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1 (10 points)   
SME of 50 people wishes to change her automatic exchange (PABX) and to assign it only to telephony. It has the following data:
- There are 40 telephones  
- The measured traffic at the peak hour reported to the station is as follows
- 5 mn/hour for the calls leaving  
- 3 mn/hour for the calls returning
- Medium traffic is half of the traffic of point  
- The activity of the company is 8 hours/day and 21 days/month.  
Determine  
a) The total traffic in Erlang  
b) The number of circuits necessary to run out this traffic with a rate of loss of 10% maximum

1 (10 分)
一个50人的PME希望改变它的自动交换系统(PABX) 并且 去安一个设备对它的电话系统, 它们有下面的一下数据:
-     40个电话机
-     一个电话机的峰值traffic被报告如下:
-     5 mn/hour for the calls leaving  
-     3 mn/hour for the calls returning
-     平均traffic是峰值traffic的一半
-     企业的avtivity是 8小时/天 , 21天/月
求:
a) 总的traffic 以Erlang为单位
b) 必须电路的数目为了保证这个trafic with一个最大10%的损失率

2 (10 points)   
Following experiments people notes that the average duration of transmission of a package of L bytes on a link is equal to L (c-µ) where c is the maximum capacity of the connection in bytes/second and µ the average charge on the link in bytes/second.  
Are A and B two routers connected by a link with 50 Ko/s.
a) Which is the average duration which a package of 1Ko spends to go from A towards B if there are 4 connections of 10 Ko/s using the connection between A and B.  
b) Briefly explain what to happen in mode “datagrams” if the fifth connection of 10 Ko/s uses the connection between A and B.
c) Same question if one uses the mode “virtual circuits”.


2 (10 分)
根据经验,人们注意到在一个连接上传输 一个L  byte的包的持续时间等于 L/(c-µ). 这里c是link的最大容量 以byte/second为单位, 并且µ 是在link上的平均负荷(chage) 以byte/second
有 A 和B 2个路由(router)由连接一个50 Kb/s的link所连接.
a)平均持续时间是多少, 从A到B发一个1Kb的包, 如果有4个10Kb/s的连接被使用在A和B之间
b)如果第5个10Kb/s的连接被使用在A和B之间,简单的解释一下将发生什么in mode “datagrams”
c)同样的问题, 如果使用the mode  “virtual circuits”(虚拟电路的形式)


3 (10 points)   
People consider a network made up of N servers of exponential service of parameter &micro;. The clients arrive in file 1 according to a process of Poisson in rate , < &micro;. At the exit of file i (i different with N), a customer exit the system with a probability ε or enters the file (i+1) with a probability (1 - ε). If the client exit the system before be passed by the file N, it is said that it is lost.  
a) To calculate the rate of arrive in the file i,  
b) What is worth, according to , ε et N the effective rate流量of the system and the probability of losing a customer.

3 (10 分)
人们考虑有一个网络,它由N个指数的服务器组成, 参数是&micro;. 客户到达file 1 按照一个Poisson process 在速率 , < &micro;. 在离开file i (i和N不等)方面, 一个客户离开系统在一个概率ε, 即也就是说 进入file (i+1) 在一个概率(1- ε). 如果一个客户离开了系统在他被通过file N前, 人们说他被丢掉了.
a)计算到达速率  在file i中的.
b)根据, ε et N, 系统的有效流量和丢客户的概率是多少?

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问了一个搞电信的朋友，他对第二题比较熟
平均持续时间是多少, 从A到B发一个1Kb的包:1/50
如果有4个10Kb/s的连接被使用在A和B之间:1/40
如果第5个10Kb/s的连接被使用在A和B之间,简单的解释一下将发生什么in mode “datagrams”:1/50
这个答案也不一定正确，感觉题目缺少上下文,或者描述不够全