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ТЕХНОЛОГИИ
Investigation of decomposition of quality indexes standardized for the Next Generation Network
This article considers the decomposition problems of quality indexes proposed for the Next Generation Network (NGN). Attention is paid to the following indexes: IP Packet Transfer Delay KsyHoids Next Generation Network, Quality (IPTD) and IP Packet Delay Variation (IPDV). Simulation model of packet connection between
of Service, lP-pcicket deloy varlatlon, user-network user-network interfaces as a multistage queuing system is proposed. For this model, some usefu
mterl^, decomp°sttlon, queutng s^m. ^ufe were obtained under different traffic parameters and number of switching nodes.
Mohammed A. A. S.,
Ph.d student of infocommunication systems department of The Bonch-Bruevich Saint - Petersburg State University of Telecommunications, ala_hth@mail.ru
Introduction
The Next Generation Network (NGN) is evolution path of separated telecommunication networks. NGN supports all services by packet technologies. A lot of quality indexes are standardized for NGN. These indexes are known as QoS (Quality of Service). As a rule, QoS is expressed in terms of the one way end-to-end delay (IPTD), jitter (IPDV), and IPLR - IP-packet Loss Probability [1, 2]. All QoS indexes are defined between user-network interfaces (UNI). Decomposition is allocation of each index among parts of network or between all switching nodes on the network.
Decomposition methods for the IPTD and IPLR
Jitter measures the variability of delay of packets in the given stream, which is important property for many applications (for example, streaming real-time applications). Ideally, packets should be delivered in a perfectly periodic fashion; however, even if the source generates an evenly spaced stream, unavoidable jitter is introduced by the network due to the variable queuing and propagation delays, and packets arrived the destination with a wide range of inter-arrival times. The jitter increases at switches along the path of a connection due to many factors, such as conflicts with other packets wishing to use the same links, and non-deterministic propagation delay in the data-link layer [4].
Jitter is a well understood concept, but there is no agreed upon statistic for measuring it. One commonly used metric, called delay jitter [5], is based on the one way end-to-end delay of the individual packets. Specifically, if we consider the differences of the end-to-end delay of successive packets, then jitter can be defined using a statistic, such as, the running average of differences over a fixed number of packets, and a percentile value such that 95% of the time these differences are less than x. Delay jitter has also been expressed as the difference between the end-to-end delay of a packet and the end-to-end propagation delay, and it is known as the delay variation. An alternative metric called
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rate jitter [4] is based on the inter-arrival times of the successive packets at the destination. It may be conveniently expressed by the means of a percentile, such as the 95th percentile, of the probability distribution of the inter-arrival time.
QoS indexes for multiservice traffic in NGN based on recommendations ITU-T Y.1540, Y.1541 h Y.1542 [1-3]. These indexes are normalized between UNIs. For NGN design and operation it is necessary to decompose the quality of service on the basic elements of a telecommunication system in which it is appropriate to choose as switching nodes or their necessary to decompose the quality of service on the basic elements of a telecommunication system in which it is appropriate to choose as switching nodes or their aggregation.
The main difficulty of decomposition appears for the index IPDV, which is called the delay variation of IP-packets, and in several publications - jitter. IPDV value equals to the difference between two values. The first value is a quantile of the distribution of IP-packets delay between the two interfaces UNI - tp. The second value is the minimum possible delivery time of IP-packets between the two interfaces UNI - t . . In current versions of
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ITU this value (the value of the distribution function) is set at 0.95or 0.999 and IPDV - 50 ms. These values will be refined as operating experience networks NGN.
Estimation of t between UNI interfaces is a simple task. Decomposition of this value on the elements of the network is performed by means of simple procedures [3]. Quantile decomposition can not be performed in the same manner. This requires analysis of multistage queuing system. This task is the subject of this article.
Model
The path between two UNI interfaces in NGN may be represented by queuing systems. For this reason, mathematical model is multistage queuing system. When studying the delay process of IP-packets, signal time propagation between UNIs can be accounted for separately, because this value is a constant. When calculating the value of the IPDV this parameter is not essential.
In [7] the model M/M/1 was investigated. Obtained results showed that the dependence of the delay quantile of the distribution can be represented by a linear function. Therefore, the task is to check if the laws for models M/M/1 are true for the more complex model. For this reason, multistage queuing system was chosen as the appropriate model.
T-Comm #8-2014
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ТЕХНОЛОГИИ
In i node (i = l,rti) enter IP-packets with intensity X ■ Time process intensity in i packet switching node in model is noted by /jr Each of stage (packet switching node) is a single-line queuing
system denoted as MIMI1 in the Kendall's classification [6]. Further, we assume that all values Xi are equal to each other. In this
case, lower indexes can be omitted. A similar hypothesis is accepted for the f_t. In this case, quantile dependence from the number of nodes is behaving linearly. For another model GID/1 lower index will be considered. The ratio of A to /.i, which is called the load and is usually denoted by the letter p, must be less than 1 [6].
The model consists of 7 switching nodes. The first node receives IP-packets. This flow can be presented by Weibull distribution with load form 0.5 to 0.9 Erl. This is achieved by controlling the shape and scale parameters of the Weibull distribution for different coefficient of variation of 2, 5 and 10. On the other nodes receives a stream with a probability of 0.333 of the first switching node. It should be mentioned that at the input each node receives other streams from different sources with load 0.5 Erl. Data are collected on the histogram for different amounts of switching nodes in our case on the 3rd, 5th and 7th. We find that the average value of IP-packet delay for the different nodes depending on the coefficient of variation.
This approach is not suitable for 1PDV decomposition. It is needed to achieve delay distribution function between UN Is - S(/). Then quantile may be calculated by solving equation S(t) = 0,999. This operation was repeated for different amounts of nodes 3, 5 and 7 and coefficient of variation of 2, 5 and 10. All results of investigation are depicted in figures 1 and 2.
Figurel. Dependence of IPTD value from coefficient of variation
Figure 2. Dependence of quantile values from coefficient of variation
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Discussion of simulation results
Analysis of dependencies depicted in the figure 1 (IPTD as a function from coefficient of variation which is equal to 2, 5 and 10 for example) shows that IPTD may be approximated by a linear function of coefficient of variation with a good accuracy. This property of IPTD obtained by using of simulation model allows us to choose a simple linear analytical model which may be used for different practical purposes when we need estimate IPTD taking in account properties of traffic. The second important fact is in the equivalence of dependencies for different number of nodes. That fact allows us to use linear model in common case, i.e. for any route in a network.
Dependencies depicted in the figure 2 (IPDV as a function from coefficient of variation which is equal to 2, 5 and 10 for example) have the same property, i.e. IPDV dependence from coefficient of variation for different number of nodes may be described by simple analytical linear model. The main conclusion of analysis is the fact that dependencies of IPTD and IPDV from coefficient of variation are very close to linear functions and may be described by lines for many practical purposes.
Conclusion
1. Delay variation decomposition by network elements is complex task. It may be solved by the network modeling as a multistage queuing system,
2. Delay variation decomposition in the simplest case, when the network may be described by MM1multistage system, may be done using of analytical expressions.
3. Results of G/DI1 multistage system simulation show dependences between the delay variation, the number of stages, the load value and the value of coefficient of variation.
4. Results of simulation shows that delay variation increases with increasing of the number of nodes, the value of load and the value of coefficient of variation.
5. Obtained dependencies may be approximated by simple analytical expressions, with a good accuracy, which may be used for practical purposes in tasks of delay variation decomposition.
References
1. ITU-T, Network performance objectives for IP-based services, Recommendation Y.! 541, Geneva, 2011.
2. ITU-T, Internet protocol data communication service - IP packet transfer and availability performance parameters, Rccommcndation Y.I540, Geneva, 2011.
3. ITU-T, Framework for achieving end-to-end IP performance objectives. Recommendation Y.1542, Geneva, 2010.
4. Mansour K. Pall-Shamir В., Jitter Control in QoS Networks, ШЕЕ/ACM Transactions on Networking, 9(4), August 200!.
5. Geleji G. On multi-domain QoS routing and rate jitter analysis. A dissertation submitted to the Graduate in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Faculty of North Carolina State University, 2011.
6. Kleinrock L. Queuing Systems, Volume I: Theory, New York: Wiley, 1975.
7. Mohammed A.A.C., Decomposition task of the IPDV value established for the next generation network, Russia, Buryat State University, mathematical and informatics issue, June 2014.
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