>>> SOLUTIONS <<< 5 pts each sub-problem. 3 pts for correct formulas and set-up for each sub-problem.

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1 Comprehensve Fnal Exam for Computer Networks (CNT 65) Fall >>> SOLUTIONS <<< Welcome to the comprehensve Fnal Exam for Computer Networks. Read each problem carefully. There are requred problems each worth ponts. There s also an addtonal extra credt queston worth ponts. You may have wth you a calculator, pencls and/or pens, erasers, blank paper, and one 8.5 x nch formula sheet. On ths formula sheet you may have anythng you want (defntons, formulas, homework answers, old exam answers, etc.) as handwrtten by you n pencl or nk on both sdes of the sheet. Photocopes, scans, or computer generated and/or prnted text are not allowed on ths sheet. Note to tablet (Pad, etc.) users you may not prnt-out your handwrtten text for the formula sheet. You have mnutes for ths exam. Please use a separate sheet of paper for the answer to each queston. Good luck and be sure to show your work! Problem # pt for each tem ( pts for top level goal) In hs paper The Desgn Phlosophes of the DARPA Internet Protocols Clark descrbes a top-level goal and seven second-level goals of the DARPA Internet Archtecture. Gve these goals n order of mportance. How do these goals dffer om an archtecture desgned for commercal deployment? The top level goal s effectve technque for multplexed utlzaton of exstng nterconnected networks. The second second level goals are: Communcatons contnue despte loss of networks or gateways Support multple types of communcaton servce Accommodate a varety of networks Permt dstrbuted management Be cost effectve Easy host attachment Resource use accountable A commercal deployment would consder accountng of resource use as a top prorty (ths s order to be able charge for usage and make money). Problem # 5 pts each sub-problem. 3 pts for correct formulas and set-up for each sub-problem. Consder a mle lnk of Mb/s capacty that s error-ee. If ths lnk s used by a sngle sender wth a saturated queue sendng 5 byte ames, what wll the lnk utlzaton be for the followng cases (hnt: sgnal propagaton s roughly 5 s per mle): a) Stop-and-Wat protocol Assumng that processng and ack transmsson delays are neglgble we have that: t U SAW t pr t Where t s the ame length n bts dvded by lnk capacty and t pr s the length of the lnk multpled by sgnal propagaton. So, for ths lnk we have that t ms and t ms, thus U SAW 5% 5

2 b) Sldng Wndow protocol wth a wndow sze of 7 For sldng wndow we have that: W t U SW max, t pr t thus 7 U SW max, % 5 Problem #3 3 pts for small ames, 3 pts for many queued statons, and 4 pts for explanaton of hgher effcency In hs paper Ethernet: Dstrbuted Packet Swtchng for Local Computer Networks Metcalfe has a result showng that Ethernet effcency (or utlzaton) s about 37%. What were the key parameter values (or condtons) for ths result and why mght t be that actual Ethernets can acheve hgher effcences than 37%? A low effcency comes om the analyss usng a small ame sze (48 bytes n the paper) and a large number of contnuously queued statons (56 n the paper). Gven the use of larger ame szes and the presence of fewer saturated statons, the effcency wll be much hgher. Smply ncreasng the ame sze to 4 bytes ncreases the effcency to over 9%. It would be rare for an actual Ethernet to only use small ame szes (data ames are usually large). In addton, artfacts of the BEB algorthm such as the short-term unfar capture effect also serve to ncrease effcency even when usng small ames. Problem #4 3 pts for Q matrx and soluton. pts for unformzaton. 3 pts for P matrx and soluton. pts for DTMC. For the below two-state CTMC gve the Q matrx and solve for steady state probabltes. Then convert the Q matrx to a P matrx usng unformzaton and solve t for steady state probabltes. Fnally, gve the DTMC correspondng to the P matrx. The Q matrx s: 5 Q 5 5 We wrte two equatons n two unknowns (breakng dependency wth sum of s ) for = Q and solve: 5 whch solves to 5 7 and 7. We can use unformzaton, P I Q example). So, we get where s the maxmum absolute value n Q (5 n the case of the above 3 5 P 5

3 We wrte two equatons n two unknowns (breakng dependency wth sum of s ) for = P and solve: 3 5 whch solves to 5 7 and 7 (as expected). The correspondng DTMC s: 3/5 /5 Problem #5 5 pts for latency domnates over capacty. 5 pts for proactve congeston control. In hs paper, On the Modelng and Analyss of Computer Networks Klenrock says Theren les the fundamental change that come about wth the ntroducton of ggabt lnks nto natonwde networks. Specfcally, we have passed om the regme (or pre-ggabt networkng) n whch we were bandwdth lmted, to the new regme of beng latency lmted n the post ggabt world. What does ths mean? What mplcatons does t have on the control of networks? In a latency lmted network t s latency, and not bandwdth or capacty, that domnates the response tme performance. Wth long dstance ggabt networks so many bts can be n flght that reactve congeston control s too sluggsh and proactve congeston control (for example, gvng users a maxmum allowable transmt rate) becomes necessary. Problem #6 pts for each subproblem. Answer the followng questons about queueng theory. a) What s the condton for stablty of a queue? (or only for determnstc arrvals and servce) wheres the arrval rate of jobs and s the servce rate. b) State Lttle s Law L W where L s the number of jobs n the system, s the arrval rate of jobs, and W s the mean wat (or delay) of jobs n the system c) FCFS s one possble servce dscplne. Name two others. Last Come Frst Servce (LCFS), prorty, round robn, and processor sharng are other possble servce dscplnes (need only two of these!). d) What does the P-K formula solve for? The P-K formula solve the mean number of jobs (or mean wat or delay) for an M/G/ queue.

4 3 Number of customers n the system Customer arrval rate Customer servce rate e) What do the Erlang-B and Erlang-C formulas solve for? The Erlang-B formula solves for the probablty of an arrvng job to an M/M/m/m system beng blocked (that s, all servers busy) and the Erlang-C formula solves for the probablty of an arrvng job to an M/M/m system beng queued (that s, all servers busy). Sad n another way, Erlang-B s for blocked calls cleared and Erlang-C s for blocked calls queued. Problem #7 Derve L (mean number of customers n the system) for the M/M/ queue. Carefully show your work. We st draw the Markov chan for the M/M/ queue. We solve the Markov chan for L. Once we have L we can easly fnd W usng Lttle s Law (L = W). Solvng for L, om local balance we wrte,,, for We can now solve for wth the knowledge that the sum of must equal one, So, now we have the steady state probabltes as, The mean then follows drectly om the defnton of mean, L CTMC s pt. Set-up s 5 pts. Correct steps and fnal expresson s 4 pts.

5 Problem #8 5 pts for each lne of code (one s changed, one s new). In appendx A s a CSIM model for an M/M/ queue. Modfy ths code such that t models an M/D// queue. Soluton s n the appendx. Problem #9 Descrpton and note of does not smooth out s pts. In the paper On the Self-Smlar Nature of Ethernet Traffc (Extended Verson) Leland et al. have a fgure that s a pctoral proof of self smlarty of Ethernet traffc. It s noted that A Pcture s Worth a Thousand Words. Descrbe (or sketch) ths fgure. What does t show? Ths fgure shows Ethernet traffc and synthetc Posson traffc at multple tme scales. At a small tme scale both the Ethernet and Posson traffc appear bursty. At a large tme scale the Ethernet traffc s stll bursty (and self-smlar to tself at a small tme scale), the Posson traffc s smooth. Ths fgure shows that Ethernet traffc s dfferent om Posson traffc n that t does not smooth-out. Problem # pts for each tem. Answer the followng questons about sensor networks. a) What are the necessary and optonal components of a WSN node? Necessary components are: sensng unt, memory (or storage), processor, communcatons, and power source. Optonal components nclude: power generatng unt (solar, vbraton, other), locaton fndng (GPS or other), and a means of moblty. b) What are the protocol stack layers and planes for a WSN node? The layers are the usual physcal, data lnk, network, transport, and applcaton. The three planes are power management, moblty management, and task management. c) Why are exstng routng protocols not well suted for WSNs? Exstng routng protocols (RIP, OSPF) are too chatty thus makng them energy neffcent. d) Descrbe two general routng methods (or protocols) for WSNs. Floodng wth broadcast, gosspng to a random neghbor, clusterng-based, and source routng (need only two). e) What s IOT? IOT = Internet of Thngs a focus of future research where many of the thngs may be wreless sensor nodes.

Extra Credt pts for concept. Descrbe the concept of energy-proportonal. Use a fgure or graph as needed. Is current network equpment (routers, lnks, etc.) energy proportonal?

6 Extra Credt pts for concept. Descrbe the concept of energy-proportonal. Use a fgure or graph as needed. Is current network equpment (routers, lnks, etc.) energy proportonal? In an energy proportonal system the power use s drectly proportonal to utlzaton (the green lne n the graph). Ths s what we seek. Exstng systems usually consume about the same power when lghtly utlzed as when hghly utlzed (the red lne n the graph). Humor From: I hope that everyone dd well

7 Appendx A Source code for Problem #8 #nclude <stdo.h> #nclude "csm.h" FACILITY Server; vod generate(double lambda, double mu); vod queue(double servce_tme); vod sm(vod) double lambda, mu; create("sm"); Server = faclty("server"); lambda =.9; mu =.; generate(lambda, mu); hold(.e6); prntf("============================================================= \n"); prntf("= Lambda = %f cust/sec \n", lambda); prntf("= Mu = %f cust/sec \n", mu); prntf("============================================================= \n"); prntf("= Utlzaton = %f %% \n",. * utl(server)); prntf("= Mean num n system = %f cust \n", qlen(server)); prntf("= Mean response tme = %f sec \n", resp(server)); prntf("= Mean servce tme = %f sec \n", serv(server)); prntf("= Mean throughput = %f cust/sec \n", tput(server)); prntf("============================================================= \n"); vod generate(double lambda, double mu) double nterarrval_tme, servce_tme; create("generate"); whle() nterarrval_tme = exponental(. / lambda); hold(nterarrval_tme); servce_tme = exponental(. / mu); queue(servce_tme); Replace wth servce_tme =. / mu; vod queue(double servce_tme) create("queue"); reserve(server); hold(servce_tme); release(server); Insert: f ((qlength(server) + num_busy(server)) >= ) return;

Calculation of the received voltage due to the radiation from multiple co-frequency sources

Calculation of the received voltage due to the radiation from multiple co-frequency sources Rec. ITU-R SM.1271-0 1 RECOMMENDATION ITU-R SM.1271-0 * EFFICIENT SPECTRUM UTILIZATION USING PROBABILISTIC METHODS Rec. ITU-R SM.1271 (1997) The ITU Radocommuncaton Assembly, consderng a) that communcatons