Điện tử viễn thông TELETRAFFIC ENGINEERING HANDBOOK ITU khotailieu

TELETRAFFIC ENGINEERING HANDBOOK ITU–D SG 2/16 & ITC Draft 2001-06-20 Contact: Villy B Iversen COM Center Technical University of Denmark Building 343, DK-2800 Lyngby Tlf.: 4525 3648 Fax.: 4593 0355 E–mail: vbi@com.dtu.dk www.tele.dtu.dk/teletraffic June 20, 2001 ii iii NOTATIONS Page/Formula a A Ac A B B c C Cn d D E E1,n (A) = E1 E2,n (A) = E2 F g h H(k) I Jν (z) k K L Lkø L m mi mi mr M n N p(i) p{i, t | j, t0 } P (i) q(i) Q(i) Q Carried traffic pr source or per channel Offered traffic = Ao Carried traffic = Y Lost traffic Call congestion Burstiness Constant Traffic congestion = load congestion Catalan’s number Slot size in multi-rate traffic Probability of delay or Deterministic arrival or service process Time congestion Erlang’s B–formula = Erlang’s formula Erlang’s C–formula = Erlang’s formula Improvement function Number of groups Constant time interval or service time Palm–Jacobæus’ formula Inverse time congestion I = 1/E Modified Besselfunction of order ν Accessibility = hunting capacity Maximum number of customers in a queueing system Number of links in a telecommuncation network or number of nodes in a queueing network Mean queue length Mean queue length when the queue is greater than zero Stochastic variable for queue length Mean value (average) = m1 i’th (non-central) moment i’th centrale moment Mean residual life time Poisson arrival process Number of servers (channels) Number of traffic streams or traffic types State probabilities, time averages Probability for state i at time t given state j at time t0 Cumulated state probabilities P (i) = ix=−∞ p(x) Relative (non normalised) state probabilities Cumulated values of q(i): Q(i) = ix=−∞ q(x) Normalisation constant ?? ?? ?? ?? (??) ?? ?? ?? ?? ?? 99 194 ??, 199 ?? ?? ?? ?? ?? 197 197 197 ?? ?? ?? (3.13) ?? ?? iv Page/Formula r R s S t T U v V w W W y Y Z Reservation parameter (trunk reservation) Mean response time Mean service time Number of traffic sources Time instant Stochastisc variable for time instant Load function Variance Virtuel waiting time Mean waiting time for delayed customers Mean waiting time for all customers Stochastisk variable for waiting time Arrival rate Poissonprocess: y = λ Carried traffic Peakedness α β ε ϑ ϕ(s) κi λ Λ µ π(i) Offered traffic per source Offered traffic per idle source Palm’s form factor Lagrange-multiplicator Laplace/Stieltjes transform i’th cumulant Arrival rate of a Poisson process Total arrival rate to a system Death rate, inverse mean service time State probabilities, customer mean values Service ratio Variance, σ = standard deviation Time-out constant or constant time-interval σ2 τ ?? ??, ?? ?? ?? ?? ?? 193 ?? ?? ?? (8.9) (8.3) (3.10) 186 (??) ?? ?? 94 ?? ?? ?? ?? Contents Introduction to Teletraffic Engineering 1.1 1.2 1.3 1.4 Modelling of telecommunication systems 1.1.1 System structure 1.1.2 The Operational Strategy 1.1.3 Statistical properties of traffic 1.1.4 Models Conventional Telephone Systems 1.2.1 System structure 1.2.2 User behaviour 1.2.3 Operation Strategy Communication Networks 1.3.1 The telephone network 1.3.2 Data networks 11 1.3.3 Local Area Networks LAN 1.3.4 Internet and IP networks 13 12 Mobile Communication Systems 13 1.4.1 Cellular systems 14 1.4.2 Third generation cellular systems 16 1.5 The International Organisation of Telephony 16 1.6 ITU-T recommendations 16 Traffic concepts and variations 17 2.1 The concept of traffic and the unit “erlang” 17 2.2 Traffic variations and the concept busy hour 20 2.3 The blocking concept 25 2.4 Traffic generation and subscribers reaction 27 Probability Theory and Statistics 35 v vi 3.1 3.2 3.3 Distribution functions 35 3.1.1 Characterisation of distributions 36 3.1.2 Residual lifetime 37 3.1.3 Load from holding times of duration less than x 40 3.1.4 Forward recurrence time 41 Combination of stochastic variables 43 3.2.1 Stochastic variables in series 3.2.2 Stochastic variables in parallel 44 Stochastic sum 45 Time Interval Distributions 4.1 43 49 Exponential distribution 49 4.1.1 Minimum of k exponentially distributed stochastic variables 51 4.1.2 Combination of exponential distributions 51 4.2 Steep distributions 53 4.3 Flat distributions 54 4.3.1 4.4 Hyper-exponential distribution 55 Cox distributions 56 4.4.1 Polynomial trial 59 4.4.2 Decomposition principles 59 4.4.3 Importance of Cox distribution 61 4.5 Other time distributions 62 4.6 Observations of life–time distribution 63 Arrival Processes 5.1 5.2 5.3 65 Description of point processes 65 5.1.1 Basic properties of number representation 67 5.1.2 Basic properties of interval representation 68 Characteristics of point process 70 5.2.1 Stationarity (Time homogeneity) 70 5.2.2 Independence 71 5.2.3 Regularity 71 Little’s theorem The Poisson process 72 75 6.1 Characteristics of the Poisson process 75 6.2 The distributions of the Poisson process 76 vii 6.3 6.4 6.2.1 Exponential distribution 77 6.2.2 The Erlang–k distribution 79 6.2.3 The Poisson distribution 81 6.2.4 Static derivation of the distributions of the Poisson process 83 Properties of the Poisson process 85 6.3.1 Palm’s theorem 85 6.3.2 Raikov’s theorem (Splitting theorem) 6.3.3 Uniform distribution - a conditional property 87 87 Generalisation of the stationary Poisson process 88 6.4.1 Interrupted Poisson process (IPP) 88 Erlang’s loss system, the B–formula 93 7.1 Introduction 93 7.2 Poisson distribution 94 7.3 7.4 7.2.1 State transition diagram 95 7.2.2 Derivation of state probabilities 96 7.2.3 Traffic characteristics of the Poisson distribution 97 Truncated Poisson distribution 98 7.3.1 State probabilities 98 7.3.2 Traffic characteristics of Erlang’s B-formula 99 Standard procedures for state transition diagrams 105 7.4.1 7.5 7.6 Evaluation of Erlang’s B-formula 107 Principles of dimensioning 109 7.5.1 Dimensioning with fixed blocking probability 109 7.5.2 Improvement principle (Moe’s principle) 110 Software 113 Loss systems with full accessibility 115 8.1 Introduction 116 8.2 Binomial Distribution 117 8.3 8.2.1 Equilibrium equations 118 8.2.2 Characteristics of Binomial traffic 120 Engset distribution 122 8.3.1 Equilibrium equations 123 8.3.2 Characteristics of Engset traffic 123 8.3.3 Evaluation of Engset’s formula 127 viii 8.4 Pascal Distribution (Negative Binomial) 131 8.5 The Truncated Pascal (Negative Binomial) distribution 131 8.6 Software 134 Overflow theory 9.1 Overflow theory 136 9.1.1 9.2 9.3 9.5 9.6 State probability of overflow systems 136 Wilkinson-Bretschneider’s equivalence method 139 9.2.1 Preliminary analysis 140 9.2.2 Numerical aspects 141 9.2.3 Parcel blocking probabilities 142 Fredericks & Hayward’s equivalence method 144 9.3.1 9.4 135 Traffic splitting 145 Other methods based on state space 146 9.4.1 BPP-traffic models 147 9.4.2 Sander & Haemers & Wilcke’s method 147 9.4.3 Berkeley’s method 148 Generalised arrival processes 148 9.5.1 Interrupted Poisson Process 149 9.5.2 Cox–2 arrival process 150 Software 151 10 Multi-Dimensional Loss Systems 153 10.1 Multi-dimensional Erlang-B formula 154 10.2 Reversible Markov processes 157 10.3 Multi-Dimensional Loss Systems 159 10.3.1 Class limitation 159 10.3.2 Generalised traffic processes 159 10.3.3 Multi-slot traffic 160 10.4 The Convolution Algorithm for loss systems 164 10.4.1 The algorithm 165 10.4.2 Other algorithms 173 10.5 Software tools 175 11 Dimensioning of telecommunication networks 177 11.1 Traffic matrices 178 11.1.1 Kruithof’s double factor method 178 ix 11.2 Topologies 181 11.3 Routing principles 181 11.4 Approximate end-to-end calculations methods 181 11.4.1 Fix-point method 181 11.5 Exact end-to-end calculation methods 182 11.5.1 Convolution algorithm 182 11.6 Load control and service protection 182 11.6.1 Trunk reservation 183 11.6.2 Virtual channel protection 184 11.7 Moe’s principle 184 11.7.1 Balancing marginal costs 185 11.7.2 Optimum carried traffic 186 12 Delay Systems 191 12.1 Erlang’s delay system M/M/n 192 12.2 Traffic characteristics of delay systems 193 12.2.1 Erlang’s C-formula 193 12.2.2 Mean queue lengths 195 12.2.3 Mean waiting times 198 12.2.4 Improvement functions for M/M/n 199 12.3 Moe’s principle applied to delay systems 199 12.4 Waiting time distribution for M/M/n, FCFS 201 12.4.1 Response time with a single server 203 12.5 Palm’s machine repair model 204 12.5.1 Terminal systems 206 12.5.2 Steady state probabilities - single server 207 12.5.3 Terminal states and traffic characteristics 209 12.5.4 n servers 213 12.6 Optimising Palm’s machine-repair model 214 12.7 Software 216 13 Applied Queueing Theory 217 13.1 Classification of queueing models 217 13.1.1 Description of traffic and structure 217 13.1.2 Queueing strategy: disciplines and organisation 219 13.1.3 Priority of customers 220 x 13.2 General results in the queueing theory 221 13.3 Pollaczek-Khintchine’s formula for M/G/1 222 13.3.1 Derivation of Pollaczek-Khintchine’s formula 222 13.3.2 Busy period for M/G/1 224 13.3.3 Waiting time for M/G/1 225 13.3.4 Limited queue length: M/G/1/k 225 13.4 Priority queueing systems M/G/1 226 13.4.1 Combination of several classes of customers 226 13.4.2 Work conserving queueing disciplines, Kleinrock’s conservation law 227 13.4.3 Non-preemptive queueing discipline 229 13.4.4 SJF-queueing discipline 232 13.4.5 M/M/n with non-preemptive priority 234 13.4.6 Preemptive-resume queueing discipline 235 13.5 Queueing systems with constant holding times 13.5.1 Historical remarks on M/D/n 236 236 13.5.2 State probabilities and mean waiting times 237 13.5.3 Mean waiting times and busy period 239 13.5.4 Waiting time distribution (FCFS) 240 13.5.5 State probabilities for M/D/n 242 13.5.6 Waiting time distribution for M/D/n, FCFS 243 13.5.7 Erlang-k arrival process: Ek /D/r 244 13.5.8 Finite queue system M/D/1,n 245 13.6 Single server queueing system GI/G/1 246 13.6.1 General results 247 13.6.2 State probabilities of GI/M/1 248 13.6.3 Characteristics of GI/M/1 249 13.6.4 Waiting time distribution for GI/M/1, FCFS 251 13.7 Round Robin (RR) and Processor-Sharing (PS) 251 13.8 Literature and history 253 14 Networks of queues 255 14.1 Introduction to queueing networks 255 14.2 Symmetric queueing systems 256 14.3 Jackson’s Theorem 257 14.3.1 Kleinrock’s independence assumption 260 14.4 Single chain queueing networks 261 296 [17] Little, J.D.C (1961): A Proof for the Queueing Formula L = λ W Operations Research, Vol (1961), pp 383–387 [18] Fry, T.C (1928): Probability and its Engineering Uses New York 1928, 470 pp [19] Jensen, Arne (1948): An Elucidation of A.K Erlang’s Statistical Works through the Theory of Stochastic Processes Published in “Erlangbogen”: E Brockmeyer, H.L Halstrøm and A Jensen: The Life and Works af A.K Erlang København 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(1937): Tekniska anordninger făor samtalsdebitering enligt tid Helsingfors Telefonfăorening, Tekniska Meddelanden 1937, No 2, pp 3248 [107] Palm, C (1941): Măattnoggrannhet vid bestăamning af trafikmăangd enligt genomsăokningsfăorfarandet (Accuracy of measurements in determining traffic volumes by the scanning method) Tekn Medd K Telegr Styr., 1941, No 7–9, pp 97–115 [108] Rabe, F.W (1949): Variations of Telephone Traffic Electrical Communications, Vol 26 (1949), 243–248 Author index Erlang, A.K., 18, 63, 296, 300 Eslamdoust, C., 175, 298 Aaltonen, P., 296 Abate, J., 225, 300 Addison, C.A, 61 Aguilar–Igartua, M., 146, 298 Ahlstedt, B.V.M, 63 Andersen, B., 280, 301 Ash, G.R., 299 Feller, W., 45, 204, 285, 301 Flannery, B.P., 297 Flo, A., 63 Fortet, R., 173, 298 Fredericks, A.A., 144, 297 Fry, T.C., 76, 237, 238, 296, 300 Basharin, G.P., 144 Baskett, F., 269, 301 Bear, D., 180, 299 Bech N.I., 138 Bech, N.I., 297 Boots, N.K., 300 Bretschneider, G., 139, 142, 297 Brockmeyer, E., 138, 236, 280, 297, 300, 301 Burke, P.J., 257, 258, 301 Bux, W., 61 Buzen, J.P., 263 Galtung, J., 295 Garc´ia–Haro, J., 146, 298 Gaustad, O., 63 Georganas, N.D., 276, 301 Gordon, W.J., 259, 301 Grandjean, Ch., 173, 298 Haemers, W.H., 147 Halstrøm, H.L., 300 Hansen, N.H., 280, 301 Hansen, S., 58 Hayward, W.S., 144 Hayward, W.S Jr., 289, 301 Herzog, U., 61 Hillier, F.S., 245 Hordijk, A., 61 Hussain, I., 296 Chandy, K.M., 60, 63, 269, 301 Chaveau, J., 297 Christensen, E.B., 63 Christensen, P.V., 296 Cobham, A., 300 Conway, A., 128 Conway, A.E., 173, 276, 297, 299, 301 Cox, D.R., 56, 65, 295 Crommelin, C.D., 237, 300 Dadswell, R.L., 63 Delbrouck, L.E.N., 173 Dickmeiss, A., 175, 176, 298 Isham, V., 295 ITU-T, 295 Iversen, V.B., 21, 23, 24, 59, 60, 63, 132, 165, 167, 173, 175, 209, 213, 214, 240, 245, 255, 276, 280, 282, 288, 289, 293, 295, 296, 298–302 Eilon, S., 72, 295 Ekberg, S., 297 Elldin, A., 142, 297 Engset, T.O., 123, 296 Jackson, J.R., 257, 259, 301 Jensen, A., 185, 186 Jensen, Arne, 76, 101, 109, 160, 195, 199, 200, 296, 298–300 303 304 Johannsen, F., 29, 295 Johansen, J., 146, 297 Johansen, K., 146, 297 Jolley, W.M., 61 Joys, L.A., 121, 127, 128, 296, 297 Karlsson, S.A., 281, 302 Kaufman, J.S., 173, 298 Keilson, J., 225, 300 Kelly, F.P., 222, 257, 300, 301 Kendall, D.G., 217, 248, 249, 300 Khintchine, A.Y., 237, 295, 300 khintchine, A.Y., 65 Kierkegaard, K., 32, 34, 295 Kingman, J.F.C., 157, 298 Kleinrock, L., 228, 251, 260, 261, 277, 278, 300, 301 Kold, N., 29, 32, 34, 295 Kosten, L., 137, 297 Kraimeche, B., 173, 299 Kristensen, M.H., 32, 34, 295 Kruithof, J., 300 Kuczura, A., 88, 149, 150, 296, 297 Kurenkov, B.E., 144 Kă uhn, P., 245 Larsen, M., 175, 176, 298 Lavenberg, S.S., 266, 301 Lazowska, E.D., 61 Lemaire, B., 224, 300 Lind, G., 142, 295, 297 Listov-Saabye, H., 167, 175, 299 Little, J.D.C., 296 Liu, W., 128, 297 Maral, G., 10, 295 Marchall, W.G., 247 Miller, H.D., 295 Moe, K., 109 Muntz, R.R., 269, 301 Newell, G.F., 259, 301 Nguyen, Thanh-Bang, 175, 299 Nielsen, B.F., 59, 60, 295 Nielsen, K.E., 29, 32, 34, 295 Nielsen, K.R., 298 Næss, A., 295 Olsson, M., 61 Pal Singh, M., 296 Palacios, F.G., 269, 301 Palm, C., 36, 54, 63, 107, 204, 285, 289, 295, 302 Pinsky, E., 127, 128, 173, 297, 299 PostigoBoix, M., 146, 298 Press, W.H., 297 Răonnblom, N., 160, 299 Rabe, F.W., 285, 302 Rahko, K., 62, 63, 142 Raikov, D.A., 87 Rasmussen, C., 146, 297 Reiser, M., 266, 301 Riordan, J., 137, 298 Roberts, J.W., 173, 299 Ross, K.W., 173, 299 Rygaard, J.M., 276, 301 Samuelson, P.A., 109 Sanders, B., 147 Sauer, C.H., 60, 63 Schehrer, R., 138 Schwartz, M., 173, 299 Stender-Petersen, N., 175, 299 Stepanov, S.N., 106, 167, 296, 298 Sutton, D.J., 157, 299 Techguide, 146, 298 Teukolsky, S.A., 297 Tijms, H., 300 Tsang, D., 173, 299 ´ 297 Vaulot, E., Vetterling, W.T., 297 Wallstrăom, B., 131 Wallstrăom, B., 91, 139, 296298 Whitt, W., 225, 300 Wilcke, R., 147 Wilkinson, R.I., 139, 298 Index BPP-traffic, 117, 158 Brockmeyer’s system, 137, 138 Burke’s theorem, 257 Burkes theorem, 301 bursty traffic, 138 Busy, 29 busy hour, 20, 22 time consistent, 22 Buzen’s algorithm, 263 A-subscriber, Aloha, 82 Aloha protocol, 101 alternative route, 135 alternative routing, 135 alternative traffic routing, 183 ANSI, 16 arrival process generalised, 148 arrival theorem, 124, 266 assignment demand, 11 fixed, 11 ATMOS-tool, 167, 175 availability see accessibility, 93, 115 call congestion, 26, 99, 167 call duration, 28 call intensity, 19 capacity allocation, 277 carried traffic, 99 carrier frequency system, 10 CCS, 19 central moment, 36, 37 central server, 263 central server system, 265 chain, 256 chains, 269 channel allocation, 14 charging, 281 circuit-switching, 10 class limitation, 159 code receiver, code transmitter, coefficient of variation, 37, 286 complementary distribution function, 36 compound distribution, 45 Poisson distribution, 285 concentration, 25 confidence interval, 290 connection-less, 11 conservation law, 227 control channel, 15 control path, B-ISDN, B-subscriber, balance detailed, 157 global, 154 local, 157 balking, 221 BBP-traffic, 160 BCMP kø-netværk, 301 BCMP queueing networks, 269 Berkeley’s method, 148 Binomial distribution, 84, 117 traffic characteristics, 120 truncated, 123 binomial distribution truncated, 123 Binomial expansion, 119 Binomial process, 83 Binomial-case, 116 Binomialprocess, 84 blocking concept, 25 305 306 Convolution algorithm multiple chains, 273 convolution algorithm, 164 queueing network, 261 cord, Cox–2 arrival process, 150 CSMA, 12 cut equations, 95 cyclic search, D/M/1, 250 data signalling speed, 20 death rate, 38 DECT, 15 Delbrouck’s algorithm, 173 dimensioning, 109 fixed blocking, 109 improvement principle, 110 direct route, 135 diva program, 176 EBHC, 19 EERT–method, 142 Engset distribution, 122 Engset’s formula recursion, 127 Engset-case, 116 equilibrium points, 224 equivalent system, 140 erlang, 17 Erlang fix-point method, 177 Erlang’s formula, 98 Erlang’s B-formula, 98, 99 recursion, 107 Erlang’s C-fomula, 193 Erlang’s C-formula, 194 Erlang’s delay system, 192 state transition diagram, 192 Erlang’s fix point method, 176 Erlang-B formula hyper-exponential service time, 155, 156 multi-dimensional, 154 Erlang-case, 116 Erlang-k distribution, 84 ERT–method, 139 exponential distribution, 79, 84 Feller-Jensen’s identity, 76 flat rate, 290 flow-balance equation, 258 forced disconnection, 27 Fortet & Grandjean’s algorithm, 173 Forward recurrence time, 41 Fredericks & Hayward’s method, 144 frequency multiplex, 10 full accessibility delay systems, 191 loss systems, 93, 115 geometric distribution, 84 GoS, 109 Grade-of-Service, 109 GSM, 15 hand-over, 15 hazard function, 38 HCS, 143 hierarchical cellular system, 143 HOL, 220 hub, 11 human-factors, 29 IDC, 68 IDI, 68 IMA, 146 improvement function, 100, 199 improvement principle, 110 improvement value, 113, 114 impulse-code-multiplex, 10 independence assumption, 260 index of dispersion counts, 68 Integrated Services Digital Network, intensity, 84 inter-active system, 206 interrupted Poisson process, 149 interval representation, 76, 280 inverse multiplexing, 146 Inversion program, 175 IPP, 90, 149 Iridium, 16 307 ISDN, ISO, 16 iterative studies, ITU, 16 ITU-R, 16 ITU-T, 16, 188 Jackson net, 257 jockeying, 221 Karlsson charging, 288, 290 Karlsson principle, 281 Kaufman & Robert’s algorithm, 173 Kleinrock’s square root law, 277 Kolmogorov’s criteria, 157, 158 Kosten’s system, 137 Kruithof’s double factor method, 178 lack of memory, 38 Lagrange multiplicator, 186, 200, 278 LAN, 12 last-look principle, 281 LCC, 94 Leaky bucket, 246 lifetime, 35 line-switching, 10 load function, 227, 228 local exchange, loss system, 25 lost calls cleared, 94 M/G/∞, 257 M/G/1-LIFO-PR, 257 M/G/1-PS, 257 M/M/n, 191 M/M/n, 192 machime repair model, 191 macro–cell, 143 man-machine, Markovian property, 38 mean value, 36 mean waiting time, 198 measurements horizontal, 282 vertical, 281 measuring methods, 280 principles, 280 measuring methods continuous, 280, 284 discrete, 280 measuring period unlimited, 286 mesh net, mesh network, 11 message-switching, 12 micro–cell, 143 microprocessor, mobile communication, 13 modelling, Moe’s Principle, 199 Moe’s principle, 109, 184 delay systems, 199 loss systems, 110 Moes princip, 299 multi-dimensional loss system, 159 multi-rate traffic, 144, 160 multi-slot traffic, 160 MVA-algorithm single chain, 256, 266 NBLOP program, 175 negative Binomial case, 116 Negative binomial distribution, 84 network management, 189 Newton-Raphson’s method, 141 NMT, 15 node equations, 95 non-central moment, 36 non//preemptive, 220 number representation, 76, 280 O’Dell grading, 135 observation interval unlimited, 284 offered traffic, 18 definition, 94, 117 on/off source., 117 Operational Strategy, overflow theory, 135 308 packet switching?, 11 packet-switching, 11 paging, 15 Palm’s form factor, 37 Palms identity, 36 Palms machine-repair model, 206 Palm-Wallstrăom-case, 116 Palms maskinproblem optimering, 214 parcel blocking, 142 Pascal distribution, 84 Pascal-case, 116 PASTA property, 154 PASTA-property, 100 PCM-system, 10 PCT-I, 94, 116 PCT-II, 116, 117 peakedness, 97, 101, 138 persistence, 30 Pincon program, 175 Poisson distribution, 82, 94 calculation, 107 truncated, 98 Poisson process, 75 Poisson-case, 116 Poissondistribution, 84 Poissonprocess, 84 polynomial distribution, 271 potential traffic, 20 preemptive, 220 preferential traffic, 30 primary route, 135 product form, 154 protocol, Pure Chance Traffic Type I, 94, 116 Pure Chance Traffic Type II, 116 QoS, 109 Quality-of-Service, 109 queueing discipline work conserving, 227 queueing networks, 255 Raikov’s theorem, 87 Rapp’s approximation, 141 reduced load method, 177 regeneration points, 224 register, 6, rejected traffic, 19 relative accuracy, 286 reneging, 221 research spiral, Residual lifetime, 37 response time, 204 reversibility, 157 reversible process, 158, 222, 257 ring net, roaming, 15 roulette simulation, 293 round robin, 251 sampling theory, 282 Sander’s method, 147 scanning method, 281, 286 secondary route, 135 service protection, 136 service ratio, 216 service time, 28 sim program, 175 slot, 82 SM, 19 smooth traffic, 138 space divided system, SPC-system, splitting theorem, 87 sporadic source, 117 spredningsindeks1interval, 68 square root law, 277 standard deviation, 37 standard procedure for state transition diagrams, 105 star net, statistical multiplexing, 25 stochastic process, stochastic sum, 45 stochastic variable ,parallel, 44 stochastic variables, 35 in series, 43 store-and-forward, 11 309 subscriber-behaviour, 29 symmetric køsystem, 221 symmetric queueing systems, 257 System Structure, table Erlang’s B-formula, 107 tele communication network, telephone system software controlled, telephone systems conventional, teletraffic theory terminology, traffic concepts, 17 TES program, 175 time congestion, 26, 99, 166 time distributions, 35 time divided system, time multiplex, 10 time-out, 27 traffic carried, 18 traffic concentration, 24 traffic congestion, 26, 100, 167 traffic intensity, 17, 284 traffic matrices, 178 traffic matrix, 178 traffic measurements, 279 traffic splitting, 145 traffic unit, 17 traffic volume, 18, 284 traffic-variations, 20 transit exchange, transit network, triangle optimisation, 187 user channels, 15 utilisation, 20, 110 variance, 37 virtual circuit protection, 159 virtual congestion, 26 virtual queue length, 195 virtual waiting time, 222, 228 voice path, VSAT, 10 waiting time distribution FCFS, 201 waiting-time distribution, 40 Weibull distribution, 39 Westerberg’s distribution, 289 Wilkinson’s equivalence method, 139 wired logic, 310 ... 290 Author index 303 Index 305 Chapter Introduction to Teletraffic Engineering Teletraffic theory is defined as the application of probability theory to the solution... ?? 193 ?? ?? ?? (8.9) (8.3) (3.10) 186 (??) ?? ?? 94 ?? ?? ?? ?? Contents Introduction to Teletraffic Engineering 1.1 1.2 1.3 1.4 Modelling of telecommunication systems 1.1.1... generally, teletraffic theory can be viewed as a discipline of planning where the tools (stochastic processes, queueing theory and numerical simulation) are taken from operations research The term teletraffic