Problem Set 1 (Due: Friday, Sept. 29, 2017)

Transcription

1 Elctrical and Computr Enginring Mmorial Univrsity of Nwfoundland ENGI Advancd Data Ntworks Fall 2017 Problm St 1 (Du: Friday, Spt. 29, 2017) Qustion 1 Considr a communications path through a packt switching ntwork with bit rrors that occur indpndntly with a probability of P Packts travlling through th ntwork ar a fixd lngth of 864 bits consisting of th following filds: Dstination Addrss 32 bits Information Fild 800 bits CRC 32 bits (a) What is th probability that a packt is lost bfor arriving at th dstination? (Assum that a packt is lost if th dstination addrss is corruptd during transit. You may assum that th probability that a packt is lost du to quu ovrflow at switchs is ngligibl.) What is th probability that a packt arriving at th dstination is dtctd as having rrors, assuming that th CRC is capabl of dtcting all rrors? (b) How many packts ar xpctd to b snt bfor a packt nds to b rtransmittd? (c) Assum that 1000 packts ar to b snt. What is th probability that thr or mor packts nd to b rtransmittd? (d) Assuming that th CRC is capabl of dtcting on, two, or thr bit rror pattrns, what is th probability that a rcivd packt has rrors that ar dtctd? What is th probability that rrors ar not dtctd? Commnt. Qustion 2 A communications protocol implmnts an rror control schm by snding th information and CRC filds of a packt 3 tims and prforming a majority vot on ach bit of th filds. For xampl, at th rcivr, bit i of th information fild is dtrmind by a majority vot on th 3 copis of bit i. For th protocol, ach packt is 864 bits long, consisting of a 32-bit dstination fild (which is not triplicatd, but is only snt onc), an 800-bit information fild and a 32-bit CRC. At th transmittr, th CRC schm is applid to th packt information fild bfor th bits ar triplicatd.. (a) Assuming that bit rrors occur indpndntly in th communications channl with a probability of P 10 6, dtrmin th probability that a bit in th information fild is in rror aftr th majority vot is applid at th rcivr. (b) Undr this scnario, rpat Qustion 1 (a) and (b). 1

2 Qustion 3 A CRC is constructd to gnrat a 5-bit FCS for a 12-bit mssag. Th gnrator polynomial is 5 2 p( x) x x x 1. (a) Dtrmin th FCS for th data squnc (lft most bit = MSB) using th gnrator polynomial p( x). (b) Now assum that th following fram is rcivd. Dtrmin whthr it is likly that an rror has occurrd in th rcivd fram (c) Draw th shift rgistr circuit that could b usd to gnrat th FCS and show that it producs th FCS calculatd in part (a). Qustion 4 A packt of siz 2000 bits travls through a packt switchd ntwork along a path that includs 8 links and 7 switchs. Whil travrsing ach link, th packt is suscptibl to random, indpndnt bit rrors. Th bit rror rat on various links is givn by th following: P on thr links, P 5 10 on thr links, and P 10 5 on two links. Th probably of packt loss in a switch du to buffr ovrflow is 10-6 for all switchs in th ntwork. Dtrmin th probability that th packt nds to b rtransmittd. Qustion 5 Considr th transmission of a fil of data ovr an rror-fr link of lngth 2000 km. Th data rat on th link is 1 Mbps and th vlocity of signal propagation is km/s. Th fil contains 10 Mbyts of information. Data is to b transmittd ovr th link in packts consisting of 48 hadr bits, 1000 data bits, and 32 CRC bits. You may assum that th tim to procss an incoming packt (of any typ) is ngligibl and acknowldgmnt packts ar 64 bits in lngth. (a) If a stop-and-wait flow control is usd on th link, how long will it tak to snd th ntir fil of data? (b) If a sliding window flow control with a maximum window siz of 8 is usd on th link, how long will it tak to snd th ntir fil of data? (c) Considr now a chang in th maximum window siz usd by th protocol. Dtrmin th window siz ndd to allow maximiz utilization of th link. Dtrmin how long it will tak to snd th ntir fil of data for this scnario. (d) Considr now that th link is not rror-fr but has a bit rror rat of Bit rrors occur randomly and indpndntly. Rpat (a) for this nw scnario assuming that all bit rrors ar dtctabl by th CRC schm. 2

3 Qustion 6 A communications link of lngth 50 km has a link rat of 10 Mbps. Data is to b transmittd in fixd-siz packts of 500 bits, with acknowldgmnt packts of lngth 32 bits. Th vlocity of signal propagation is km/s and th bit rror rat is P Th procssing tim for any packt is ngligibl. Th protocol to b usd is a slctiv-rjct ARQ protocol, with a CRC that dtcts all rrors. What is th minimum siz of th squnc numbr fild to nsur th maximum possibl utilization of th link. What is th maximum utilization? HINT: Considr a faild transmission as ovrhad in th calculation of th utilization. Qustion 7 Considr th communications systm blow. Data is transmittd from A to B and thn from B to C using fixd siz packts of 1000 bits. Th protocol usd on link AB is a stop-and-wait ARQ. Th packts arriving at B ar forwardd onto C using a go-back-n ARQ protocol with th numbr of bits in th squnc numbr fild givn by k = 3. Th on-way propagation dlay on link AB is 5 s and th on-way propagation dlay on link BC is 50 s. Th link rat for link BC is 100 Mbps. (a) Assuming that th bit rror rat on both links AB and BC is zro, what is th maximum link rat on link AB to nsur that th buffrs at B do not ovrflow? You may assum that acknowldgmnt packts ar ngligibl in siz and that thr ar no dlays in a rcivr snding an ACK aftr a data packt has bn rcivd. B sur to stat any othr assumptions that you fl ar rasonabl to mak in your analysis. (b) Rpat (a) assuming that th bit rror rat on link AB is P = 10-4 and link BC is rror-fr. Assum that th CRC is abl to dtct all rrors. stop&wait 5 s prop. rat =? go-back-n 50 s prop. rat = 100 Mbps A B C 3

4 Qustion 8 Considr th communications systm blow. Data is transmittd from nod A to nod C in fixdsiz packts of 1064 bits, of which 64 bits ar control information such as a CRC fram chck squnc, and data is transmittd from nod B to nod C in fixd-siz packts of 264 bits, of which 64 bits ar control information such as a CRC fram chck squnc. At nod C, th data fild of ach arriving packt from nod A is dividd into 5 blocks of data and ach block has 64 bits of control information addd and is thn snt to nod D as a 264 bit packt. Packts from nod B ar passd on to nod D as 264 bit packts. Th data rat and propagation dlay for ach link is shown on th diagram blow, xcpt that th rat on link CD is to b dtrmind. Assum that th links ar rror fr. Givn that stop-and-wait flow control is usd on link AC and link CD and that sliding window flow control with maximum window siz of W = 7 is usd on link BC, dtrmin th minimum rat rquird on link CD to nsur that th buffrs at nod C do not ovrflow. You may assum that th transmission tim for an acknowldgmnt packt and th procssing tims for any packts ar ngligibl. Nod A 10 Mbps Link AC Nod C rat? Link CD Nod D 10 s 5 s Nod B 5 Mbps Link BC 5 s Qustion 9 (a) Considr communication btwn two stations A and C which must communicat through nod B and ovr two rror-fr links - AB and BC. Th distancs btwn th nods and data rats on th links ar: Link AB - 15 km, 5 Mbps Link BC - 10 km, 2 Mbps Assuming that th packt sizs on both links ar 1000 bits, dtrmin th bst cas utilization of both links AB and BC for th following flow control protocols: (i) stop-and-wait flow control (ii) sliding window flow control with a maximum window siz of W = 8 In your answr, assum that ACK packts ar ngligibly small and ar snt immdiatly upon rcipt of a data packt at station C. At nod B it may b ncssary to dlay ACKs as a mans of flow control. Us th vlocity of signal propagation of 2 x 10 5 km/s. (b) Assum that th links in (a) ar not rror fr. Assum that on both links th probability that a packt is in rror is Dtrmin th bst cas utilization for (i) stop-and-wait ARQ (ii) slctiv rjct ARQ with a maximum window siz of W = 8 4

5 ANSWERS: Q1. (a) P(lost packt) = , P(damagd packt) = (b) packts (c) (d) P(rrors dtctd) = (although not idntical to th answr in part (a)), P(rrors not dtctd) = Q2. (a) (b) (a) P(lost packt) = , P(damagd packt) = (b) packts Q3. (a) (b) rmaindr = 1110, thrfor rror has probably occurrd (c) answr not availabl Q Q5. (a) 1774 sconds (b) 222 sconds (c) window siz must b 20 or gratr, 90.6 sconds (d) 1976 sconds Q6. 5 bits, 90.48% Q7. (a) 175 Mbps (b) 237 Mbps Q Mbps Q9. (a) (i) UAB = 33.33%, UBC = 83.33% (ii) UAB = 40%, UBC = 100% (b) (i) UAB = 30.2%, UBC = 75.4% (ii) UAB = 36.2%, UBC = 90.5% 5