Optimization Ownership for Internet Protocol TV

Size: px
Start display at page:

Download "Optimization Ownership for Internet Protocol TV"

Transcription

1 340 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr 009 pimizaion wnrship for Inrn Proocol TV Won, Dalsoo, Dparmn of ompur Scinc Informaion, Bawha Womns Univrsiy, Soul,Kora Summary Th Toal os of wnrship (T) for dvloping communicaion srvics compriss from wo pars; APial EXpndiur (APEX) and Praional EXpndiur (PEX). Ths wo yps of coss ar inrrlad and affc any srvic providr s dploymn sragy. In many radiional mhods, slcion of criical lmns of a nw srvic is prformd in a hurisic mannr aimd a rducing only h PEX par of h T which is no ncssarily opimal. In h currn work, h T opimizaion problm of Inrn Proocol TlVision (IPTV) srvic is formulad as a nonlinar programming on. Th soluion of h proposd opimizaion problm can rack h dynamic changs of h T and lad o a im-varying opimal soluion. Simulaion rsuls vrify h dvlopd mhod. Ky words: Inrn Proocol TlVision (IPTV),Toal os of wnrship (T), APial EXpndiur (APEX), Praional EXpndiur (PEX) 1. Inroducion Inrn Proocol TlVision (IPTV) uss IP as h ranspor plaform o snd vido daa o h lvision via high-spd Inrn conncions such as fibr-o-h-x conncions (FTTx) and/or nx-gnraion digial subscribr lins (xdsl). Wih his chnology, consumrs will b in compl conrol of wha, whn, and whr hy wach lvision programming. Morovr, givn h vrsailiy of h IP nwork, consumrs will hav h opporuniy o mbrac a plhora of srvics ha go byond vido daa. Srvic providrs and /opraors hav o minimiz apial Expndiurs (apx) and praional Expndiurs (px), achiv on im srvic launch, dlivr qualiy of srvic ha will driv srvic adopion and dfin an archicur ha provids upward scalabiliy for siz and srvics. A srvic providr considring h dlivry of an IPTV srvic should considr h oal cos of ownrship (T) whn assssing h mris of diffrn srvic dlivry approachs. Toal cos of ownrship (T) is a financial sima dsignd o hlp consumrs and nrpris managrs assss dirc and indirc coss commonly rlad o sofwar or hardwar. I is a form of full cos accouning. Middlwar and ohr sysms ndd o provid vido ar also par of h oal APEX. In a businss cas, APEX can b brokn ino fixd and variabl pars; fixd bing hos coss o build h rquisi sysm and infrasrucur o dlivr h srvics, and variabl bing hos coss incurrd wih individual subscribr ak ras. PE and in hom insallaion ar considrd variabl coss, along wih DSL lin cards, sinc h APEX is incurrd only whn srvic is akn. Idally, fixd APEX should b minimizd sinc i is h a risk invsmn o nr ino h businss. Variabl APEX, alhough dircly rlad o acual srvic ak ra and rvnu, canno b so xcssiv as o prsn a RI (Rurn on Invsmn ha i cras unaccpabl RI. IPTV businss cass as wll as acual dploymns hav shown ha h in hom PE and insallaion coss amoun o 60% or mor of h oal insalld cos for h IPTV sysm [1]. Wih PE and in-hom insallaion rprsning h largs porion of oal insalld cos, i is h ara bs argd for cos rducion. PEX is composd of funds usd by a company o acquir or upgrad physical asss such as propry, indusrial buildings or quipmn.this yp of oulay is mad by companis o mainain or incras h scop of hir opraion. Ths xpndiurs includ vryhing from rpairing a roof o building a brand nw facory. Vido-on-Dmand (VoD) is a subs of h IPTV srvic. Iniial rials hav bn wll rcivd by cusomrs and nwork opraors ar dploying VoD o incras subscribr rvnus and srvic profiabiliy. VoD allows subscribrs o rqus h programming of hir choic, whn hy wan whr hy wan i. I is his flxibiliy ha appals o h broadr cusomr bas whn compard wih rgularly schduld nwork programming of broadcas vido. In mos radiional mhods, h only objciv is o minimiz h PEX par of h T by slcing criical componns of h srvic in a hurisic mannr. Bu, his approach may no ncssarily rsul in opimal soluion for h srvic providrs. For xampl, in dploying h IPTV srvic in Iran, h srvic providrs slc h numbr of h rquird dg srvrs in ordr o minimiz h PEX par of h T []. Bcaus of is saic naur, his mhod dosn considr h inrrlaions bwn PEX and APEX which varis wih im. For xampl, hough choosing a spcific iniial numbr of dg srvrs may b opimal a h firs sags of srvic dploymn, his may no lad o an opimal Manuscrip rcivd Novmbr 5, 009 Manuscrip rvisd Novmbr 0, 009

2 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr soluion for T minimizaion problm as im lapss. Any soluion for minimizing h T mus ak ino h accoun h dynamic characrisics of h problm as im lapss. In h currn work, a mahmaical approach is dvlopd o minimiz h T. Th proposd mhod racks h dynamic changs in h numbr of subscribrs and aks ino h accoun h subscribrs gographical disribuions and im. Th rs of h papr is organizd as follows: In Scion, w hav an ovrviw on h rlad works. In Scion 3, a brif dscripion of h IPTV srvic and is comprising lmns is givn. Scion 4 is abou h T minimizaion problm. A firs h problm is formulad using appropria modls for APEX and PEX pars of ach IPTV lmn, hn, using appropria numrical mhods [3], a cos opimizaion sragy is dvlopd. Scion 5 dscribs simulaion rsuls and w nd h papr wih som concluding rmarks in h Scion 6.. Rlad works Toal cos of ownrship modling is a ool ha sysmaically accouns for all coss rlad o an IT invsmn dcision. T modls wr iniially dvlopd by Garnr Rsarch orporaion in 1987 and ar now widly accpd. Simply sad, T includs all coss, dirc and indirc, incurrd hroughou h lif cycl of an ass, including acquisiion and procurmn, opraions and mainnanc, and nd-of-lif managmn. T analysis has bn dvlopd in a numbr of diffrn mhodologis and sofwar ools sinc A T assssmn idally offrs a final samn rflcing no only h cos of purchas bu all aspcs in h furhr us and mainnanc of h quipmn, dvic, or sysm considrd. This includs h coss of raining suppor prsonnl and h usrs of h sysm, coss associad wih failur or ouag (plannd and unplannd), diminishd prformanc incidns (i.. if usrs ar kp waiing), coss of scuriy brachs (in loss of rpuaion and rcovry coss), coss of disasr prpardnss and rcovry, floor spac, lcriciy, dvlopmn xpnss, sing infrasrucur and xpnss, qualiy assuranc, boo imag conrol, marginal incrmnal growh, dcommissioning, - was handling, and mor. Whn incorporad in any financial bnfi analysis T provids a cos basis for drmining h conomic valu of ha invsmn. Th T concp is widly usd in h auomobil indusry. In his conx, h T dnos h cos of owning a vhicl from h purchas, hrough is mainnanc, and finally is sal as a usd car. omparaiv T sudis bwn various modls hlp consumrs choos a car o fi hir nds and budg. In [] afr xnsiv mark rsarch, an simaion abou h APEX and PEX of ach IPTV componn is drivd from which w hav dvlopd a mahmaical modl for h T of IPTV srvic in Scion IPTV srvic IPTV dscribs a sysm whr a digial lvision srvic is dlivrd using h Inrn Proocol ovr a nwork infrasrucur,which may includ dlivry by a broadband conncion [4]. For rsidnial usrs, IPTV is ofn providd in conjuncion wih VoD and may b bundld wih Inrn srvics such as Wb accss and VoIP. Th commrcial bundling of IPTV, VoIP and Inrn accss is rfrrd o as a Tripl Play. Adding h mobil voic srvic lads o h Quadrupl Play dnominaion. IPTV is ypically supplid by a broadband opraor using a closd nwork infrasrucur. This closd nwork approach is in compiion wih h dlivry of TV conn ovr h public Inrn. This yp of dlivry is widly calld TV ovr Inrn or Inrn Tlvision. In businsss, IPTV may b usd o dlivr lvision conn ovr corpora LANs and businss nworks. Prhaps a simplr dfiniion of IPTV would b lvision conn ha, insad of bing dlivrd hrough radiional formas and cabling, is rcivd by h viwr hrough h chnologis usd for compur nworks. Broadcas IPTV has wo major archicur forms: fr and f basd. This scor is growing rapidly and major lvision broadcasrs worldwid ar ransmiing hir broadcas signal ovr h Inrn. IPTV channls rquir only an Inrn conncion and an Inrn nabld dvic such as a prsonal compur, ipod, HDTV conncd o a compur or vn a 3G cll/mobil phon o wach h IPTV broadcass. A ypical IPTV scnario is dpicd in h Fig.1. Th basic componns of IPTV srvic ar, vido sraming srvrs [5], dg sraming srvrs usd for load balancing purposs, ncodd conn, ranspor and accss QoS-nabld nworks, (Broadband Rmo Accss Srvr), DSLAM (Digial Subscribr Lin Accss Muliplxr), (S Top Box) and ADSL (Asymmric DSL) modms.

3 34 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr 009 Fig. 1 Typical IPTV srvic scnario Each IPTV componn is associad wih an incurrd APEX and PEX. Som componns such as ranspor nwork ar ou of h srvic providr s conrol and impos only a long-rm PEX on h srvic providr s dploymn sragy and som of h componns such as conn only consis of an iniial APEX and don impos any imporan PEX on h srvic dvlopmn. In h following scions, mahmaical modls for h APEX and PEX of ach IPTV componn ar dvlopd and basd on h proposd modls; a dynamic soluion for h T minimizaion problm is inroducd. 4. Looking a IPTV oal cos of ownrship Thr ar wo approachs o assss h oal cos of ownrship for an IPTV srvic: A hrognous approach,in which mulipl vndors provid diffrn componns of h soluion, ofn wih on or mor sysms ingraors providing h srvics ha bind hs hrognous soluions ino a singl srvic dlivry soluion. In his approach, opraions managmn is ypically layrd on op of h srvic dlivry sysm afr h fac. Mos of h currn IPTV dploymns o da adop his approach. A homognous approach, in which a singl soluions vndor dsigns, builds, ss, validas, and suppors h IPTV srvic dlivry and opraions managmn soluion. Th oal cos of ownrship associad wih an IPTV srvic dpnds on a variy of facors, including: apial xpndiur (APEX) for h srvic dlivry hardwar, sofwar, and nwork infrasrucur. praing xpndiur (PEX) for h dvlopmn, ongoing dlivry, and mainnanc of h srvic dlivry infrasrucur. Som of h PEX will b sar-up coss, such as hos associad wih iniial dploymn, and hos rlad o h ingraion of h IPTV infrasrucur.wih xising businss suppor sysms (BSS), and opraions suppor sysms (SS). hr PEX ar ongoing, including h xpns of day-o-day monioring and managing of h infrasrucur. Sill ohr PEX will aris as h rsul of dcisions o volv h srvic dlivry nwork. Ths xpnss can b sn as projc rlad xpnss, bu dcisions akn upfron abou how h srvic providr will dlivr h IPTV srvic can lad o highr opraions coss, and projcs ha ar mor complx whn i is im o upgrad h srvic dlivry nwork. Ths downsram coss mus b facord ino h T quaion. In addiion o APEX and PEX, srvic providrs can ncounr coss associad wih conn acquisiion. Ths coss can vary basd on rvnu opporuniis a srvic providr can offr a conn providr. Typically, h conn coss ar basd on h numbr of subscribrs. Howvr, h xpandd srvic dlivry opporuniis affordd by IPTV may chang his. If, for xampl, h IPTV srvic offrs subscribrs a chanc o slc alrna camra fds from a sporing vn, h conn providr ha owns hs fds may charg a highr f for conn han i would if subscribrs wr unabl o swich bwn camra fds on hir own. Thrfor, hr may b som variaions in pricing for conn dlivrd ovr IPTV. Howvr, bcaus i is anicipad ha srvic providrs will pass along his yp of addiional conn fs in h form of highr subscripion fs, h n ffc of any conn cos variaions upon T will b ngligibl. onsqunly, conn coss ar no a criical componn in h calculaion of T for h purpos of his aricl. Infrasrucur coss o offr IPTV as a subscribr-orind srvic rquirs invsmn in a plaform o dlivr and manag h srvic. Th srvic providr mus acquir sysms for ncoding and dlivring liv conn as wll as sysms for ncoding, soring, and dlivring vido on dmand (VoD) conn. Th srvic providr mus dploy sysms o manag his conn and is dlivry; i mus also dploy sysms o monior and mainain h nwork, h conn dlivry, and h managmn sysms hmslvs - and ha is jus a high-lvl dscripion of a cnral had-nd insallaion. Thr ar mulipl mro had-nd configuraions o dploy, and hs involv local conn dlivry srvrs, local VD srvrs, local managmn srvrs and mor. T for such a nwork infrasrucur dpnd in par on h srvic dlivry approach ha h providr slcs. A srvic providr, as prviously xplaind, can choos bwn homognous or hrognous approachs. Afr many yars of building voic nworks, h hrognous approach may b familiar o lcos. I

4 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr offrs crain aracions, bcaus i nabls a srvic providr o build a srvic dlivry soluion basd on bs of brd componns ha may hav bn fin-und for h dlivry of IPTV. A h sam im, lcos ar familiar wih h downsid of his approach: bcaus bs of brd producs ar so prcisly focusd on doing on hing wll, hy ar ofn buil on spcializd or propriary archicurs ha ar cosly o acquir and suppor. Morovr, individual componn vndors ar unlikly o hav buil hir producs o inrac wih prcisly h collcion of componns in a givn hrognous srvic dlivry configuraion; hr ar simply oo many possibl configuraions and variaions. Bcaus no singl soluions vndor has sd and validad h nir soluion prior o h srvic providr s acquisiion of hs spara componns, h craion of a hrognous soluion rquirs a cosly and im-consuming sysms ingraion and sing ffor. praions and mainnanc coss Toal cos of ownrship involvs mor han h cos of dploying h hardwar and sofwar associad wih h cor srvic dlivry plaform. Mainaining h highs qualiy of srvic (QoS) across a disribud nwork dmands 4-hour suppor. Th annual cos, fully loadd, of a wll qualifid suppor chnician,, rcurring PEX coss can b among h mos imporan o considr whn calculaing T. Rducing T rquirs an approach o IPTV ha nabls a small opraions managmn am o work fficinly. If h srvic providr chooss h hrognous sysms approach, PEX coss may b much highr han if h srvic providr chooss a homognous sysms approach. Thr ar wo ky rasons why his is ru. Bcaus h individual componns in a hrognous soluion ar ypically spcializd or propriary, hy ypically rquir h anion of suppor prsonnl wih spcializd raining and xprinc - who ypically command highr salaris in h markplac. Morovr, bcaus opraions managmn in h hrognous approach is ypically layrd on op of h soluion as an afrhough, h opraions managmn componn may no b abl o provid h lvls of auomaion and fficincy ha would nabl h srvic providr o suppor a larg disribud nwork wih a lan opraions am. An approach o opraions and mainnanc ha nabls a srvic providr o rly on a lanr and lss cosly suppor saff can hav a dramaic impac on T. Soluions ha rly on sandards-basd commodiy hardwar involv lowr APEX han propriary chnologis. Homognous soluions ypically lowr day-o-day IPTV PEX bcaus hy maks h mos of auomaion, provid nd-o-nd monioring and managmn capabiliis, and rly on asily obainabl profssional skills; ompl, fully archicd, packags can lowr cos and risk. Th providrs of homognous soluions hav don h work o dfin and dsign h soluion, nabling h srvic providr o dploy i o subscribrs and hav i bgin gnraing rvnu - in a mar of days, no monhs. Morovr, wih a compl packag ha includs profssional suppor srvics, h srvic providr always knows whr o go if i has a qusion. In a hrognous srvic dlivry nvironmn, hr is no singl rsourc for all h srvic providr s suppor nds and no singl niy o archic and valida h soluion on an ongoing basis. As a providr s IPTV srvic nds and opporuniis volv ovr im, h dvloprs of homognous packags can mak h changs asir and lss cosly. Thy can anicipa how a srvic providr can volv srvic dlivry and prpar bs pracics guidlins in advanc o hlp h srvic providr ransform is srvic dlivry infrasrucur. Wih h soluion providr acing o valida h nir srvic dlivry nvironmn, h srvic providr can b confidn ha whn an upda or nhancmn is mad o h soluion, vry par of h soluion ha could b affcd by h chang has bn sd and validad alrady. Ulimaly, a srvic providr s goal is o dlivr a compiiv srvic ha can hlp i incras is rvnus and subscribr bas a h lows possibl cos. Wih a comprhnsiv archicur and guidlins, ingrad sysms managmn srvics, and flxibl dploymn opions, homognous, compl, IPTV soluions can b dsignd o hlp h srvic providr m hir goals. 5. Problm Formulaion In ordr o minimiz h T (APEX+PEX) of an IPTV srvic, w hav dvlopd in a hurisic mannr, h mahmaical modls associad wih h APEX and PEX of ach componn which is involvd in h srvic. In pracic, dvlopmn of a comprhnsiv modl for minimizing h oal cos of ownrship of an IPTV srvic is vry difficul. In his scion w ignor som paramrs dscribd in prvious scion o mak h mahmaical modling possibl. DSLAM,, ADSL modm, Edg Srvr, Main srvr ar among h dvics which oghr build an IPTV soluion. In his scion, mahmaical modls for APEX and PEX of hs componns ar prsnd. To do so, w firs mak an simaion of h iniial cos of ach componn individually basd on h rsarch accomplishd in []. Th iniial cos of, ADSL modm, DSLAM,, main srvr, dg srvr, conn and infrasrucur ar dnod by x DSLM,

5 344 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr 009 x NT rspcivly. Tabl 1 shows h iniial cos of h dvics normalizd by h iniial cos of ADSL modm. Tabl 1: Iniial cos of IPTV dvics normalizd by ADSL modm cos Dvic os Dvic os x 3.33 x 176 x 1 x xdslm 18 xnt x 10 x 100 I mus b mniond ha h abov normalizd valus in abl (1) ar obaind from a survy on h prics of ach IPTV componn which was invsigad abou h Iran s IT mark in []. In ordr o covr h dynamic naur of h mniond componns of h T, h mahmaical modls for APEX and PEX ar chosn o b funcions of im, numbr of subscribrs n and numbr of dg srvrs m. In h following quaions, paramrs bginning wih rprsn APEX and hos bginning wih rprsn PEX.Th APEX and PEX ar modld as follows: = -0 ( ) zn ( x + ( y x ) ) 1 = -0 ( ) ( x + ( y x ) 1 ( ) 0 DSLM ( DSLM DSLM 1 DSLM ( ) 0 ( 1 ( ) 0 ( ( ) ( ) 0 ( 1 NT NT zn zm = ( x + y ) sn ( p q ) u ( v w ) (1) () (3) (4) (5) (6) (8) (7) Whr w hav [6]: y = 0.8x ; y = 0.8x ; 7 y = 0.11y NSTR ; = ; = ; z 1 = z = z = ; u = ; p = q = s 1; = =1.1; w = 0.1 v ; Th valu of 0 and 1 for ach dvic is considrd as 0.1x. As w s in h abov quaions, h APEX of ach IPTV componn is a dcrasing funcion of h numbr of subscribrs n and an incrasing funcion of im bcaus i is assumd ha h APEX can b rducd as h rqus (n) incrass and can b incrasd for h sak of inflaion as im ( volvs. Th PEX of ach IPTV componn is assumd iniially o b null and can incras as im and numbr of subscribrs incras. From rsarch adopd in [6], h PEX associad wih Infrasrucur par of h nwork is assumd o b a dcrasing funcion of m and an incrasing funcion of boh n and. Finally, T for an IPTV srvic is: n Tm, = n( + ) + n( + ) + θ (9) ( DSLM + DSLM + + ) + NT + ( + ) + m( + ) + + Whr, x is h smalls ingr numbr which is grar han or qual o x and θ is h numbr of DSLAM pors. In his papr w hav assumd ha θ =18. In h currn work, w hav rid o rack h changs which ar imposd on h opimal T as im volvs by rgulaing h numbr of dg srvrs m as a funcion of im. By work prsnd in [6] i is rsuld ha h numbr of dg srvrs can b rgardd as a major paramr affcing h T of h IPTV soluion. Thus, h objciv is o choos h opimal valu of m so ha h T is minimizd. Th so-calld T minimizaion can b formulad as h following nonlinar programming problm [7]: * m = arg min T m, (10 m 0 ) An appropria numrical approach is usd o solv h problm for h opimal m and his mhod lads o h im-varying minimizd T [3]. ;

6 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr Simulaion W hav usd h scnario dpicd in h Fig. which is similar o on adopd in [6] for dploymn of h IPTV srvic in Iran. In ordr o minimiz h oal cos (T) of h IPTV srvic, h minimizaion was prformd wih rspc o m (numbr of dg srvrs). In ohr words, in quaion 9, w hav o drmin h opimal valu of m so ha h oal cos in his quaion is minimizd for a spcific numbr of subscribrs n and im. Tim mans h numbr of yars which hav lapsd sinc IPTV srvic was firs dployd (=0). In h scnario, i is assumd ha h nd-usrs ar disribud uniformly in a circular gographical rgion and for ach n /θ usr hr xis a and a DSLAM. Each dg srvr can b conncd o a las on DSLAM for sraming mor dmanding conns. Firs, w supposd ha h numbr of subscribrs is consan and is qual o 5000 (n=5000). Thn w calculad h m ha minimizs h oal cos a h firs yar of srvic dploymn or =0. Th diagram of h oal cos vrsus m for n=5000 and =0 is shown in Fig.3. n=5000 subscribrs and =10 yars. As h Fig.4 shows h opimal m is 53. Th Figs.5 and 6 show h diagrams of oal cos for h cass (n=500000, =0) and (n=500000, =10). pimal m in hs cass is 1159 and 1163 rspcivly. Figs.3-6 show ha h valu of m which minimizs h oal cos of IPTV changs as ihr h numbr of subscribrs or im changs. Fig. 4 T for n=5,000 and =10 Fig. Simulad IPTV srvic scnario Fig. 5 T for n=500,000 and =0 Fig. 3 T for n=5,000 and =0 As i is clar from Fig.3, oal cos is minimum a m=49. To s h ffc of im on h opimal m (h m which maks oal cos minimum), w again calculad h opimal m for Fig. 6 T for n=500,000 and =10

7 346 IJSNS Inrnaional Journal of ompur Scinc and Nwork Scuriy, VL.9 No.11, Novmbr 009 To s h ffc of im mor clarly, w skchd h diagram of h oal cos for n=5000 during h mporal priod of = [0 1 0]. Fig.7 shows h rsul. A las o s h changs of opimal m vrsus im and numbr of subscribrs, w hav calculad h opimal m for n= [ ] subscribrs and = [0 1 0] yars. Th rsul is shown in Fig.8. Fig. 7 pimal numbr of dg srvrs vs. im Fig.9 shows h variaions occurring in h T of IPTV dploymn wih incrasing im and numbr of subscribrs. Fig. 8 pimal numbr of dg srvrs vs. im and numbr of subscribrs 6. onclusion Though IPTV and VD srvics ar vry araciv o h nd usrs, hy ar highly xpnsiv and his has causd hm o b dvlopd wih a vry slow pac. Minimizing h T (APEX+PEX) of hs srvics is a challng o all IPTV and VD srvic providrs. In an IPTV scnario on of h major facors ha drmin h cos of h srvic is h numbr of dg srvrs. W usd an algorihm o minimiz h T using slcion of an opimal numbr of dg srvrs in a ypical IPTV scnario. This lads o h lows cos of srvic dploymn. Th proposd algorihm has provd o b qui fficin and dynamic in minimizing h T of IPTV as h numbr of subscribrs incrass and im lapss. Rfrncs [1] Zhon chnologis, In-hom ripl play dlivry, whi papr, 004, USA. [] Iran Tlcom Rsarch nr (ITR), Invsigaing h chnical, rgulaory and businss rquirmns of AS (Advancd ommunicaion Srvics) dploymn in Iran, chnical rpor, 006. [3] Lunbrgr, D.G., Linar and Nonlinar Programming, nd Ed. Addison-Wsly Publishing ompany, [4] ATIS IIF s IPTV Archicur Rquirmns, ATIS [5] Inrn Sraming Mdia Allianc (ISMA) Implmnaion Spcificaion V. April 005. [6] Invsigaing h chnical aspcs of dvloping IPTV srvic in IRAN, chnical rpor, Iran Tlcom Rsarch nr, 006. [7] Brskas, Dimiri P. (1999). Nonlinar Programming: nd Ediion. Ahna Scinific Won, Dalsoo rcivd h B.E. dgr in ompur Scinc from Soonsil Univrsiy in H also rcivd his M.S dgr in ompur Scinc from Soongsil Univrsiy in H has workd as an xcuiv dircor in h Hyundai Informaion Tchnology o. from 1996 o 00. His rsarch inrs includs Nwork Digial Imag Procssing, Imag, Nwork Scuriy, and Vido Broadcasing ovr Nwork. H is currnly wih Bawha Womns Univrsiy as a faculy mmbr. Fig. 9 T vs. im and numbr of subscribrs

Section. Problem Representation. Substation. Protection Device. protection equipments. Substation. Client. EPDS divided in blocks connected by

Section. Problem Representation. Substation. Protection Device. protection equipments. Substation. Client. EPDS divided in blocks connected by HIERARCHICAL MULTIPLE CRITERIA OPTIMIZATION OF MAINTENANCE ACTIVITIES ON POWER DISTRIBUTION NETWORKS Problm Rprsaion EPDS comprising: Subsaions, primary nworks, scondary, nworks; Fdrs (cabls, lins, pols,

More information

Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule

Lecture 1: Numerical Integration The Trapezoidal and Simpson s Rule Lcur : Numrical ngraion Th Trapzoidal and Simpson s Rul A problm Th probabiliy of a normally disribud (man µ and sandard dviaion σ ) vn occurring bwn h valus a and b is B A P( a x b) d () π whr a µ b -

More information

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano

CHAPTER CHAPTER14. Expectations: The Basic Tools. Prepared by: Fernando Quijano and Yvonn Quijano Expcaions: Th Basic Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER14 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard 14-1 Today s Lcur Chapr 14:Expcaions: Th Basic Th

More information

Institute of Actuaries of India

Institute of Actuaries of India Insiu of Acuaris of India ubjc CT3 Probabiliy and Mahmaical aisics Novmbr Examinaions INDICATIVE OLUTION Pag of IAI CT3 Novmbr ol. a sampl man = 35 sampl sandard dviaion = 36.6 b for = uppr bound = 35+*36.6

More information

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees

CPSC 211 Data Structures & Implementations (c) Texas A&M University [ 259] B-Trees CPSC 211 Daa Srucurs & Implmnaions (c) Txas A&M Univrsiy [ 259] B-Trs Th AVL r and rd-black r allowd som variaion in h lnghs of h diffrn roo-o-laf pahs. An alrnaiv ida is o mak sur ha all roo-o-laf pahs

More information

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b 4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs

More information

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o

More information

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument

On the Derivatives of Bessel and Modified Bessel Functions with Respect to the Order and the Argument Inrnaional Rsarch Journal of Applid Basic Scincs 03 Aailabl onlin a wwwirjabscom ISSN 5-838X / Vol 4 (): 47-433 Scinc Eplorr Publicaions On h Driais of Bssl Modifid Bssl Funcions wih Rspc o h Ordr h Argumn

More information

CSE 245: Computer Aided Circuit Simulation and Verification

CSE 245: Computer Aided Circuit Simulation and Verification CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy

More information

Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016

Applied Statistics and Probability for Engineers, 6 th edition October 17, 2016 Applid Saisics and robabiliy for Enginrs, 6 h diion Ocobr 7, 6 CHATER Scion - -. a d. 679.. b. d. 88 c d d d. 987 d. 98 f d.. Thn, = ln. =. g d.. Thn, = ln.9 =.. -7. a., by symmry. b.. d...6. 7.. c...

More information

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review

Spring 2006 Process Dynamics, Operations, and Control Lesson 2: Mathematics Review Spring 6 Procss Dynamics, Opraions, and Conrol.45 Lsson : Mahmaics Rviw. conx and dircion Imagin a sysm ha varis in im; w migh plo is oupu vs. im. A plo migh imply an quaion, and h quaion is usually an

More information

Midterm Examination (100 pts)

Midterm Examination (100 pts) Econ 509 Spring 2012 S.L. Parn Midrm Examinaion (100 ps) Par I. 30 poins 1. Dfin h Law of Diminishing Rurns (5 ps.) Incrasing on inpu, call i inpu x, holding all ohr inpus fixd, on vnuall runs ino h siuaion

More information

MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control

MEM 355 Performance Enhancement of Dynamical Systems A First Control Problem - Cruise Control MEM 355 Prformanc Enhancmn of Dynamical Sysms A Firs Conrol Problm - Cruis Conrol Harry G. Kwany Darmn of Mchanical Enginring & Mchanics Drxl Univrsiy Cruis Conrol ( ) mv = F mg sinθ cv v +.2v= u 9.8θ

More information

Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors

Boyce/DiPrima 9 th ed, Ch 2.1: Linear Equations; Method of Integrating Factors Boc/DiPrima 9 h d, Ch.: Linar Equaions; Mhod of Ingraing Facors Elmnar Diffrnial Equaions and Boundar Valu Problms, 9 h diion, b William E. Boc and Richard C. DiPrima, 009 b John Wil & Sons, Inc. A linar

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd

More information

The Optimal Timing of Transition to New Environmental Technology in Economic Growth

The Optimal Timing of Transition to New Environmental Technology in Economic Growth h Opimal iming of ransiion o Nw Environmnal chnology in Economic Growh h IAEE Europan Confrnc 7- Spmbr, 29 Vinna, Ausria Akira AEDA and akiko NAGAYA yoo Univrsiy Background: Growh and h Environmn Naural

More information

The Science of Monetary Policy

The Science of Monetary Policy Th Scinc of Monary Policy. Inroducion o Topics of Sminar. Rviw: IS-LM, AD-AS wih an applicaion o currn monary policy in Japan 3. Monary Policy Sragy: Inrs Ra Ruls and Inflaion Targing (Svnsson EER) 4.

More information

Elementary Differential Equations and Boundary Value Problems

Elementary Differential Equations and Boundary Value Problems Elmnar Diffrnial Equaions and Boundar Valu Problms Boc. & DiPrima 9 h Ediion Chapr : Firs Ordr Diffrnial Equaions 00600 คณ ตศาสตร ว ศวกรรม สาขาว ชาว ศวกรรมคอมพ วเตอร ป การศ กษา /55 ผศ.ดร.อร ญญา ผศ.ดร.สมศ

More information

Microscopic Flow Characteristics Time Headway - Distribution

Microscopic Flow Characteristics Time Headway - Distribution CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,

More information

Midterm exam 2, April 7, 2009 (solutions)

Midterm exam 2, April 7, 2009 (solutions) Univrsiy of Pnnsylvania Dparmn of Mahmaics Mah 26 Honors Calculus II Spring Smsr 29 Prof Grassi, TA Ashr Aul Midrm xam 2, April 7, 29 (soluions) 1 Wri a basis for h spac of pairs (u, v) of smooh funcions

More information

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 )

AR(1) Process. The first-order autoregressive process, AR(1) is. where e t is WN(0, σ 2 ) AR() Procss Th firs-ordr auorgrssiv procss, AR() is whr is WN(0, σ ) Condiional Man and Varianc of AR() Condiional man: Condiional varianc: ) ( ) ( Ω Ω E E ) var( ) ) ( var( ) var( σ Ω Ω Ω Ω E Auocovarianc

More information

14.02 Principles of Macroeconomics Problem Set 5 Fall 2005

14.02 Principles of Macroeconomics Problem Set 5 Fall 2005 40 Principls of Macroconomics Problm S 5 Fall 005 Posd: Wdnsday, Novmbr 6, 005 Du: Wdnsday, Novmbr 3, 005 Plas wri your nam AND your TA s nam on your problm s Thanks! Exrcis I Tru/Fals? Explain Dpnding

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 4/25/2011. UW Madison conomics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 4/25/2011 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 21 1 Th Mdium Run ε = P * P Thr ar wo ways in which

More information

Logistic equation of Human population growth (generalization to the case of reactive environment).

Logistic equation of Human population growth (generalization to the case of reactive environment). Logisic quaion of Human populaion growh gnralizaion o h cas of raciv nvironmn. Srg V. Ershkov Insiu for Tim aur Exploraions M.V. Lomonosov's Moscow Sa Univrsi Lninski gor - Moscow 999 ussia -mail: srgj-rshkov@andx.ru

More information

General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract

General Article Application of differential equation in L-R and C-R circuit analysis by classical method. Abstract Applicaion of Diffrnial... Gnral Aricl Applicaion of diffrnial uaion in - and C- circui analysis by classical mhod. ajndra Prasad gmi curr, Dparmn of Mahmaics, P.N. Campus, Pokhara Email: rajndraprasadrgmi@yahoo.com

More information

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED 006-0 Asian Rsarch Publishing work (ARP). All righs rsrvd. USTEADY FLOW OF A FLUID PARTICLE SUSPESIO BETWEE TWO PARALLEL PLATES SUDDELY SET I MOTIO WITH SAME SPEED M. suniha, B. Shankr and G. Shanha 3

More information

A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER

A THREE COMPARTMENT MATHEMATICAL MODEL OF LIVER A THREE COPARTENT ATHEATICAL ODEL OF LIVER V. An N. Ch. Paabhi Ramacharyulu Faculy of ahmaics, R D collgs, Hanamonda, Warangal, India Dparmn of ahmaics, Naional Insiu of Tchnology, Warangal, India E-ail:

More information

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT [Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI

More information

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA

A MATHEMATICAL MODEL FOR NATURAL COOLING OF A CUP OF TEA MTHEMTICL MODEL FOR NTURL COOLING OF CUP OF TE 1 Mrs.D.Kalpana, 2 Mr.S.Dhvarajan 1 Snior Lcurr, Dparmn of Chmisry, PSB Polychnic Collg, Chnnai, India. 2 ssisan Profssor, Dparmn of Mahmaics, Dr.M.G.R Educaional

More information

Methodology for Analyzing State Tax Policy By Orphe Pierre Divounguy, PhD, Revised by Andrew J. Kidd, PhD (May 2018)

Methodology for Analyzing State Tax Policy By Orphe Pierre Divounguy, PhD, Revised by Andrew J. Kidd, PhD (May 2018) Mhodology for Analyzing Sa Tax Policy By Orph Pirr Divounguy, PhD, Rvisd by Andrw J. Kidd, PhD (May 2018) Inroducion To analyz how changs o ax policy impacs no only govrnmn rvnus bu also conomic aciviy

More information

B) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of

B) 25y e. 5. Find the second partial f. 6. Find the second partials (including the mixed partials) of Sampl Final 00 1. Suppos z = (, y), ( a, b ) = 0, y ( a, b ) = 0, ( a, b ) = 1, ( a, b ) = 1, and y ( a, b ) =. Thn (a, b) is h s is inconclusiv a saddl poin a rlaiv minimum a rlaiv maimum. * (Classiy

More information

Final Exam : Solutions

Final Exam : Solutions Comp : Algorihm and Daa Srucur Final Exam : Soluion. Rcuriv Algorihm. (a) To bgin ind h mdian o {x, x,... x n }. Sinc vry numbr xcp on in h inrval [0, n] appar xacly onc in h li, w hav ha h mdian mu b

More information

4.3 Design of Sections for Flexure (Part II)

4.3 Design of Sections for Flexure (Part II) Prsrssd Concr Srucurs Dr. Amlan K Sngupa and Prof. Dvdas Mnon 4. Dsign of Scions for Flxur (Par II) This scion covrs h following opics Final Dsign for Typ Mmrs Th sps for Typ 1 mmrs ar xplaind in Scion

More information

Lecture 4: Laplace Transforms

Lecture 4: Laplace Transforms Lur 4: Lapla Transforms Lapla and rlad ransformaions an b usd o solv diffrnial quaion and o rdu priodi nois in signals and imags. Basially, hy onvr h drivaiv opraions ino mulipliaion, diffrnial quaions

More information

3(8 ) (8 x x ) 3x x (8 )

3(8 ) (8 x x ) 3x x (8 ) Scion - CHATER -. a d.. b. d.86 c d 8 d d.9997 f g 6. d. d. Thn, = ln. =. =.. d Thn, = ln.9 =.7 8 -. a d.6 6 6 6 6 8 8 8 b 9 d 6 6 6 8 c d.8 6 6 6 6 8 8 7 7 d 6 d.6 6 6 6 6 6 6 8 u u u u du.9 6 6 6 6 6

More information

Solutions to End-of-Chapter Problems for Chapters 26 & 27 in Textbook

Solutions to End-of-Chapter Problems for Chapters 26 & 27 in Textbook Soluions o End-of-Chapr Problms for Chaprs 26 & 27 in Txbook Chapr 26. Answrs o hs Tru/Fals/Uncrain can b found in h wrin x of Chapr 26. I is lf o h sudn o drmin h soluions. 2. For his qusion kp in mind

More information

Discussion 06 Solutions

Discussion 06 Solutions STAT Discussion Soluions Spring 8. Th wigh of fish in La Paradis follows a normal disribuion wih man of 8. lbs and sandard dviaion of. lbs. a) Wha proporion of fish ar bwn 9 lbs and lbs? æ 9-8. - 8. P

More information

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is 39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h

More information

Let s look again at the first order linear differential equation we are attempting to solve, in its standard form:

Let s look again at the first order linear differential equation we are attempting to solve, in its standard form: Th Ingraing Facor Mhod In h prvious xampls of simpl firs ordr ODEs, w found h soluions by algbraically spara h dpndn variabl- and h indpndn variabl- rms, and wri h wo sids of a givn quaion as drivaivs,

More information

ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 11

ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER 11 8 Jun ANSWERS TO EVEN NUMBERED EXERCISES IN CHAPTER SECTION : INCENTIVE COMPATABILITY Exrcis - Educaional Signaling A yp consulan has a marginal produc of m( ) = whr Θ = {,, 3} Typs ar uniformly disribud

More information

The Firm s Value and Timing of Adopting E-Commerce Using Real Options Analysis under Uncertainty *

The Firm s Value and Timing of Adopting E-Commerce Using Real Options Analysis under Uncertainty * Th Firm s Valu and Timing of Adoping E-Commrc Using Ral Opions Analysis undr Uncrainy * David S. Shyu Dparmn of Financ, Naional Sun Ya-sn Univrsiy, Kaohsiung, Taiwan dshyu@cm.nsysu.du.w Kuo-Jung L Dparmn

More information

Charging of capacitor through inductor and resistor

Charging of capacitor through inductor and resistor cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.

More information

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35 MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h

More information

SOLUTIONS. 1. Consider two continuous random variables X and Y with joint p.d.f. f ( x, y ) = = = 15. Stepanov Dalpiaz

SOLUTIONS. 1. Consider two continuous random variables X and Y with joint p.d.f. f ( x, y ) = = = 15. Stepanov Dalpiaz STAT UIUC Pracic Problms #7 SOLUTIONS Spanov Dalpiaz Th following ar a numbr of pracic problms ha ma b hlpful for compling h homwor, and will lil b vr usful for suding for ams.. Considr wo coninuous random

More information

EE 434 Lecture 22. Bipolar Device Models

EE 434 Lecture 22. Bipolar Device Models EE 434 Lcur 22 Bipolar Dvic Modls Quiz 14 Th collcor currn of a BJT was masurd o b 20mA and h bas currn masurd o b 0.1mA. Wha is h fficincy of injcion of lcrons coming from h mir o h collcor? 1 And h numbr

More information

Mundell-Fleming I: Setup

Mundell-Fleming I: Setup Mundll-Flming I: Sup In ISLM, w had: E ( ) T I( i π G T C Y ) To his, w now add n xpors, which is a funcion of h xchang ra: ε E P* P ( T ) I( i π ) G T NX ( ) C Y Whr NX is assumd (Marshall Lrnr condiion)

More information

Study on the Lightweight checkpoint based rollback recovery mechanism

Study on the Lightweight checkpoint based rollback recovery mechanism 9 Inrnaional Confrnc on Compur Enginring and Applicaions II vol. IAI rss, Singapor Sudy on h ighwigh chcpoin basd rollbac rcovry mchanism Zhang i,3, ang Rui Dai Hao 3, Ma Mingai 3 and i Xianghong 4 Insiu

More information

Voltage v(z) ~ E(z)D. We can actually get to this wave behavior by using circuit theory, w/o going into details of the EM fields!

Voltage v(z) ~ E(z)D. We can actually get to this wave behavior by using circuit theory, w/o going into details of the EM fields! Considr a pair of wirs idal wirs ngh >, say, infinily long olag along a cabl can vary! D olag v( E(D W can acually g o his wav bhavior by using circui hory, w/o going ino dails of h EM filds! Thr

More information

Modelling of repairable items for production inventory with random deterioration

Modelling of repairable items for production inventory with random deterioration IOSR Journal of Mahmaics IOSR-JM -ISSN: 78-78, p-issn: 9-7X. Volum, Issu Vr. IV Jan - Fb., PP -9 www.iosrjournals.org Modlling of rpairabl ims for producion invnory wih random drioraion Dr.Ravish Kumar

More information

Routing in Delay Tolerant Networks

Routing in Delay Tolerant Networks Rouing in Dlay Tolran Nworks Primary Rfrnc: S. Jain K. Fall and R. Para Rouing in a Dlay Tolran Nwork SIGCOMM 04 Aug. 30-Sp. 3 2004 Porland Orgon USA Sudn lcur by: Soshan Bali (748214) mail : sbali@ic.ku.du

More information

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline. Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.

More information

The transition:transversion rate ratio vs. the T-ratio.

The transition:transversion rate ratio vs. the T-ratio. PhyloMah Lcur 8 by Dan Vandrpool March, 00 opics of Discussion ransiion:ransvrsion ra raio Kappa vs. ransiion:ransvrsion raio raio alculaing h xpcd numbr of subsiuions using marix algbra Why h nral im

More information

Software Reliability using SPRT: Inflection S- shaped Model

Software Reliability using SPRT: Inflection S- shaped Model Volum 2, Issu 6, Jun 23 ISSN 239-4847 Sofwar Rliabiliy using SPRT: Inflcion S- shapd Modl Dr. R. Saya Prasad, K. Prasada Rao 2 and G. Krishna Mohan3 Associa Profssor, Dp. of Compur Scinc & Engg., Acharya

More information

EXERCISE - 01 CHECK YOUR GRASP

EXERCISE - 01 CHECK YOUR GRASP DIFFERENTIAL EQUATION EXERCISE - CHECK YOUR GRASP 7. m hn D() m m, D () m m. hn givn D () m m D D D + m m m m m m + m m m m + ( m ) (m ) (m ) (m + ) m,, Hnc numbr of valus of mn will b. n ( ) + c sinc

More information

Poisson process Markov process

Poisson process Markov process E2200 Quuing hory and lraffic 2nd lcur oion proc Markov proc Vikoria Fodor KTH Laboraory for Communicaion nwork, School of Elcrical Enginring 1 Cour oulin Sochaic proc bhind quuing hory L2-L3 oion proc

More information

I) Title: Rational Expectations and Adaptive Learning. II) Contents: Introduction to Adaptive Learning

I) Title: Rational Expectations and Adaptive Learning. II) Contents: Introduction to Adaptive Learning I) Til: Raional Expcaions and Adapiv Larning II) Conns: Inroducion o Adapiv Larning III) Documnaion: - Basdvan, Olivir. (2003). Larning procss and raional xpcaions: an analysis using a small macroconomic

More information

H is equal to the surface current J S

H is equal to the surface current J S Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion

More information

Lecture 2: Current in RC circuit D.K.Pandey

Lecture 2: Current in RC circuit D.K.Pandey Lcur 2: urrn in circui harging of apacior hrough Rsisr L us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R and a ky K in sris. Whn h ky K is swichd on, h charging

More information

Chapter 12 Introduction To The Laplace Transform

Chapter 12 Introduction To The Laplace Transform Chapr Inroducion To Th aplac Tranorm Diniion o h aplac Tranorm - Th Sp & Impul uncion aplac Tranorm o pciic uncion 5 Opraional Tranorm Applying h aplac Tranorm 7 Invr Tranorm o Raional uncion 8 Pol and

More information

Estimation of Metal Recovery Using Exponential Distribution

Estimation of Metal Recovery Using Exponential Distribution Inrnaional rd Journal o Sinii sarh in Enginring (IJSE).irjsr.om Volum 1 Issu 1 ǁ D. 216 ǁ PP. 7-11 Esimaion o Mal ovry Using Exponnial Disribuion Hüsyin Ankara Dparmn o Mining Enginring, Eskishir Osmangazi

More information

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =

More information

Transfer function and the Laplace transformation

Transfer function and the Laplace transformation Lab No PH-35 Porland Sa Univriy A. La Roa Tranfr funcion and h Laplac ranformaion. INTRODUTION. THE LAPLAE TRANSFORMATION L 3. TRANSFER FUNTIONS 4. ELETRIAL SYSTEMS Analyi of h hr baic paiv lmn R, and

More information

Ma/CS 6a Class 15: Flows and Bipartite Graphs

Ma/CS 6a Class 15: Flows and Bipartite Graphs //206 Ma/CS 6a Cla : Flow and Bipari Graph By Adam Shffr Rmindr: Flow Nwork A flow nwork i a digraph G = V, E, oghr wih a ourc vrx V, a ink vrx V, and a capaciy funcion c: E N. Capaciy Sourc 7 a b c d

More information

Impulsive Differential Equations. by using the Euler Method

Impulsive Differential Equations. by using the Euler Method Applid Mahmaical Scincs Vol. 4 1 no. 65 19 - Impulsiv Diffrnial Equaions by using h Eulr Mhod Nor Shamsidah B Amir Hamzah 1 Musafa bin Mama J. Kaviumar L Siaw Chong 4 and Noor ani B Ahmad 5 1 5 Dparmn

More information

HiFi: A Hierarchical Filtering Algorithm for Caching of Online Video

HiFi: A Hierarchical Filtering Algorithm for Caching of Online Video HiFi: A Hirarchical Filring Algorihm for Caching of Onlin Vido Shahid Akhar Vlocix Alcal-Lucn Plano, TX, USA shahid.akhar@alcallucn.com Andr Bck Bll Labs Alcal-Lucn Naprvill, IL, USA andr.bck@alcal-lucn.com

More information

Control System Engineering (EE301T) Assignment: 2

Control System Engineering (EE301T) Assignment: 2 Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also

More information

CHAPTER-5 PROBABILISTIC MODEL FOR RELIABILITY ANALYSIS IN WIRELESS SENSOR NETWORKS

CHAPTER-5 PROBABILISTIC MODEL FOR RELIABILITY ANALYSIS IN WIRELESS SENSOR NETWORKS PROBBILISTIC MODEL FOR RELIBILITY NLYSIS IN WIRELESS SENSOR NETWORS CHPTER-5 PROBBILISTIC MODEL FOR RELIBILITY NLYSIS IN WIRELESS SENSOR NETWORS dancmn in wirlss snsor nwors chnology nabls a wid rang of

More information

On the Speed of Heat Wave. Mihály Makai

On the Speed of Heat Wave. Mihály Makai On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.

More information

A Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate

A Condition for Stability in an SIR Age Structured Disease Model with Decreasing Survival Rate A Condiion for abiliy in an I Ag rucurd Disas Modl wih Dcrasing urvival a A.K. upriana, Edy owono Dparmn of Mahmaics, Univrsias Padjadjaran, km Bandung-umng 45363, Indonsia fax: 6--7794696, mail: asupria@yahoo.com.au;

More information

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t

THE SHORT-RUN AGGREGATE SUPPLY CURVE WITH A POSITIVE SLOPE. Based on EXPECTATIONS: Lecture. t t t t THE SHORT-RUN AGGREGATE SUL CURVE WITH A OSITIVE SLOE. Basd on EXECTATIONS: Lcur., 0. In Mankiw:, 0 Ths quaions sa ha oupu dvias from is naural ra whn h pric lvl dvias from h xpcd pric lvl. Th paramr a

More information

Chapter 17 Handout: Autocorrelation (Serial Correlation)

Chapter 17 Handout: Autocorrelation (Serial Correlation) Chapr 7 Handou: Auocorrlaion (Srial Corrlaion Prviw Rviw o Rgrssion Modl o Sandard Ordinary Las Squars Prmiss o Esimaion Procdurs Embddd wihin h Ordinary Las Squars (OLS Esimaion Procdur o Covarianc and

More information

Double Slits in Space and Time

Double Slits in Space and Time Doubl Slis in Sac an Tim Gorg Jons As has bn ror rcnly in h mia, a am l by Grhar Paulus has monsra an inrsing chniqu for ionizing argon aoms by using ulra-shor lasr ulss. Each lasr uls is ffcivly on an

More information

Integrity Control in Nested Certificates

Integrity Control in Nested Certificates Ingriy onrol in Nsd s $OEHUW/HYLDQG08IXNdD OD\DQ %R D]LoL8QLYHUVLW\'HSDUWPHQWRI&RPSXWHU(QJLQHHULQJ Bbk, Isanbul 80815, Turky lvi@boun.du.r caglayan@boun.du.r Absrac Nsd crificas [3,4] ar proposd as crificas

More information

Consider a system of 2 simultaneous first order linear equations

Consider a system of 2 simultaneous first order linear equations Soluon of sysms of frs ordr lnar quaons onsdr a sysm of smulanous frs ordr lnar quaons a b c d I has h alrna mar-vcor rprsnaon a b c d Or, n shorhand A, f A s alrady known from con W know ha h abov sysm

More information

Transient Performance Analysis of Serial Production Lines

Transient Performance Analysis of Serial Production Lines Univrsiy of Wisconsin Milwauk UWM Digial Commons Thss and Dissraions Augus 25 Transin Prformanc Analysis of Srial Producion Lins Yang Sun Univrsiy of Wisconsin-Milwauk Follow his and addiional works a:

More information

CHAPTER CHAPTER15. Financial Markets and Expectations. Prepared by: Fernando Quijano and Yvonn Quijano

CHAPTER CHAPTER15. Financial Markets and Expectations. Prepared by: Fernando Quijano and Yvonn Quijano Financial Marks and Prpard by: Frnando Quijano and Yvonn Quijano CHAPTER CHAPTER15 2006 Prnic Hall Businss Publishing Macroconomics, 4/ Olivir Blanchard Bond Prics and Bond Yilds Figur 15-1 U.S. Yild Curvs:

More information

The Variance-Covariance Matrix

The Variance-Covariance Matrix Th Varanc-Covaranc Marx Our bggs a so-ar has bn ng a lnar uncon o a s o daa by mnmzng h las squars drncs rom h o h daa wh mnsarch. Whn analyzng non-lnar daa you hav o us a program l Malab as many yps o

More information

Chapter 5 The Laplace Transform. x(t) input y(t) output Dynamic System

Chapter 5 The Laplace Transform. x(t) input y(t) output Dynamic System EE 422G No: Chapr 5 Inrucor: Chung Chapr 5 Th Laplac Tranform 5- Inroducion () Sym analyi inpu oupu Dynamic Sym Linar Dynamic ym: A procor which proc h inpu ignal o produc h oupu dy ( n) ( n dy ( n) +

More information

Influence of Preventive Maintenance Policy on Manufacturing Systems Performances

Influence of Preventive Maintenance Policy on Manufacturing Systems Performances rocdings of h World Congrss on Enginring 9 Vol I WCE 9, July 1-3, 9, London, U.K. Influnc of rvniv Mainnanc olicy on Manufacuring Sysms rformancs Anonio C. Capuo, aolo Salini Absrac rvniv mainnanc (M)

More information

British Journal of Economics, Finance and Management Sciences 64 October 2011, Vol. 2 (1)

British Journal of Economics, Finance and Management Sciences 64 October 2011, Vol. 2 (1) riish Journal of conomics, Financ and Managmn Scincs 64 Ocobr 2011, ol. 2 (1 An mpirical valuaion of Using h Rsidual Incom Modl for rdicion of Sock ric Mhdi Sarikhani Dparmn of Accouning, Safashahr ranch,

More information

Homework #2: CMPT-379 Distributed on Oct 2; due on Oct 16 Anoop Sarkar

Homework #2: CMPT-379 Distributed on Oct 2; due on Oct 16 Anoop Sarkar Homwork #2: CMPT-379 Disribud on Oc 2 du on Oc 16 Anoop Sarkar anoop@cs.su.ca Rading or his homwork includs Chp 4 o h Dragon book. I ndd, rr o: hp://ldp.org/howto/lx-yacc-howto.hml Only submi answrs or

More information

Two Products Manufacturer s Production Decisions with Carbon Constraint

Two Products Manufacturer s Production Decisions with Carbon Constraint Managmnt Scinc and Enginring Vol 7 No 3 pp 3-34 DOI:3968/jms9335X374 ISSN 93-34 [Print] ISSN 93-35X [Onlin] wwwcscanadant wwwcscanadaorg Two Products Manufacturr s Production Dcisions with Carbon Constraint

More information

Airline Revenue Management with Shifting Capacity

Airline Revenue Management with Shifting Capacity Airlin Rvnu Managmn wih Shifing Capaciy Kvin Pak, Rommr Dkkr and Grard Kindrvar ERIM REPORT SERIES RESEARCH IN MANAGEMENT ERIM Rpor Sris rfrnc numr Pulicaion 2003 Numr of pags 25 Email addrss corrsponding

More information

LaPlace Transform in Circuit Analysis

LaPlace Transform in Circuit Analysis LaPlac Tranform in Circui Analyi Obciv: Calcula h Laplac ranform of common funcion uing h dfiniion and h Laplac ranform abl Laplac-ranform a circui, including componn wih non-zro iniial condiion. Analyz

More information

ON THE USP CALCULATION UNDER SOLVENCY II AND ITS APPROXIMATION WITH A CLOSED FORM FORMULA

ON THE USP CALCULATION UNDER SOLVENCY II AND ITS APPROXIMATION WITH A CLOSED FORM FORMULA ON HE USP CALCULAION UNDER SOLVENCY II AND IS APPROXIMAION WIH A CLOSED FORM FORMULA Filippo SIEGENHALER Zurich Insuranc Group Ld Valnina DEMARCO Univrsiy of Calabria Rocco Robro CERCHIARA Dparmn of Economics,

More information

14.02 Principles of Macroeconomics Fall 2005 Quiz 3 Solutions

14.02 Principles of Macroeconomics Fall 2005 Quiz 3 Solutions 4.0 rincipl of Macroconomic Fall 005 Quiz 3 Soluion Shor Quion (30/00 poin la a whhr h following amn ar TRUE or FALSE wih a hor xplanaion (3 or 4 lin. Each quion coun 5/00 poin.. An incra in ax oday alway

More information

Optimal policies for aircraft fleet management in the presence of unscheduled maintenance

Optimal policies for aircraft fleet management in the presence of unscheduled maintenance 22nd Inrnaional Congrss on Modlling and Simulaion Hobar Tasmania Ausralia 3 o 8 Dcmbr 2017 mssanz.org.au/modsim2017 Opimal policis for aircraf fl managmn in h prsnc of unschduld mainnanc J.R. Lookr a V.

More information

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields

Lecture 37 (Schrödinger Equation) Physics Spring 2018 Douglas Fields Lctur 37 (Schrödingr Equation) Physics 6-01 Spring 018 Douglas Filds Rducd Mass OK, so th Bohr modl of th atom givs nrgy lvls: E n 1 k m n 4 But, this has on problm it was dvlopd assuming th acclration

More information

Reliability Analysis of a Bridge and Parallel Series Networks with Critical and Non- Critical Human Errors: A Block Diagram Approach.

Reliability Analysis of a Bridge and Parallel Series Networks with Critical and Non- Critical Human Errors: A Block Diagram Approach. Inrnaional Journal of Compuaional Sin and Mahmais. ISSN 97-3189 Volum 3, Numr 3 11, pp. 351-3 Inrnaional Rsarh Puliaion Hous hp://www.irphous.om Rliailiy Analysis of a Bridg and Paralll Sris Nworks wih

More information

C From Faraday's Law, the induced voltage is, C The effect of electromagnetic induction in the coil itself is called selfinduction.

C From Faraday's Law, the induced voltage is, C The effect of electromagnetic induction in the coil itself is called selfinduction. Inducors and Inducanc C For inducors, v() is proporional o h ra of chang of i(). Inducanc (con d) C Th proporionaliy consan is h inducanc, L, wih unis of Hnris. 1 Hnry = 1 Wb / A or 1 V sc / A. C L dpnds

More information

Modelling of three dimensional liquid steel flow in continuous casting process

Modelling of three dimensional liquid steel flow in continuous casting process AMME 2003 12h Modlling of hr dimnsional liquid sl flow in coninuous casing procss M. Jani, H. Dyja, G. Banasz, S. Brsi Insiu of Modlling and Auomaion of Plasic Woring Procsss, Faculy of Marial procssing

More information

Asymptotic Solutions of Fifth Order Critically Damped Nonlinear Systems with Pair Wise Equal Eigenvalues and another is Distinct

Asymptotic Solutions of Fifth Order Critically Damped Nonlinear Systems with Pair Wise Equal Eigenvalues and another is Distinct Qus Journals Journal of Rsarch in Applid Mahmaics Volum ~ Issu (5 pp: -5 ISSN(Onlin : 94-74 ISSN (Prin:94-75 www.usjournals.org Rsarch Papr Asympoic Soluions of Fifh Ordr Criically Dampd Nonlinar Sysms

More information

DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018

DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS. Assoc. Prof. Dr. Burak Kelleci. Spring 2018 DEPARTMENT OF ELECTRICAL &ELECTRONICS ENGINEERING SIGNALS AND SYSTEMS Aoc. Prof. Dr. Burak Kllci Spring 08 OUTLINE Th Laplac Tranform Rgion of convrgnc for Laplac ranform Invr Laplac ranform Gomric valuaion

More information

A Simple Procedure to Calculate the Control Limit of Z Chart

A Simple Procedure to Calculate the Control Limit of Z Chart Inrnaional Journal of Saisics and Applicaions 214, 4(6): 276-282 DOI: 1.5923/j.saisics.21446.4 A Simpl Procdur o Calcula h Conrol Limi of Z Char R. C. Loni 1, N. A. S. Sampaio 2, J. W. J. Silva 2,3,*,

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

Wave Equation (2 Week)

Wave Equation (2 Week) Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris

More information

( ) C R. υ in RC 1. cos. ,sin. ω ω υ + +

( ) C R. υ in RC 1. cos. ,sin. ω ω υ + + Oscillaors. Thory of Oscillaions. Th lad circui, h lag circui and h lad-lag circui. Th Win Bridg oscillaor. Ohr usful oscillaors. Th 555 Timr. Basic Dscripion. Th S flip flop. Monosabl opraion of h 555

More information

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to:

1. Inverse Matrix 4[(3 7) (02)] 1[(0 7) (3 2)] Recall that the inverse of A is equal to: Rfrncs Brnank, B. and I. Mihov (1998). Masuring monary policy, Quarrly Journal of Economics CXIII, 315-34. Blanchard, O. R. Proi (00). An mpirical characrizaion of h dynamic ffcs of changs in govrnmn spnding

More information

ERROR ANALYSIS A.J. Pintar and D. Caspary Department of Chemical Engineering Michigan Technological University Houghton, MI September, 2012

ERROR ANALYSIS A.J. Pintar and D. Caspary Department of Chemical Engineering Michigan Technological University Houghton, MI September, 2012 ERROR AALYSIS AJ Pinar and D Caspary Dparmn of Chmical Enginring Michigan Tchnological Univrsiy Houghon, MI 4993 Spmbr, 0 OVERVIEW Exprimnaion involvs h masurmn of raw daa in h laboraory or fild I is assumd

More information

A SWITCH CRITERION FOR DEFINED CONTRIBUTION PENSION SCHEMES

A SWITCH CRITERION FOR DEFINED CONTRIBUTION PENSION SCHEMES A SWTCH CTEON O DENED CONTBUTON PENSON HEMES Bas Ars CP Via al Collgio 3 14 Moncaliri (TO, aly Tl +39 11 644 ax +39 11 64368 E-mail: bas_ars@yahoo.com Elna Vigna Univrsià di Torino Diparimno di Saisica

More information