[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2012.30.1_2.135

COMPARISONS OF LOSS FORMULAS FOR A CIRCUIT GROUP WITH OVERFLOW TRAFFIC

Park, Chul-Geun (Department of Information and Communications Engineering, Sunmoon University)
Han, Dong-Hwan (Department of Mathematics, Sunmoon University)

Publication Information

Journal of applied mathematics & informatics / v.30, no.1_2, 2012 , pp. 135-145 More about this Journal

Abstract

Traditionally, ERM (Equivalent Random Method) is used to determine number of circuits in an overflow circuit group with rough traffic which has vmr(variance to mean ratio) greater than one. Recently, IPP(Interrupted Poisson Process) approximate method which represents the collective feature of the overflow has been introduced. The negative binomial loss formula can be applied to determine the required number of circuits in the overflow circuit group. In this paper, we deal with the negative binomial loss formula and determination method of number of circuits. We also analyze and compare these three loss formulas.

Keywords

Overflow traffic; Loss formula; Negative binomial; ERM; IPP;

Citations & Related Records

Reference

1	D.L. Jagerman, Methods in Traffic Calculations, AT&T Bell Lab. Technical Journal 63, (1984), 1283-1309. DOI
2	ITU-T Recommendation E.524, Overflow approximations for non-random inputs, May, 1999.
3	ITU-T Recommendation E.527, Dimensioning at a circuit group with multi-slot bearer services and overflow traffic, March, 2000.
4	J. Kubasik, On some numerical methods for the computation of Erlang and Engset functions, Proceedings of the 11th ITC, (1985) 958-964.
5	R. Mina, Introduction to Teletraffic Engineering, Telephony publishing corporation, 1972.
6	V.K. Rohatgi, An Introduction to Probability Theory and Mathematical Statistics, John Wiley & Sons, 1976.
7	R.B. Cooper, Introduction to Queueing Theory, North Holland, 1977.
8	A. Kukzura, The interrupted Poisson process as an overflow process, AT&T Bell Lab. Technical Journal 52 (1973), 437-448.
9	H. Heffes and D.M. Lucantony, A Markov modulated characterization of packetized voice, data traffic and related statistical multiplexer performance, IEEE J. Selected Areas Comm. 4 (1986), 856-868. DOI
10	M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models-an Algorithmic Approach, The Johns Hopkins Univ. Press, 1981.
11	D.M. Lucantoni and V. Ramaswami, Efficient algorithm for solving the non-linear matrix equations arising in phase type queue, Comm. Statist.-Stochastic Models 1, (1985), 29-51. DOI
12	K.S. Meier-Hellstern, The Analysis of a Queue Arising in Overflow Model, IEEE Trans. on Comm.37, (1989), 367-372. DOI