45. Milchtaich, I.: Network topology and the efficiency of equilibrium. Games Econ. Behav. 57, 321–346 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  46. Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River, NJ (1989)

    MATH  Google Scholar 

  47. Mohapatra, P., Krishnamurthy, S. (eds.): Ad Hoc Networks: Technologies and Protocols. Springer, New York (2005)

    Google Scholar 

  48. Nanz, S., Hankin, C.: A framework for security analysis of mobile wireless networks. Theor. Comput. Sci. 367(1–2), 203–227 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  49. Nehra, N., Patel, R.B., Bhat, V.K.: Routing with load balancing in ad hoc network: a mobile agent approach. In: Proceedings of ICIS 2007. IEEE (2007)

  50. Park, D.: Concurrency and automata on infinite sequences. In: Theoretical Computer Science, volume 104 of LNCS, pp. 167–183. Springer (1981)

  51. Petrioli, C., Spenza, D., Tommasino, P., Trifiletti, A.: A novel wake-up receiver with addressing capability for wireless sensor nodes. In: Proceedings of DCOSS, pp. 18–25. IEEE (2014)

  52. Phillips, C.A.: The network inhibition problem. In: Proceedings of STOC, pp. 776–785. ACM Press (1993)

  53. Roughgarden, T.: On the severity of braess’s paradox: designing networks for selfish users is hard. J. Comput. Syst. Sci. 72(5), 922–953 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  54. Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge Universtity Press, Cambridge (2012)

    MATH  Google Scholar 

  55. Shankar, P.M.: Introduction to Wireless Systems. Wiley, New York (2001)

    Google Scholar 

  56. Shen, H., Liang, W.: Efficient enumeration of all minimal separators in a graph. Theor. Comput. Sci. 180(1–2), 169–180 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  57. Singh, A., Ramakrishnan, C.R., Smolka, S.A.: A process calculus for mobile ad hoc networks. Sci. Comput. Program. 75(6), 440–469 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  58. Singh, J.P., Dutta, P., Chakrabarti, A.: Ad Hoc Networks: A Statistical Perspective. Springer, New York (2018)

    Book  Google Scholar 

  59. Spenza, D., Magno, M., Basagni, S., Benini, L., Paoli, M., Petrioli, C.: Beyond duty cycling: wake-up radio with selective awakenings for long-lived wireless sensing systems. In: Proceedings of INFOCOM, pp. 522–530. IEEE (2015)

  60. Stockmeyer, L., Meyer, A.: Word problems requiring exponential time. In: Proceedings of STOC, pp. 1–9. ACM (1973)

  61. Toh, C.: Ad Hoc Mobile Wireless Networks: Protocols and Systems. Prentice Hall, Upper Saddle River, NJ (2002)

    Google Scholar 

  62. Tonguz, O.K., Ferrari, G.: Ad Hoc Wireless Networks: A Communication-Theoretic Perspective. Wiley, New York (2006)

    Book  Google Scholar 

  63. van Glabbeek, R.J.: The linear time-branching time spectrum (extended abstract). In: Proceedings of CONCUR, volume 458 of LNCS, pp. 278–297. Springer (1990)

  64. van Glabbeek, R.J.: The linear time - branching time spectrum II. In: Proceedings of CONCUR, volume 715 of LNCS, pp. 66–81. Springer (1993)

  65. van Glabbeek, R.J., Höfner, P., Portmann, M., Tan, W.L.: Modelling and verifying the AODV routing protocol. Distrib. Comput. 29(4), 279–315 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  66. Zanjireh, M.M., Larijani, H.: A survey on centralised and distributed clustering routing algorithms for WSNS. In: IEEE 81st Vehicular Technology Conference, pp. 1–6 (2015)

Download references

Acknowledgements

We wish to thank to Flavio Chierichetti for his valuable support in the proof of Theorem 5 and Gabriele Libianchi for his contribution to make Algorithm 2 simpler. Novella Bartolini, Irene Finocchi, Fabrizio Grandoni, and Chiara Petrioli provided helpful discussions about the topics of this paper. Finally, the anonymous reviewers gave many fruitful suggestions to improve the presentation of the paper.

Author information

Authors and Affiliations

  1. Department of Computer Science, Sapienza University of Rome, Rome, Italy

    Pietro Cenciarelli, Daniele Gorla & Ivano Salvo

Authors
  1. Pietro Cenciarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniele Gorla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ivano Salvo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniele Gorla.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cenciarelli, P., Gorla, D. & Salvo, I. Depletable channels: dynamics, behaviour, and efficiency in network design. Acta Informatica 56, 405–431 (2019). https://doi.org/10.1007/s00236-018-0329-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-018-0329-6

Search

Navigation