Handbook teletraffic engineering

Handbook teletraffic engineering

ITU–D Study Group 2 Question 16/2 Handbook “TELETRAFFIC ENGINEERING” Geneva, December 2003 ii iii PREFACE This first edition of the Teletraffic Engineering Handbook has been worked out as a joint venture between the • International Telecommunication Union <http://www.itu.int>,andthe • International Teletraffic Congress <http://www.i teletraffic.org>. The handbook covers the basic theory of teletraffic engineering. The mathematical back- ground required is elementary probability theory. The purpose of the handbook is to enable engineers to understand ITU–T recommendations on traffic engineering, evaluate tools and methods, and keep up-to-date with new practices. The book includes the following parts: • Introduction: Chapter 1 – 2, • Mathematical background: Chapter 3 – 6, • Telecommunication loss models: Chapter 7 – 11, • Data communication delay models: Chapter 12 – 14, • Measurements: Chapter 15. The purpose of the book is twofold: to serve both as a handbook and as a textbook. Thus the reader should, for example, be able to study chapters on loss models without studying the chapters on the mathematical background first. The handbook is based on many years of experience in teaching the subject at the Technical University of Denmark and from ITU training courses in developing countries by the editor Villy B. Iversen. ITU-T Study Group 2 (Working Party 3/2) has reviewed Recommendations on traffic engineering. Many engineers from the international teletraffic community and students have contributed with ideas to the presentation. Supporting material, such as software, exercises, advanced material, and case studies, is available at <http://www.com.dtu.dk/teletraffic> where comments and ideas will also be appreciated. The handbook was initiated by the International Teletraffic Congress (ITC), Committee 3 (Developing countries and ITU matters), reviewed and adopted by ITU-D Study Group 2 in 2001. The Telecommunication Development Bureau thanks the International Teletraffic iv Congress, all Member States, Sector Members and experts, who contributed to this publi- cation. Hamadoun I. Tour´e Director Telecommunication Development Bureau International Telecommunication Union v vi Notations a Carried traffic per source or per channel A Offered traffic = A o A c Carried traffic = Y A  Lost traffic B Call congestion B Burstiness c Constant C Traffic congestion = load congestion C n Catalan’s number d Slot size in multi-rate traffic D Probability of delay or Deterministic arrival or service process E Time congestion E 1,n (A)=E 1 Erlang’s B–formula = Erlang’s 1. formula E 2,n (A)=E 2 Erlang’s C–formula = Erlang’s 2. formula F Improvement function g Number of groups h Constant time interval or service time H(k) Palm–Jacobæus’ formula I Inverse time congestion I =1/E J ν (z) Modified Bessel function of order ν k Accessibility = hunting capacity Maximum number of customers in a queueing system K Number of links in a telecommuncation network or number of nodes in a queueing network L Mean queue length L kø Mean queue length when the queue is greater than zero L Random variable for queue length m Mean value (average) = m 1 m i i’th (non-central) moment m  i i’th centrale moment m r Mean residual life time M Poisson arrival process n Number of servers (channels) N Number of traffic streams or traffic types p(i) State probabilities, time averages p{i, t | j, t 0 } Probability for state i at time t given state j at time t 0 P (i) Cumulated state probabilities P (i)=  i x=−∞ p(x) q(i) Relative (non normalised) state probabilities Q(i) Cumulated values of q(i): Q(i)=  i x=−∞ q(x) Q Normalisation constant r Reservation parameter (trunk reservation) R Mean response time vii s Mean service time S Number of traffic sources t Time instant T Random variable for time instant U Load function v Variance V Virtual waiting time w Mean waiting time for delayed customers W Mean waiting time for all customers W Random variable for waiting time x Variable X Random variable y Arrival rate. Poisson process: y = λ Y Carried traffic Z Peakedness α Offered traffic per source β Offered traffic per idle source γ Arrival rate for an idle source ε Palm’s form factor ϑ Lagrange-multiplicator κ i i’th cumulant λ Arrival rate of a Poisson process Λ Total arrival rate to a system µ Service rate, inverse mean service time π(i) State probabilities, arriving customer mean values ψ(i) State probabilities, departing customer mean values  Service ratio σ 2 Variance, σ = standard deviation τ Time-out constant or constant time-interval viii Contents 1 Introduction to Teletraffic Engineering 1 1.1 Modelling of telecommunication systems 2 1.1.1 Systemstructure 2 1.1.2 Theoperationalstrategy 3 1.1.3 Statisticalpropertiesoftraffic 3 1.1.4 Models 3 1.2 Conventionaltelephonesystems 5 1.2.1 Systemstructure 5 1.2.2 Userbehaviour 6 1.2.3 Operationstrategy 7 1.3 Communicationnetworks 8 1.3.1 Thetelephonenetwork 8 1.3.2 Datanetworks 11 1.3.3 LocalAreaNetworks(LAN) 12 1.4 Mobilecommunicationsystems 12 1.4.1 Cellularsystems 13 1.5 ITUrecommendationsontrafficengineering 15 1.5.1 TrafficengineeringintheITU 15 1.5.2 Trafficdemandcharacterisation 17 1.5.3 GradeofServiceobjectives 21 1.5.4 Trafficcontrolsanddimensioning 26 1.5.5 Performancemonitoring 33 1.5.6 Otherrecommendations 34 1.5.7 Work program for the Study Period 2001–2004 34 1.5.8 Conclusions 35 2 Traffic concepts and grade of service 37 2.1 Conceptoftrafficandtrafficunit[erlang] 37 2.2 Trafficvariationsandtheconceptbusyhour 40 2.3 Theblockingconcept 43 2.4 Trafficgenerationandsubscribersreaction 45 ix x CONTENTS 2.5 IntroductiontoGrade-of-Service=GoS 51 2.5.1 ComparisonofGoSandQoS 53 2.5.2 SpecialfeaturesofQoS 53 2.5.3 Networkperformance 54 2.5.4 Referenceconfigurations 54 3 Probability Theory and Statistics 57 3.1 Distributionfunctions 57 3.1.1 Characterisationofdistributions 58 3.1.2 Residuallifetime 60 3.1.3 Load from holding times of duration less than x 62 3.1.4 Forwardrecurrencetime 63 3.1.5 Distribution of the j’th largest of k randomvariables 65 3.2 Combinationofrandomvariables 66 3.2.1 Randomvariablesinseries 66 3.2.2 Randomvariablesinparallel 67 3.3 Stochasticsum 67 4 Time Interval Distributions 71 4.1 Exponentialdistribution 71 4.1.1 Minimum of k exponentiallydistributedrandomvariables 73 4.1.2 Combinationofexponentialdistributions 73 4.2 Steepdistributions 74 4.3 Flatdistributions 76 4.3.1 Hyper-exponentialdistribution 76 4.4 Coxdistributions 77 4.4.1 Polynomialtrial 81 4.4.2 Decompositionprinciples 81 4.4.3 ImportanceofCoxdistribution 83 4.5 Othertimedistributions 84 4.6 Observationsoflife-timedistribution 85 5 Arrival Processes 87 5.1 Descriptionofpointprocesses 88 5.1.1 Basicpropertiesofnumberrepresentation 89 5.1.2 Basicpropertiesofintervalrepresentation 89 5.2 Characteristicsofpointprocess 91 5.2.1 Stationarity(Timehomogeneity) 91 5.2.2 Independence 91 5.2.3 Simplepointprocess 92 [...]... engineering The Recommendations on traffic engineering can be classified according to the four major traffic engineering tasks: 16 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING • Traffic demand characterisation; • Grade of Service (GoS) objectives; • Traffic controls and dimensioning; • Performance monitoring The interrelation between these four tasks is illustrated in Fig 1 The initial tasks in traffic engineering. .. on traffic engineering The ITU–T is divided into Study Groups Study Group 2 (SG2) is responsible for Operational Aspects of Service Provision Networks and Performance Each Study Group is divided into Working Parties Working Party 3 of Study Group 2 (WP 3/2) is responsible for Traffic Engineering 1.5.1 Traffic engineering in the ITU Although Working Party 3/2 has the overall responsibility for traffic engineering, ... Iridium was unsuccessful, but newer systems such as the Inmarsat system is now in use 1.5 ITU RECOMMENDATIONS ON TRAFFIC ENGINEERING 1.5 15 ITU recommendations on traffic engineering The following section is based on ITU–T draft Recommendation E.490.1: Overview of Recommendations on traffic engineering See also (Villen, 2002 [101]) The International Telecommunication Union (ITU) is an organisation sponsored... not notice anything If several subscribers are waiting for the same microprocessor, they will normally get service in random order independent of the time of arrival 8 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING The way by which control devices of the same type and the cords share the work is often cyclic, such that they get approximately the same number of call attempts This is an advantage... network planning, the objective is to optimise network structures and traffic routing under the consideration of traffic demands, service and reliability requirement etc 10 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING I I T L T L L T L L L T L L L Figure 1.6: In a telecommunication network all exchanges are typically arranged in a threelevel hierarchy Local-exchanges or subscriber-exchanges (L), to... single packet, it is denoted message–switching Since the exchanges in a data network are computers, it is feasible to apply advanced strategies for traffic routing 12 1.3.3 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING Local Area Networks (LAN) Local area networks are a very specific but also very important type of data network where all users through a computer are attached to the same digital transmission... so-called control channel and an identification of the subscriber takes place The control channel is a radio channel used by the base station for control The remaining 14 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING channels are traffic channels A call request towards a mobile subscriber (B-subscriber) takes place the following way The mobile telephone exchange receives the call from the other subscriber... include a.o the determination of the number of circuits in a trunk group, the number of operators at switching boards, the number of open lanes in the supermarket, 1 2 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING and the allocation of priorities to jobs in a computer system Long term decisions include e.g decisions concerning the development and extension of dataand telecommunication networks,... Even though common habits of subscribers imply that daily variations follows a predictable pattern, it is impossible to predict individual call attempts or duration of 4 CHAPTER 1 INTRODUCTION TO TELETRAFFIC ENGINEERING Observation Model Deduction Data Verification Figure 1.2: Teletraffic theory is an inductive discipline From observations of real systems we establish theoretical models, from which we... Traffic engineering in the ITU Although Working Party 3/2 has the overall responsibility for traffic engineering, some recommendations on traffic engineering or related to it have been (or are being) produced by other Groups Study Group 7 deals in the X Series with traffic engineering for data communication networks, Study Group 11 has produced some recommendations (Q Series) on traffic aspects related to system . ITU–D Study Group 2 Question 16/2 Handbook TELETRAFFIC ENGINEERING Geneva, December 2003 ii iii PREFACE This first edition of the Teletraffic Engineering Handbook has been worked out as a joint venture. Congress <http://www.i teletraffic. org>. The handbook covers the basic theory of teletraffic engineering. The mathematical back- ground required is elementary probability theory. The purpose of the handbook. both as a handbook and as a textbook. Thus the reader should, for example, be able to study chapters on loss models without studying the chapters on the mathematical background first. The handbook