This article is devoted to the search for a generating function for network delay simulation. We justify the choice of the measurement system used to collect delay data with microsecond accuracy. Experimental data are employed in order to form a hypothesis regarding the exponential type of delay. The paper is restricted to the study of the simplest two cases: the linear and quadratic dependence of the delay distribution function. The application of the Pearson criterion led to the conclusion that an exponential distribution can be used to describe network delay, but is valid only for small periods from 10 to 30 minutes. We also justify the expression for the distribution function and generating function for further theoretical and experimental calculations.
G.Almes, S.Kalidindi and M.Zekauskas, A one-way delay metric for IPPM, RFC 2679, September 1999.
2.
G.Almes, S.Kalidindi and M.Zekauskas, A round-trip delay metric for IPPM, RFC 2681, September 1999.
3.
Y.Sato, S.Ata, I.Oka and C.Fujiwara, Using mixed distribution for modeling end-to-end delay characteristics, in: Proceedings of the 8th Asia–Pacific Network and Management Symposium (APNOMS 2005), Japan, Okinawa, 2005.
4.
A.Botta, A.Dainotti and A.Pescapé, A tool for the generation of realistic network workload for emerging networking scenarios, Computer Networks56(15) (2012), 3531–3547. doi:10.1016/j.comnet.2012.02.019.
5.
G.Buticchi, D.Barater, E.Lorenzani and G.Franceschini, Digital control of actual grid-connected converters for ground leakage current reduction in PV transformerless systems, Industrial Informatics, IEEE Transactions on8(3) (2012), 563–572. doi:10.1109/TII.2012.2192284.
6.
P.Calyam, M.Sridharan, W.Mandrawa and P.Schopis, Performance measurement and analysis of H.323 traffic, in: Passive and Active Measurement Workshop (PAM), 2004.
7.
L.Carbone, F.Coccetti, P.Dini, R.Percacci and A.Vespignani, The spectrum of Internet performance, in: Passive and Active Measurements (PAM2003), 2003.
8.
B.-Y.Choi, S.Moon, Z.-L.Zhang, K.Papagiannaki and C.Diot, Analysis of point-to-point packet delay in an operational network, in: Infocom 2004, Hong Kong, 2004, pp. 1797–1807.
9.
A.Corlett, D.I.Pullin and S.Sargood, Statistics of one-way Internet packet delays, in: 53rd IETF, 2002.
10.
C.Demichelis and P.Chimento, RFC 3393: IP packet delay variation metric for IP performance metrics (IPPM), in: IETF, November 2002, 2002.
11.
C.Dovrolis, P.Ramanathan and D.Moore, Packet-dispersion techniques and a capacity-estimation methodology, IEEE/ACM Transactions on Networking12(6) (2004), 963–977. doi:10.1109/TNET.2004.838606.
12.
A.B.Downey, Using pathchar to estimate Internet link characteristics, in: Proc. ACM SICCOMM, September 1999, 1999, pp. 222–223.
13.
T.Elteto and S.Molnar, On the distribution of round-trip delays in TCP/IP networks, in: The Proceedings of the Local Computer Networks (LCN 99) Conference, IEEE, 1999, pp. 172–181. doi:10.1109/LCN.1999.802014.
14.
F.Georgatos, F.Gruber, D.Karrenberg, M.Santcroos, A.Susanj, H.Uijterwaal and R.Wilhelm, Providing active measurements as a regular service for ISP’s, in: PAM2001, 2001.
15.
P.E.Greenwood, A Guide to Chi-Squared Testing, John Wiley&Sons, 1996, v. 280.
16.
M.S.Hasan, C.Harding, H.Yu and A.Griffiths, Modeling delay and packet drop in networked control systems using network simulator NS2, International Journal of Automation and Computing2(2) (2005), 187–194. doi:10.1007/s11633-005-0187-x.
17.
N.Hohn, D.Veitch, K.Papagiannaki and C.Diot, Bridging router performance and queuing theory, in: Proc. ACM SIGMETRICS, New York, USA, June 2004, 2004.
18.
G.Hooghiemstra and P.Van Mieghem, Delay distributions on fixed internet paths, Delft University of Technology, 2001.
19.
J.Hu, Z.Wang, H.Gao and L.K.Stergioulas, Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities, Industrial Electronics, IEEE Transactions on59(7) (2012), 3008–3015. doi:10.1109/TIE.2011.2168791.
20.
E.Jammeh, I.Mkwawa, A.Khan, M.Goudarzi, L.Sun and E.Ifeachor, Quality of experience (QoE) driven adaptation scheme for voice/video over IP, Telecommunication Systems49(1) (2012), 99–111. doi:10.1007/s11235-010-9356-5.
21.
M.Kalman and B.Girod, Modeling the delays of successively-transmitted Internet packets, in: Multimedia and Expo, 2004. ICME’04. 2004 IEEE International Conference on, Vol. 3, IEEE, 2004, pp. 2015–2018.
22.
W.Matthews and L.Cottrell, The PingER project: Active Internet performance monitoring for the HENP community, Communications Magazine, IEEE38(5) (2000), 130–136. doi:10.1109/35.841837.
F.Palmieri, GMPLS-based service differentiation for scalable QoS support in all-optical grid applications, Future Generation Computer Systems22(6) (2006), 688–698. doi:10.1016/j.future.2005.11.003.
25.
D.Papagiannaki, S.Moon, C.Fraleigh, P.Thiran, F.Tobagi and C.Diot, Analysis of measured single-hop delay from an operational backbone network, in: Proc. IEEE INFOCOM 2002, New York, New York, June 2002, 2002.
26.
C.Pelsser, L.Cittadini, S.Vissicchio and R.Bush, From Paris to Tokyo: On the suitability of ping to measure latency, in: Proceedings of the 2013 Conference on Internet Measurement Conference, ACM, October2013, pp. 427–432. doi:10.1145/2504730.2504765.
27.
Ripe Test Box, http://ripe.net/projects/ttm/.
28.
Y.Tipsuwan and M.-Y.Chow, Control methodologies in networked control systems, Control Engineering Practice11 (2003), 1099–1111. doi:10.1016/S0967-0661(03)00036-4.
W.Zhang, M.S.Branicky and S.M.Phillips, Stability of networked control systems, IEEE Control System Magazine21(1) (2001), 84–99. doi:10.1109/37.898794.
