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INST 346 H1 Solutions

University of Maryland – College Park

INST 346 H1 Networks Basics * XCY is the same as X choose Y

1.Suppos eus e r ss ha r ea3Mb psl i n ka nde a c hus e rr e q u i r e s150kb pswhe n t r a ns mi t t i n g .Ea c hus e r ,ho we v e r ,o nl yt r a ns mi t swi t hp r oba b i l i t yp=0. 1 ( i . e . ,1 0pe r c e n toft h et i me ) . a .I fc i r c ui ts wi t c h i n gi sus e d,wh a ti st h ema x i mu mn umbe ro fus e r s t hel i n kc a ns up por t ? 30 00kbps/150kbps=20us e r s b .Fort her e ma i n de roft hi spr o bl e m,s uppos epa c k e ts wi t c hi n gi s us e da n dt h a tt heus e r sa r ea c t i n gi n de pe nde nt l y( i nt hes t a t i s t i c a l s e ns e ,s of ore xa mpl et wou s e r st r a ns mi ta tt hes a met i mewi t h pr oba bi l i t yp *p) .Wh a ti st hepr oba bi l i t yt ha tagi v e nus e ri s t r a ns mi t t i n g ? p=0. 1,e as yo ne c. Su ppos et hene t wor kc ont a i ns120u s e r s .Wha ti st hepr o ba bi l i t y

t ha t ,a ta n ygi v e nt i me ,e x a c t l yNus e r sa r et r a ns mi t t i n g s i mu l t a ne ous l y ?( Hi nt :Us et heb i nomi a ldi s t r i b ut i on.I fy o une e d ar e mi nd e roft hef o r mul af ort hebi no mi a l di s t r i but i on,Wi ki pe di ami ghtbehe l pf u l ) . N P( Nus e r sar et r ans mi t t i ng)=P( X=N)=120CN *0. 1 *( 10. 1) ( 1 2 0– N)

d .Thene t wor kwoul dr e a c hc a p a c i t yi f20( =3M/ 1 50k)us e r swe r et o bes e nd i n ga tt hes a met i me .Wh a ti st hepr o ba bi l i t yt ha t21o r mor eus e r sa r et r a ns mi t t i n gs i mu l t a ne ous l y ? P( >21us e r st r ans mi t t i ng)=P( X>2 1) = Σ ( 1 2 0–N) *( 1 0. 1)

1 2 0 n=2 1t o1 20

N CN *0. 1

Thi samo unt st oa bout0. 007 9( y o uc anc al c ul a t eus i nga c al c ul a t or/c ode ) , whi c hi sv e r ys ma l l .

INST 346 H1 Solutions

University of Maryland – College Park

e .No wc ons i de rane t wor kofM us e r s .Gi v eaf or mul ai nt e r msofp , M,a ndNf o rt hepr o ba bi l i t yt ha tNormor eus e r sa r es e nd i n gda t a a tt hes a met i me . P( X>=N)= Σ

n=N>M

M ( M –n) Cn*pn *( 1p) ) (

2.Us et he s er e s ul t sa ndy ourunde r s t a ndi n gf r o mt her e a di n ga ndo urc l a s s di s c us s i ont ohe l py o ua ns we rt hef o l l o wi n gq ue s t i on s . a .Wha ta r et hea d v a nt a g e sofc i r c ui ts wi t c he dne t wor ko v e rapa c k e t s wi t c he dne t wor k ? Si mpl es har i ngr ul e s ,guar ant e e dba ndwi dt h/t r ans mi s s i on r at e .Nowai t i ng,que ui ngde l a y s /c ong e s t i on. I nt hea bo v e pr obl e m,3Mbpst r ans mi s s i onr a t ei sguar ant e e df oral lt he20 us e r st hene t wor kc anac c ommoda t e . b .Wha ta r et hea d v a nt a g e sofpa c k e ts wi t c he dne t wor ko v e rc i r c u i t s wi t c he dne t wor k ? Be t t e rr e s our c es har i ng,ac c ount sf ori dl eus e r sandc an s uppor tmanyus e r si nt hes amei nf r as t r uc t ur e .Pa c ke t s wi t c hi ngi sus e f ulwhe nt hepr obabi l i t yt ha tmul t i pl eus e r s t r ans mi ts i mul t ane ous l yi ss mal l ,a si nt hea bo v epr obl e m. Ci r c ui ts wi t c hi ngc anonl yac c ommoda t e20us e r swhi l epac ke t s wi t c hi ngc oul dac c ommoda t eal o tmor e . 3.Wes a wi ne q ua t i on( 1. 1)i nSe c t i o n1. 3. 1t ha td=N*L/ Ri st hef or mu l a f ore ndt oe ndde l a yf ors e nd i n gon epa c k e tofl e n g t hLo v e rNl i nk s , e a c hwi t ht r a ns mi s s i onr a t eR, whe ns t o r e a ndf or wa r dpa c k e ts wi t c he s a r eus e d( i gnor i n gq ue ui n g ,p r opa g a t i o nde l a y , a ndpr o c e s s i n gt i me ) . Ge ne r a l i z et hef o r mul af ors e ndi n gKs uc hpa c k e t sba c k t oba c ko v e rt he Nl i n ks .Exp l a i n. St or ea ndf or war df r ame wor k-byt het i meapac ke tr e ac he st he de s t i na t i on,t hef ol l o wi ngpa c ke ti ss t o r e di nt her out e radj ac e ntt o t hede s t i na t i onands oon.Soe ac hpa c ke taf t e rt hefir s tonl yhasL/ R de l a y . De l a y=N*L/ R+( L/ R)>( K1)t i me s=( N+K1) *L/ R

INST 346 H1 Solutions

University of Maryland – College Park

4.Su ppos et he r ei se x a c t l yonepa c k e ts wi t c hbe t we e nas e n di n gho s ta nda r e c e i vi n ghos t ,t het r a n s mi s s i o nr a t e sb e t we e nt h es e ndi n gh os ta ndt h e s wi t c ha ndbe t we e nt hes wi t c ha ndt her e c e i v i n ghos ta r eR1a ndR2, r e s pe c t i v e l ya ndt ha tt hes wi t c hus e ss t or e a ndf or wa r dpa c k e ts wi t c hi n g . Wha ti st het o t a le ndt oe ndde l a yt os e n dapa c k e tofl e n g t hL?( I gnor e q ue u i n g ,pr opa g a t i onde l a y ,a ndp r oc e s s i n gde l a y . )Exp l a i n. Se ndi nghos tt os wi t c h,t het r ans mi s s i onde l a yi s( L/ R1) . Swi t c ht or e c e i vi nghos t ,t het r ans mi s s i onde l a yi s( L/ R2) . To t alde l a yi st hes um oft het wo. De l a y=( L/ R1)+( L/ R2) 5.Su ppos ey oune e dt ode l i v e ra40t e r a b y t eda t a s e tf r o m Bos t o nt oLo s An g e l e s .Youha v ea v a i l a bl ea100Mbpsde di c a t e dl i n kf orda t at r a ns f e r . Woul dy o up r e f e rt ot r a ns mi tt heda t av i at hi sl i nko ri ns t e a dus eFe dEx o v e r ni ghtde l i v e r yt os e n das e tofdi s kdr i v e s ?Expl a i n. Bec a r e f ulwi t h t hedi ffe r e nc ebe t we e nb y t e s( B)a ndb i t s( b)whe na ns we r i n gq ue s t i ons i n v ol vi n gt r a ns mi s s i o nr a t e s . 6 40t e r abyt e s=4*1012*8bi t s ;100Mbps=100*10 bi t spe rs e c 6 I fus i ngt hede di c a t e dl i nk,i twi l lt a ke40*1012*8/( 1 00*10 )=32 5 *1 0s e c onds=37da y s .ButFe dExo v e r ni ghtde l i v e r y ,y ouc an guar ant e et heda t aar r i v e si noneda yandi ts houl dc os tl e s st han $1 00....