ITU-T E 524-1999 Overflow Approximations for Non-Random Inputs《非随机输入的溢出近似值 E系列 全面网络操作 电话服务 服务操作和人员因素 网络管理和通信工程》.pdf

《ITU-T E 524-1999 Overflow Approximations for Non-Random Inputs《非随机输入的溢出近似值 E系列 全面网络操作 电话服务 服务操作和人员因素 网络管理和通信工程》.pdf》由会员分享，可在线阅读，更多相关《ITU-T E 524-1999 Overflow Approximations for Non-Random Inputs《非随机输入的溢出近似值 E系列 全面网络操作 电话服务 服务操作和人员因素 网络管理和通信工程》.pdf（18页珍藏版）》请在麦多课文档分享上搜索。

1、STD-ITU-T RECMN E.524-ENGL 1977 I 4862591 ObbLbBb 90T INTERNATIONAL TELECOMMUNICATION UNION ITU-T TELECOMMUNICATION STANDARDIZATION SECTOR OF ITU E.524 (05/99) SERIES E: OVERALL NETWORK OPERATION, TELEPHONE SERVICE, SERVICE OPERATION AND HUMAN FACTORS Quality of service, network management and traff

2、ic engineering - Traffic engineering - Determination of the number of circuits in automatic and semi-automatic operation Overflow approximations for non-random inputs IT U -T Recommendation E. 524 (Previously CCITT Recommendation) STD=ITU-T RECMN E.524-ENGL 3799 4862591 Ob63687 B4b = ITU-T E-SERIES

3、RECOMMENDATIONS OVERALL NETWORK OPERATION, TELEPHONE SERVICE, SERVICE OPERATION AND HUMAN FACTORS OPERATION, NUMBERING, ROUTING AND MOBILE SERVICES INTERNATIONAL OPERATION Definitions General provisions concerning Administrations General provisions concerning users Operation of international telepho

4、ne services Numbering plan of the international telephone service International routing plan Tones in national signalling systems Maritime mobile service and public land mobile service OPERATIONAL PROVISIONS RELATING TO CHARGING AND ACCOUNTING IN THE INTERNATIONAL TELEPHONE SERVICE Charging in the i

5、nternational telephone service Measuring and recording call durations for accounting purposes UTILIZATION OF THE INTERNATIONAL TELEPHONE NETWORK FOR NON- TELEPHONY APPLICATIONS General Phototelegraphy ISDN PROVISIONS CONCERNING USERS QUALITY OF SERVICE, NETWORK MANAGEMENT AND TRAFFIC ENGINEERING NET

6、WORK MANAGEMENT International service statistics International network management Checking the quality of the international telephone service TRAFFIC ENGINEERING Measurement and recording of traffic Forecasting of traffic Determination of the number of circuits in manual operation E. 1 OO-E. 103 E.

7、104-E. 1 I9 E. 120-E. 139 E. 140-E. 159 E.160-E.169 E. 170-E. 179 E. 180-E. I 99 E. 200-E. 229 E.230-E.249 E.260-E.269 E.300-E.319 E.320-E.329 E. 330-E. 399 E.400-E.409 E.410-E.419 E.420-E.489 E.490-E.505 E.506-E.509 E.51 O-E. 51 9 Definitions ISDN traffic engineering Mobile network traffic engineer

8、ing QUALITY OF TELECOMMUNICATION SERVICES: CONCEPTS, MODELS, OBJECTIVES AND DEPENDABILITY PLANNING Terms and definitions related to the quality of telecommunication services Models for telecommunication services E.600-E.699 E.700-E.749 E.750-E.799 E.800-E.809 E. 8 1 O-E. 844 Objectives for quality o

9、f service and related concepts of telecommunication services Field data collection and evaluation on the performance of equipment, networks and services E.845-E.859 E.880-E.899 Use of quality of service objectives for planning of telecommunication networks E.860-E.879 For further details, please ref

10、er to ITU-T List ojRecommendations. STD-ITU-T RECMN E.524-ENGL 1999 Iia 48b2571 Obblb8 782 ITU-T RECOMMENDATION E.524 OVERFLOW APPROXIMATIONS FOR NON-RANDOM INPUTS Summary To ensure accurate network design and planning in the presence of multiple streams (arising, e.g. from different services on the

11、 same network), it is imperative to determine the individual means and variances of the overflows of the different traffic streams offered to a common trunk group arrangement. The exact calculation of these parameters for the individual overflow streams is a very hard problem. Thus, this Recommendat

12、ion introduces different approximate methods for the calculation of the individual overflows. These methods are evaluated in terms of accuracy, processing time, memory requirements and programming effort. This Recommendation also provides sample numerical results based on exact calculations to which

13、 the results based on these methods may be compared. Source ITU-T Recommendation E.524 was revised by ITU-T Study Group 2 (1 997-2000) and was approved under the WTSC Resolution No. 1 procedure on the 10th of May 1999. Recommendation E.524 (05/99) STD.ITU-T RECMN E.524-ENGL 1797 m 4862591 OhhLh87 hL

14、9 = FOREWORD ITU (International Telecommunication Union) is the United Nations Specialized Agency in the field of telecommunications. The ITU Telecommunication Standardization Sector (ITU-T) is a permanent organ of the ITU. The ITU-T is responsible for studying technical, operating and tariff questi

15、ons and issuing Recommendations on them with a view to standardizing telecommunications on a worldwide basis. The World Telecommunication Standardization Conference (WTSC), which meets every four years, establishes the topics for study by the ITU-T Study Groups which, in their turn, produce Recommen

16、dations on these topics. The approval of Recommendations by the Members of the ITU-T is covered by the procedure laid down in WTSC Resolution No. 1. In some areas of information technology which fall within ITU-Ts purview, the necessary standards are prepared on a collaborative basis with IS0 and IE

17、C. NOTE In this Recommendation the term recognized operating agency (ROA) includes any individual, company, corporation or governmental organization that operates a public correspondence service. The terms Administration, ROA and public correspondence are defined in the Constitution of the ITU (Gene

18、va, 1992). INTELLECTUAL PROPERTY RIGHTS The ITU draws attention to the possibility that the practice or implementation of this Recommendation may involve the use of a claimed Intellectual Property Right. The ITU takes no position concerning the evidence, validity or applicability of claimed Intellec

19、tual Property Rights, whether asserted by ITU members or others outside of the Recommendation development process. As of the date of approval of this Recommendation, the ITU had not received notice of intellectual property, protected by patents, which may be required to implement this Recommendation

20、. However, implementors are cautioned that this may not represent the latest information and are therefore strongly urged to consult the TSB patent database. O ITU 1999 All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanica

21、l, including photocopying and microfilm, without permission in writing from the ITU. 11 Recommendation E.524 (05199) _ - 1 2 J 4 5 6 6.1 6.2 6.3 6.4 7 8 9 Page Scope References Terms and definitions . Abbreviations . Introduction Proposed methods . IPP method . EC method AWW method . 6.3.1 Blocking

22、of overflow traffic 6.3.2 Wallstrm formula for individual blocking 6.3.3 Handling of overflow variances EPS method Examples and criteria for comparison Summary of results . History i i 1 2 2 6 12 12 . Recommendation E.524 (05/99) 111 - Recommendation ES24 OVERFLOW APPROXIMATIONS FOR NON-RANDOM INPUT

23、S (revised in 1999) 1 Scope This Recommendation introduces approximate methods for the calculation of means and variances of overflows for individual (non-random) traffic streams offered to a circuit group arrangement. 2 References The following ITU-T Recommendations and other references contain pro

24、visions which, through reference in this text, constitute provisions of this Recommendation. At the time of publication, the editions indicated were valid. All Recommendations and other references are subject to revision; all users of this Recommendation are therefore encouraged to investigate the p

25、ossibility of applying the most recent edition of the Recommendations and other references listed below. A list of the currently valid ITU-T Recommendations is regularly published. - CCITT Recommendation ES21 (1988), Calculation of the number of circuits in a group carrying overflow trafic. ITU-T Re

26、commendation E.600 (1 993), Terms and definitions of traffic engineering. - 3 Terms and definitions General terms and definitions are given in Recommendation E.600; notations used in the description of the proposed methods appear with the methods themselves in clause 6. 4 Abbreviations This Recommen

27、dation uses the following abbreviations: AWW approximate Wilkinson Wallstrm EC equivalent capacity EPS equivalent Poisson stream ERT equivalent random traffic IPP interrupted Poisson process 5 Introduction This Recommendation provides approximate methods for the calculation of means and variances of

28、 overflows for individual (non-random) traffic streams in a circuit group arrangement. The considered methods are necessary complements to those included in the existing Recommendation E.521 where it is required to take into account concepts such as cluster engineering with service equalization, ser

29、vice protection and end-to-end grade of service. Recommendation E.521 is then insufficient as it is concerned with the grade of service for only one non-random traffic stream in a circuit group. Recommendation 33.524 (05t99) 1 Design methods concerning the above-mentioned areas are subject to furthe

30、r study and this Recommendation will serve as a reference when, in the future, Recommendation E.521 is complemented or replaced. In this Recommendation the proposed methods are evaluated in terms of accuracy, processing time, memory requirements and programming effort. Other criteria may be relevant

31、 and added in the future. The proposed methods are described briefly in clause 6. Clause 7 defines a set of examples of circuit group arrangements with exactly calculated (exact resolution of equations of state) individual means and variances, to which the result of the methods can be compared. This

32、 leads to Table 2, where for each method the important criteria are listed. The publications cited in the bibliography section at the end contain detailed information about the mathematical background of each of the methods. 6 Proposed methods The following methods are considered: 4 IPP method; b) E

33、C method; c AWW method; d) EPS method. 6.1 IPP method IPP method is a Poisson process interrupted by a random switch. Theon-/off-duration of the random switch has a negative exponential distribution. Overflow traffic from a circuit group can be accurately approximated by an IPP, since IPP can repres

34、ent bulk characteristics of overflow traffic. IPP has three parameters, namely, on-period intensity and mean on-/off-period durations. To approximate overflow traffic by an IPP, those three parameters are determined so that some moments of overflow traffic will coincide with those of IPP. The follow

35、ing two kinds of moment match methods are considered in this Recommendation: - three-moment match method 11 where IPP parameters are determined so that the first three moments of IPP will coincide with those of overflow traffic; four-moment ratio match method 2 where IPP parameters are determined so

36、 that the first moment and the ratios of the 2nd3rd and 7tW8th binomial moments of IPP will coincide with those of overflow traffic. To analyse a circuit group where multiple Poisson and overflow traffic streams are simultaneously offered, each overflow stream is approximated by an IPP. The IPP meth

37、od is well suited to computer calculation. State transition equations of the circuit group with IPP inputs can be solved directly and no introduction of equivalent models is necessary. Characteristics of overflow traffic can be obtained from the solution of state transition equations. The main featu

38、re of the IPP method is that the individual means and variances of the overflow traffic can be solved. - 2 Recommendation E.524 (05/99) 6.2 EC method The EC method 3 does not use the traffic-moments but the transitional behaviour of the primary traffic, by introducing a certain function p(n) versus

39、the equivalent capacity (n) of the partial overflow traffic, as defined by the recurrent process: do) = Em(a) Erlang loss formula - (m + n - a) + a - p(n - i) li- if y2 is a positive integer, and approximated by linear interpolation if not. A practical approximation, considering the predominant over

40、flow congestion states only, leads to the equations: k=l with: D,(n) = 1 + ai pi(n) -pi(n - i) (6-3) defining the equivalent capacity (ni) of the partial overflow traffic labelled i, and influenced by the mutual dependency between the partial overflow traffic streams. The mean value of the partial s

41、econd overflow is: O, = a, 7i pi(?,) where .n is the time congestion of the overflow group. The partial GOS (grade of service) equalization is fulfilled if: Pi (ni) = C C being a constant to be chosen. (6-4) (6-5) 6.3 AWW method The AWW method uses an approximate ERT model based on an improvement of

42、 Rapps approximation. The total overflow traffic is split up in the individual parts by a simple expression, see equations (6-7) and (6-9). To calculate the total overflow traffic, any method can be used. An approximate Erlang formula calculation for which the speed is independent of the size of the

43、 calculated circuit group is given in 4. The following notations are used: A4 V z VIA4 B mi, vi, zi, bi N mean of total offered traffic variance of total offered traffic mean blocking of the studied group corresponding quantities for an individual traffic stream is used for overflow quantities. Reco

44、mmendation E.524 (05/99) 3 - - 6.3.1 Blocking of overflow traffic For overflow calculations, an approximate ERT model is used. By numerical investigations, a considerable improvement has been found to Rapps classical approximation for the fictitious traffic. The error added by the approximation is s

45、mall compared to the error of the ERT model. It is known that ERT underestimates low blockings when mixing traffic of diverse peakedness 2. The formula, which was given in 4 (although with one printing error), is for 2 1 : A“ = v+ Z(Z- 1) (2 + y) where: M(Z+ z-l 1.5) 1 y (2.36 2- 2.17) log 1 + and:

46、= 2/(1.5 M+ 2 2- 1.3) 6-61 6.3.2 There has been much interest in finding a simple and accurate formula for the individual blocked traffic mi . Already in 1967, Katz SI proposed a formula of the type: Wallstrm formula for individual blocking mi =rni(l-w+wzi /z) (6-7) with w being a suitable expressio

47、n. Wallstrm proposed a very simple one but with reasonable results 6 and 2: w=l-B (6-8) One practical problem is, however, that a small peaked substream could have a blocking bi 1 with this formula. To avoid such unreasonable results, a modification is used in this case. Let zmaX be the largest indi

48、vidual zi. Then the value used is: il- if z, O (6-12b) where the stream fractionsx are: J; = a,(i)/Xa,(i) a,(i), mean of equivalent Poisson traffic of stream i, is given by: (6-12) a,(;) = aizi + 3zj (si - 1) (6-13) The mean total overflow O = CUi and the corresponding variance V are: O = a, B(s + s

49、, a,) V= O (1 - O + aJ(s + se + 1 -a, + O) where a, and se are given by: a, = v + 32 (z - I) se = a, (a + z)/(a + z - 1) - a - 1 (6-14a) (6- 1 4 b) (6-15a) (6-15b) Recommendation E.524 (05/99) 5 STD*ITU-T RECflN E-52Y-ENGL 1999 W 4862593 0661696 859 B denotes the Erlang B formula. Peakedness 2 of the total overflow, equal to V/, is: Z= 1 - O + aJ(s + se + I - a, + O) (6-1 6) The covariance between overflow streams i and j is: C(i, j) =JA (V- O) Similarly, (6- 17) zi- 1 =J;(Z- 1) (6- 18) Clearly, as the input peaked streams