A Mathematical Model of Shifted Gamma Distribution for Internet Traffic Packet Delay over a Next Generation Core Internetwork

Broadband Internet traffic is transported over the next generation core internetworks, which are composed of several IP/MPLS/GE network sections and transport multi-services. In practice, IP packet delay is normally measured in each separated network section but not over a whole internetwork. It is proved in the paper that packet delay distribution of Internet traffic component in core network sections can be approximately expressed as a shifted gamma distribution. Moreover a new explicit mathematical model based on shifted gamma distribution has also been proposed to compose delay distribution of Internet traffic packet transported over a core internetwork from component ones in each network section. It is resulted from this model that Internet packet delay over an internetwork inherits distribution properties from that over component networks. Other properties and parameters relationship of the model such as additive property of shape and location parameters, the relation between distribution lower moments and parameters, the dependence of distribution on parameters variation are also exposed in the paper. The proposed model of IP packet delay distributions has a certain scientific significance and plays an important role in practical performance analysis, network planning, designing and traffic engineering for improving the quality of service

Download Full-text

Improved Model of Load Balancing in the Infocommunication Network

Problemi telekomunìkacìj ◽

10.30837/pt.2020.2.05 ◽

2020 ◽

pp. 56-67

Author(s):

Oleksandr Lemeshko ◽

Anastasiia Kruhlova ◽

Anna Zhuravlova ◽

Valentyn Lemeshko

Keyword(s):

Mathematical Model ◽

Load Balancing ◽

Upper Bound ◽

Traffic Engineering ◽

Network Performance ◽

Multipath Routing ◽

Access Network ◽

Mixed Integer ◽

Core Network ◽

Network Links

The paper proposes an improved mathematical model of load balancing in the infocommunication network (ICN), corresponding to the Traffic Engineering (TE) concept principles. The model mathematically formalizes the case of ICN construction when each access network is switched simultaneously to not one but to several border routers to increase fault tolerance. Therefore, it is proposed to improve the load balancing level in the ICN according to the TE criterion by ensuring the distribution of traffic at the access level between several border routers that create a default virtual gateway. The proposed mathematical model is based on the conditions of implementation of single or multipath routing; load balancing at the access level; flow conservation at the access level and the network itself; overload prevention of communication links, which act as conditions for load balancing in ICN. Within the proposed model, the load balancing task in ICN is formulated as an optimization problem of mixed-integer linear programming. The results of the study confirmed the effectiveness of the proposed solution. Ensuring coordinated load balancing at both access and core network levels, in general, has increased network performance by 25.45% compared to a solution based on multipath routing, but without access level balancing, and 2.76 times compared to the model in which load balancing in the ICN was absent. Within the available load for each of the compared models, the use of the proposed solution allowed to reduce the upper bound of the network links utilization by an average from 20% to 60%. Lowering the upper bound of the network links utilization positively affects the quantitative values of the main Quality of Service indicators – the average end-to-end delay, jitter, and packet loss probability.

Download Full-text

Defining Quantiles for Estimating IP Packet Delay Variation in NGN Core Networks

REV Journal on Electronics and Communications ◽

10.21553/rev-jec.27 ◽

2011 ◽

Vol 1 (03) ◽

Author(s):

Dao Ngoc Lam ◽

Le Nhat Thang ◽

Le Huu Lap

Keyword(s):

Network Performance ◽

Estimation Method ◽

Packet Delay ◽

Distribution Functions ◽

Estimation Accuracy ◽

Core Network ◽

Approximate Methods ◽

Core Networks ◽

Ip Packet ◽

Delay Variation

Traffic delay is one of the important metrics used for evaluating network performance. Delay and delay variation characteristics of IP packets transferred over multi-section networks can be derived, estimated or composed from component distributions of IP package delay in each network section. Approximate methods are needed in the cases of unknown or complicated delay distribution functions, which are unavailable or unusable in practice. The ITU-T has proposed a method for estimating IP packet delay variation. One of noticeable factors affecting the estimation accuracy is the packet delay population quantile which has not been adequately considered. The objective of this paper is to examine the optimal range of quantiles used for estimating the IP packet delay variation in the NGN (Next Generation Network) core networks. The paper is composed from the following ideas. Firstly, several concepts and mathematical formulas related to delay metrics based on probability and statistics theory are defined. The approximate method of ITU-T for estimating the IP packet delay variation in a multi-section network is revised. Then, another method based on convolution for composing the empirical IPTD distribution functions is proposed for the same target as the first one. Secondly, a number of test cases are implemented to measure the IP packet delay on several sections of an NGN core network. Sample data are used for computing and estimating the IP packet delay variation for multi-section networks by two methods with certain hypotheses. Finally, these methods are compared and evaluated both theoretically and empirically in regards to the estimation accuracy versus quantiles of the IP packet transfer delay. The best range of quantiles is determined to ensure the accuracy of the estimation method applied for the NGN core network.

Download Full-text