通信网理论基础习题答案 完整版

《通信网理论基础习题答案 完整版》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、通信网理论基础习题答案完整版2.2求M/M/m（n）中，等待时间w的概率密度函数。解：M/M/m（n）的概率分布为：?m?1(m?)k(m?)m1??n?m?1?p0???p0??k!m!1???r?0??1?(m?)k?k!p0?pk??mmk?k!?p0?0?0?k?m?1m?k?nk?n假定n>m，n≥0，现在来计算概率P{w>x}，既等待时间大于x的概率。P{w?x}??pj?Pj{w?x}j?0n其中，Pj{w>x}的概率为：Pj{w?x}?0Pj{w?x}?0?j?m?1?m?x?ei?0j?m(m

2、?x)i?i!m?j?n?1m?j?nPj{w?x}?1可得：P{w?x}??Pj??ej?mi?0n?1j?m?m?x(m?x)i??Pni!?mm?n?1jj?m?m?x(m?x)i?P0?????e???n?m!?j?mi!i?0?mmn?m?1?m?x(m?x)i?m?i??n?P0?e??Pnm!i!1??i?0若n??则P0(?m)m?(m???)xP{w?x}??e1??m!特别的，新到顾客需等待的概率为：P0(?m)mP{W?0}??1??m!共33页而n?m?1n?m?2mmP0(?x)i?m?xmm(?x)f

3、w(x)?e[?(m???)??m??m!(1??)i!(n?m?1)!i?0?m??n(m??)](n?m?1)!n?m?1在n??注：mmP0fw(x)??m(m???)e?(m???)xm!(1??)m?1k?0P{w?0}??PkP{w??}?Pn2.4求M/D/1排队问题中等待时间W的一、二、三阶矩m1、m2、m3，D表示服务时间为定值b，到达率为?。解：G(s)?s(1??)s????B(S)其中B(s)???0?(t?b)e?stdt?e?sb?s(1??)i从而G(s)?又G(s)?gs?i?sbs????ei?

4、0?(?sb)j??i?????gis???s??????j!j?0?i?0?????s(1??)??1????b2(1??)(1??)(2?b3??2b4)g0?g1?g2?231??b2(1??b)12(1??b)?(1?2?b)(1??)?b4g3??424(1??b)(?b??)?b2m1??G?(0)??g1?2(1??)m2?G??(0)?g2?2?(2??)?b6(1??)23(1?2?)?b4m3??G???(0)?g3?6?4(1??)32.5求M/B/1，B/M/1和B/B/1排队问题的平均等待时间，其中B是

5、二阶指数分布：f(t)???1e??1t?(1??)?2e??2t?1,?2?00???1共33页解：M/B/1B(S)??f(t)e?stdt?0???1(1??)?2??1?s?2?sw2?B??(0)?2?w1??B?(0)??1????1?2?m2??1????12???22??22(1??)?1?2????1?22?(1??)??12?2B/M/1???12?2(1??)?22??1??????w1?????????2??1??B(????)??1(1??)?2?????????1??????2取0???1的根令?1?

6、?1?2??21??1??2??(?1??2)2?2(1?2?)(?1??2)??2???(1??)?1??1??2??(?1??2)2?2(1?2?)(?1??2)?(1??1??2??(?1??2)2?2(1?2?)(?1??2))??1tB/B/1设到达的概率密度函数为f(t)???1e?(1??)?2e??2t设离去的概率密度函数为f(t)???3e假设?1??2????3t?(1??)?4e??4t?1??3?2??4共33页A(s)?B(s)???1(1??)?2??1?s?2?s???1(1??)?2????1(1

7、??)?2????A(?s)B(s)?1???????s????s??1??s??s22?1??1??????21????1?(1??)?2?s2?s4t2s2?s4?(?1?s)(?2?s)(?1?s)(?2?s)(?1?s)(?2?s)(?1?s)(?2?s)222?取??(s)?s(t?s)(?1?s)(?2?s)w(s)?k??(s)??(s)?s(t?s)(?1?s)(?2?s)k?lim??(s)t?s?0s?1?2k(?1?s)(?2?s)(t?s)22Sw(s)????Sw(s)?s?0?'?1?2?(?

8、1??2)t?1?2t22其中t??1??2?(??1?(1??)?2)2?(1??2)?1?(2???2)?2?2?(1??)?1?22.6在D/D/1排队问题中，顾客到达的时间间隔为a，服务时间为b，均为恒定值，且a>b，求：稳定状态时系统的队列长度为