Parametric Modeling Approach for Call Holding Times for IP based Public Safety Networks via EM Algorithm
This paper presents parametric probability density
models for call holding times (CHTs) into emergency call center
based on the actual data collected for over a week in the public
Emergency Information Network (EIN) in Mongolia. When the set of
chosen candidates of Gamma distribution family is fitted to the call
holding time data, it is observed that the whole area in the CHT
empirical histogram is underestimated due to spikes of higher
probability and long tails of lower probability in the histogram.
Therefore, we provide the Gaussian parametric model of a mixture of
lognormal distributions with explicit analytical expressions for the
modeling of CHTs of PSNs. Finally, we show that the CHTs for
PSNs are fitted reasonably by a mixture of lognormal distributions
via the simulation of expectation maximization algorithm. This result
is significant as it expresses a useful mathematical tool in an explicit
manner of a mixture of lognormal distributions.
[1] A. M. Law, W. D. Kelton, Simulation Modeling and Analysis, New
York: McGraw-Hill, 1991.
[2] Al. Ajarmeh, J. Yu, M. Amezziane, "Framework for Modeling Call
Holding Time for VoIP Tandem Networks: Introducing the Call Cease
Rate Function," in Proc. GLOBECOM 2011, Chicago, IL, USA, 5-9
Dec. 2011, pp. 1- 6.
[3] F. Barcelo, J. Jordan, "Channel Holding Time Distribution in Cellular
Telephony," Elect. Letter, vol. 34, no. 2, pp.146-147, 1998.
[4] V. A. Bolotin, "Modeling call holding time distributions for CCS
network design and performance analysis," IEEE J. Select. Areas
Commun., vol. 12, no. 3, pp. 433-438, 1994.
[5] W-E Chen, H. Hung, Y. Lin, "Modeling VoIP Call Holding Times for
Telecom," IEEE Network, vol. 21, no. 6, pp. 22-28, 2007.
[6] Y. Fang and I. Chlamtic, "Teletraffic Analysis and Mobility Modeling of
the PCS networks," IEEE Trans. on Communications, vol. 47, no.7, July
1999.
[7] C. Jedrzycky, V. C. M. Leung, "Probability distribution of channel
holding time in cellular telephony system," in Proc. IEEE Vech.
Technol. Conf., Atlanta, GA, May. 1996, pp. 247-251.
[8] J. Jordan, F. Barcelo, "Statistical of Channel Occupancy in Trunked
PAMR systems," Teletraffic Contributions for the Information Age
(ITC-15), Elsevier Science, pp. 1169-1178, 1997.
[9] D. Sharp, N. Cackov., and L.Trajkovic, "Analysis of Public Safety
Traffic on Trunked Land Mobile Radio Systems," IEEE J. Select. Areas
Commun., vol. 22, no.7, pp. 1197-1202, 2004.
[10] F. Barcel├▓, J. Jordan, "Channel Holding Time Distribution in Public
Telephony System (PAMR and PCS)," IEEE Transaction on Vechular
Technology, vol. 49, no.5, pp.1615-1625, 2000.
[11] B. Vujicic, H. Chen, and Lj. Trajkovic, "Prediction of traffic in a public
safety network," in Proc. IEEE Int. Symp. Circuits and Systems, Kos,
Greece, May 2006, pp. 2637-2640.
[12] E. Chelbus, "Empirical validation of call holding time distribution in
cellular communication systems," Teletraffic Contributions of the
Information Age, Elsevier Science, pp.1179 -1189, 1997.
[13] L. Brown, N. Gans., and L. Zhao, "Statistical Analysis of a Telephone
Call Center: A Queueing - Science Perspective," Journal of the
American Statistical Association, vol. 100, no. 469, March. 2005.
[14] Dempster AP, Laird NM, Rubin DB, "Maximum Likelihood from
Incomplete Data Via the EM Algorithm," Journal of the Royal
Statistical Society, no. 39. vol.1, pp.1-38, 1977.
[15] T. Benaglia, D. Chauveau, DR. Hunter, and DS. Young, "Mixtools: An
R package for analyzing finite mixture models," Journal of Statistical
Software, vol. 32, no. 6, pp.1-29, 2009.
[16] G. J. McLachlan, T. Krishnan, The EM Algorithm and Extensions, 2nd
ed, John Wiley and Sons, New York, 2008.
[17] I. Tang, X. Wei, "Existence of maximum likelihood estimation for
Three-parameter lognormal Distribution, reliability and safety," in Proc.
8th International Conference ICRMS, 20-24 July, 2009.
[18] L. Eckhard, A. Werner, A. Markus, "Log-normal Distributions across
the Sciences: Keys and Clues," BioScience, vol. 51, no. 5, pp. 341-351,
May. 2001.
[19] R. Vernic, S. Teodorescu, E. Pelican, "Two Lognormal Models for Real
Data," Annals of Ovidius University, Series Mathematics, vol. 17, no. 3,
pp. 263-277, 2009.
[20] J.A.Bilmes, "A Gentle Tutorial of the EM Algorithm and its Application
to Parameter Estimation for Gaussian Mixture and Hidden Markov
Models," International Computer Science Institute, Berkeley, California,
April, 1998.
[1] A. M. Law, W. D. Kelton, Simulation Modeling and Analysis, New
York: McGraw-Hill, 1991.
[2] Al. Ajarmeh, J. Yu, M. Amezziane, "Framework for Modeling Call
Holding Time for VoIP Tandem Networks: Introducing the Call Cease
Rate Function," in Proc. GLOBECOM 2011, Chicago, IL, USA, 5-9
Dec. 2011, pp. 1- 6.
[3] F. Barcelo, J. Jordan, "Channel Holding Time Distribution in Cellular
Telephony," Elect. Letter, vol. 34, no. 2, pp.146-147, 1998.
[4] V. A. Bolotin, "Modeling call holding time distributions for CCS
network design and performance analysis," IEEE J. Select. Areas
Commun., vol. 12, no. 3, pp. 433-438, 1994.
[5] W-E Chen, H. Hung, Y. Lin, "Modeling VoIP Call Holding Times for
Telecom," IEEE Network, vol. 21, no. 6, pp. 22-28, 2007.
[6] Y. Fang and I. Chlamtic, "Teletraffic Analysis and Mobility Modeling of
the PCS networks," IEEE Trans. on Communications, vol. 47, no.7, July
1999.
[7] C. Jedrzycky, V. C. M. Leung, "Probability distribution of channel
holding time in cellular telephony system," in Proc. IEEE Vech.
Technol. Conf., Atlanta, GA, May. 1996, pp. 247-251.
[8] J. Jordan, F. Barcelo, "Statistical of Channel Occupancy in Trunked
PAMR systems," Teletraffic Contributions for the Information Age
(ITC-15), Elsevier Science, pp. 1169-1178, 1997.
[9] D. Sharp, N. Cackov., and L.Trajkovic, "Analysis of Public Safety
Traffic on Trunked Land Mobile Radio Systems," IEEE J. Select. Areas
Commun., vol. 22, no.7, pp. 1197-1202, 2004.
[10] F. Barcel├▓, J. Jordan, "Channel Holding Time Distribution in Public
Telephony System (PAMR and PCS)," IEEE Transaction on Vechular
Technology, vol. 49, no.5, pp.1615-1625, 2000.
[11] B. Vujicic, H. Chen, and Lj. Trajkovic, "Prediction of traffic in a public
safety network," in Proc. IEEE Int. Symp. Circuits and Systems, Kos,
Greece, May 2006, pp. 2637-2640.
[12] E. Chelbus, "Empirical validation of call holding time distribution in
cellular communication systems," Teletraffic Contributions of the
Information Age, Elsevier Science, pp.1179 -1189, 1997.
[13] L. Brown, N. Gans., and L. Zhao, "Statistical Analysis of a Telephone
Call Center: A Queueing - Science Perspective," Journal of the
American Statistical Association, vol. 100, no. 469, March. 2005.
[14] Dempster AP, Laird NM, Rubin DB, "Maximum Likelihood from
Incomplete Data Via the EM Algorithm," Journal of the Royal
Statistical Society, no. 39. vol.1, pp.1-38, 1977.
[15] T. Benaglia, D. Chauveau, DR. Hunter, and DS. Young, "Mixtools: An
R package for analyzing finite mixture models," Journal of Statistical
Software, vol. 32, no. 6, pp.1-29, 2009.
[16] G. J. McLachlan, T. Krishnan, The EM Algorithm and Extensions, 2nd
ed, John Wiley and Sons, New York, 2008.
[17] I. Tang, X. Wei, "Existence of maximum likelihood estimation for
Three-parameter lognormal Distribution, reliability and safety," in Proc.
8th International Conference ICRMS, 20-24 July, 2009.
[18] L. Eckhard, A. Werner, A. Markus, "Log-normal Distributions across
the Sciences: Keys and Clues," BioScience, vol. 51, no. 5, pp. 341-351,
May. 2001.
[19] R. Vernic, S. Teodorescu, E. Pelican, "Two Lognormal Models for Real
Data," Annals of Ovidius University, Series Mathematics, vol. 17, no. 3,
pp. 263-277, 2009.
[20] J.A.Bilmes, "A Gentle Tutorial of the EM Algorithm and its Application
to Parameter Estimation for Gaussian Mixture and Hidden Markov
Models," International Computer Science Institute, Berkeley, California,
April, 1998.
@article{"International Journal of Information, Control and Computer Sciences:54316", author = "Badarch Tuyatsetseg", title = "Parametric Modeling Approach for Call Holding Times for IP based Public Safety Networks via EM Algorithm", abstract = "This paper presents parametric probability density
models for call holding times (CHTs) into emergency call center
based on the actual data collected for over a week in the public
Emergency Information Network (EIN) in Mongolia. When the set of
chosen candidates of Gamma distribution family is fitted to the call
holding time data, it is observed that the whole area in the CHT
empirical histogram is underestimated due to spikes of higher
probability and long tails of lower probability in the histogram.
Therefore, we provide the Gaussian parametric model of a mixture of
lognormal distributions with explicit analytical expressions for the
modeling of CHTs of PSNs. Finally, we show that the CHTs for
PSNs are fitted reasonably by a mixture of lognormal distributions
via the simulation of expectation maximization algorithm. This result
is significant as it expresses a useful mathematical tool in an explicit
manner of a mixture of lognormal distributions.", keywords = "A mixture of lognormal distributions, modeling call
holding times, public safety network.", volume = "7", number = "1", pages = "52-8", }
