1、排队论,引言 排队论在通信网络中的应用,1. Telecommunication system,Telecommunication system from the traffic point of view:Ideas:the system serves the incoming trafficthe traffic is generated by the users of the system,Interesting questions,Given the system and incoming traffic,what is the quality of service experienc
2、ed by the user?Given the incoming traffic and required quality of service,how should the system be dimensioned? Given the system and required quality of service,what is the maximum traffic load?,General purpose,Determine relationships between the following three factors:quality of servicetraffic loa
3、dsystem capacity,Example,Telephone call traffic = telephone calls by everybody system = telephone network quality of service = probability that the phone rings at the destination,Relationships between the three factors,Qualitatively, the relationships are as follows:,To describe the relationships qu
4、antitatively, mathematical models are needed,Teletraffic models,Teletraffic models are stochastic (= probabilistic) systems themselves are usually deterministic， but traffic is typically stochastic “you never know, who calls you and when”It follows that the variables in these models are random varia
5、bles, e.g. number of ongoing calls number of packets in a bufferRandom variable is described by its distribution, e.g. probability that there are n ongoing calls probability that there are n packets in the bufferStochastic process describes the temporal development of a random variable,Difference be
6、tween the real system and the model,Typically, the model describes just one part or property of the real system under consideration and even from one point of view the description is not very accurate but rather approximative Thus, caution is needed when conclusions are drawn,Practical goals,Network
7、 planning dimensioning optimization performance analysis Network management and control efficient operation fault recovery traffic management routing accounting,2. Teletraffic models,Two phases in modelling: modelling of the incoming traffic traffic model modelling of the system itself system model
8、Two types of system models: loss systems waiting/queueing systems These models can be combined to create models for whole telecommunication networks loss network models queueing network models Next we will present a simple teletraffic model describing a single resource,Simple teletraffic model,Custo
9、mers arrive at rate (customers per time unit) 1/ = average inter-arrival timeCustomers are served by n parallel serversWhen busy, a server serves at rate (customers per time unit) 1/ = average service time of a customerThere are m waiting placesIt is assumed that blocked customers (arriving in a ful
10、l system) are lost,Pure loss system,Pure waiting system,Mixed system,Infinite system,Littles formula,Consider a system where new customers arrive at rate Assume stability: Every now and then, the system is empty Consequence: Customers depart from the system at rate Let N =average number of customers
11、 in the system T =average time of customers spends in the system Littles formula: N= T,3 Classical model for telephone traffic,Loss models have traditionally been used to describe (circuit-switched) telephone networks Pioneering work made by Danish mathematician A.K. Erlang (1878-1929) Consider a li
12、nk between two telephone exchanges traffic consists of the ongoing telephone calls on the link Erlang modelled this as a pure loss system (m = 0),Traffic process,Traffic intensity,Example,Characteristic traffic,Blocking,Call rates,Traffic streams,Teletraffic analysis,Erlangs blocking formula,Example
13、,Required capacity vs. traffic,Required quality of service vs. traffic,Required quality of service vs. capacity,4 Classical model for data traffic,Traffic process,Traffic load,Example,Teletraffic analysis,Waiting time formula for an M/M/1 queue,Example,Required link speed vs. arrival rate,Required q
14、uality of service vs. arrival rate,Required quality of service vs. link speed,5 Telecommunication network,Shared medium as an access network,Example: Why networks? (1),Example: Why networks? (2),Example: Why networks? (3),Example: Why networks? (4),Network level: switching and routing,Switching mode
15、s,Routing methods in telephone networks,Queueing network model,Link level: multiplexing and concentration,Transmission: multiplexing,Teletraffic model for a statistical multiplexer,Teletraffic model for a concentrator,Multiple access techniques used in mobile telephone networks,Teletraffic modelling
16、 of various multiple access techniques,Multiple access techniques in computer LANs,Random Access,Analysis of ALOHA,Analysis of Slotted ALOHA,课程介绍,教材： 任何一本排队论及相关的书籍 图书馆内相关书籍： 排队论 陆传赉编著 北京邮电学院出版社, 1994.5 排队论及其在计算机通信中的应用 盛友招 编著 北京邮电大学出版社, 1998 排队论与随机服务系统 (美)华兴编著上海翻译出版公司, 1987 排队论基础及应用 孟玉珂编著 同济大学出版, 1989. Queueing systems: Vol.1.theory. Kleinrock,L, N.Y. : John Wiley & Sons , 1975. Queueing Systems Vol 2 Computer Applications Kleinrock,L, N.Y. : John Wiley & Sons , 1975.,联系方式电话： 87556711Email：,
