AN INFINITE PHASE-SIZE BMAP/M/1 QUEUE AND ITS APPLICATION TO SECURE GROUP COMMUNICATION

Hiroshi Toyoizumi

Abstract

We derive the bounds of the mean queue length of an infinite phase size BM AP /M/1 queue which has an M/M /∞-type phase transition, and use them to evaluate the performance of secure group communication. Secure communication inside a groups on an open network is critical to enhance the internet capability. Extending the usual matrix analysis to the operator analysis, we derive a new estimation of the degradation of secure group communication model.

References

  1. Harney, H. and Muckenhirn, C. (1997a). Group key management protocol (gkmp) architecture. RFC 2094.
  2. Harney, H. and Muckenhirn, C. (1997b). Group key management protocol (gkmp) sepcification. RFC 2093.
  3. Kleinrock, L. (1975). Queueing Systems Vol. 1. John Wiley and Sons.
  4. Latouche, G. and Ramaswami, V. (1999). Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM.
  5. Makimoto, N. (2001). Machigyouretsu Algorithm (Algorithm of Queueing System). Asakura.
  6. Sengupta, B. (1989). Markov processes whose steady state distribution is matrix-exponential with an application to the gi1 queue. Adv. Appl. Prob., (21):159-180.
  7. Thomas, S. A. (2000). SSL and TLS Essentials: Securing the Web. John Wiley and Sons.
  8. Toyoizumi, H. and Takaya, M. (2004). Performance evaluation of secure group communication. Journal of the Operations Research Society of Japan, 47(1):38-50.
  9. Tweedie, R. (1982). Operator-geometric stationary distribution for markov chains, with applications to queueing models. Adv. Appl. Prob., (14):368-391.
  10. Wallner, D., Harder, E., and Agee, R. (1999). Key management for multicast: Issues and architectures. Request for Comments: 2627.
  11. Wolff, R. (1989). Stochastic modeling and the theory of queues. Princeton-Hall.
  12. Wong, C., Gouda, M., and Lam, S. (2000). Secure group communications using key graphs. IEEE/ACM Trans. on Networking, 8(1):16-30.
Download


Paper Citation


in Harvard Style

Toyoizumi H. (2006). AN INFINITE PHASE-SIZE BMAP/M/1 QUEUE AND ITS APPLICATION TO SECURE GROUP COMMUNICATION . In Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2006) ISBN 978-972-8865-63-4, pages 283-288. DOI: 10.5220/0002095202830288


in Bibtex Style

@conference{secrypt06,
author={Hiroshi Toyoizumi},
title={AN INFINITE PHASE-SIZE BMAP/M/1 QUEUE AND ITS APPLICATION TO SECURE GROUP COMMUNICATION},
booktitle={Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2006)},
year={2006},
pages={283-288},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002095202830288},
isbn={978-972-8865-63-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2006)
TI - AN INFINITE PHASE-SIZE BMAP/M/1 QUEUE AND ITS APPLICATION TO SECURE GROUP COMMUNICATION
SN - 978-972-8865-63-4
AU - Toyoizumi H.
PY - 2006
SP - 283
EP - 288
DO - 10.5220/0002095202830288