Little s Law & Bottleneck Law

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Little s Law & Bottleneck Law"

Transcription

1 Lttle s Law & Bottleneck Law Dec 20 I professonals have shunned performance modellng consderng t to be too complex and napplcable to real lfe. A lot has to do wth fear of mathematcs as well. hs tutoral provdes the foundaton of performance modellng. Usng elementary mathematcs two fundamental laws are dscussed. Lttle s Law s the most popular law n performance modellng and s applcable to all I systems. he bottleneck law s also very applcable and though used qualtatvely, t s seldom appled quanttatvely. hs tutoral shows the applcablty of both these laws to a varety of stuatons that are relevant to the I ndustry. opyrght () 20 Rajesh Mansharaman Permsson s granted to copy, dstrbute and/or modfy ths document under the terms of the GNU Free Documentaton Lcense, Verson.3 or any later verson publshed by the Free Software Foundaton; wth no Invarant Sectons, no Front-over exts, and no Back-over exts. A copy of the lcense s ncluded n the secton enttled "GNU Free Documentaton Lcense".

2 Lttle s Law & Bottleneck Law wo smple laws are ntroduced n ths document, whch have wdespread applcablty. hese fundamental paradgms should suffce for a lot of quanttatve analyss of I systems, as wll be shown through a set of examples provded and a set of exercses at the end of the document. Before we get nto the laws let us ntroduce the basc set of terms and notaton that wll be used to derve the laws. hereafter we get n to Lttle s Law and then the Bottleneck Law. Lttle s Law provdes a relatonshp between response tme, number n the system and throughput. he Bottleneck Law shows where the system wll bottleneck n terms of system throughput and usng t we can derve useful response tme and throughput bounds.. Defntons of Fundamental erms We defne seven fundamental terms n ths secton, three are wdely used n the software ndustry today, and the other four wll be useful for the purpose of dscusson. Response tme, throughput, and number of concurrent users are popular terms used by software and I systems professonals. he other four terms of nterest to us are thnk tme, servce tme, vst count, and demand. By default all notaton that we use wll stand for averages, unless otherwse stated. hus for example, R wll be used to denote average response tme.. System, Resource, Entty, and Work onservng System he fundamental terms to be defned are n the context of a system. As shown n Fgure, a system s composed of a set of sub-systems, the most granular of whch s a sngle resource. Enttes flow through the system requestng servces from varous resources. For example, a data centre for a large bank s a system and a bankng transacton such as a depost s an entty. he bankng transacton vsts varous system resources such as network, PUs of the web, applcaton, and database servers, as well as dsks attached to the database server. In ths context, a network swtch s also a system, where the enttes flowng through t are network packets. It s assumed that a resource can servce only one request at any gven nstant of tme. hus, when a PU s servcng a request at any nstant of tme, even f t s n tme slcng mode, t s not servcng any other request at that pont n tme. Note that ths dscusson s only for one resource at an nstant of tme. A system s sad to be work conservng f no work s generated wthn the system and no work gets destroyed wthn the system. For example, consder a bank, whch provdes for deposts and wthdrawal transactons. hen work conservng means that a depost or a wthdrawal transacton s not generated unless there s a vald customer request, and once a transacton s accepted t s not dened by the bank.

3 Fgure : System and Entty.2 Response me Response tme of an entty s the tme dfference between entry and ext of the entty from the system. hus, response tme of a depost transacton n the data centre s the tme the transacton exts from the data centre network mnus the tme t enters n to the data centre network. However, f we consder end user response tme, then we need to extend our system boundary to the end user termnals, so that the wde area network tme as well as the tme spent at the user termnal s counted. he symbol R wll be used to denote average response tme. If we observe the system for a perod of tme, and enttes leave the system durng that tme, wth response tmes R,...,R then we can compute the average response tme R as.3 hroughput R = (R + R R ) / hroughput of a system s ts rate of processng enttes. hus number of bankng transactons per day, number of web hts per second, number of I/Os per second, as well as network bandwdth n Kbps or Mbps, are all measures of throughput. he symbol X wll be used to denote throughput. If we observe the system for a perod of tme, and enttes leave the system durng that tme, then we have throughput as: X hroughput and response tme are the two most mportant metrcs for I systems. A hgh throughput means more busness transactons and a low response tme means better end-user satsfacton..4 Number n the System, hnk me, and Number of oncurrent Users he number of enttes beng served n any system s a very useful measure for system capacty plannng. We nterchangeably use the terms number n the system and number of enttes n the system. hs s a functon of tme, snce at 2

4 dfferent ponts n tme the number n the system wll vary. If the system s work conservng, then we have number n the system at any tme t as: N(t) = Number of Arrvals up to tme t Number of Departures up to tme t he symbol N wll be used to denote average number n the system. If we observe the system for a perod of tme, then we have average number n the system as : N 0 N( t) dt A very wdely used term n the I ndustry s the number of concurrent users. In ths context, we are speakng of end-users. he user s actvtes wll n turn mpact the rate at whch enttes come n to the system. We wll use the term thnk tme to denote the tme between recevng a response to a request and submttng the next request. he end user could be revewng the response, or could be enterng data n to the next request s screens, or could have stepped out and come back. Essentally, the user s stll part of the system but has not submtted any entty for processng. In some lterature thnk tme s also referred to as sleep tme. We wll use the symbol Z to denote average thnk tme. As shown n Fgure 2, the number of concurrent users n the system s essentally the number of end-users who are usng the system; they could, for example, be ether thnkng or could have enttes submtted for processng. Fgure 2: oncurrent Users.5 Servce me, Vst ount, and Demand Servce tme s the tme spent by a resource n servcng a sngle request by an entty. For example, a sngle bankng transacton makes 5 requests to a web server wth an average of 5ms PU tme per request, 2 requests to an applcaton server wth an average of 0ms PU tme per request, 4 requests to a database server o fnd out average of a functon, one needs to take a number of samples, add them up and dvde the sum by the number of samples. For a functon whch changes rapdly wth tme, the number of samples needs to enough to cover all changes. hus when the number of samples tends to nfnty, the summaton becomes an ntegral. 3

5 wth an average of 20ms PU tme per request, and 0 requests to the dsk subsystem wth an average of 5ms dsk servce tme per request. Note that the servce tmes n ths example are tme spent n servcng the request, and they do not ncludng queung tme or wat tme at the resource, whch forms part of response tme. In other words, servce tme at a resource can be thought of as response tme at the resource under dle condtons. We use the symbol S to denote average servce tme. In the prevous example we saw that a sngle transacton makes multple vsts to sub-systems and resources. he average number of vsts to a resource s called the vst count of that entty at the resource. Note that vst count by defnton s an average. Also note that vst count s a relatve number. In the example above, one bankng transacton makes 4 requests to the database server and 0 requests to the dsk subsystem. hus the vst count s 4 at the database server and 0 at the dsk subsystem. hs s relatve to the bankng transacton. At the dsk subsystem the vst count relatve to the database s 2.5 (0/4). Vst count can also be a fracton, whch less than one. In the example above, f we have 8 PUs at the database server, then the vst count per PU s 4/8 = 0.5. We use the symbol V to denote vst count. Whether we make 4 requests to the database server wth servce tme 20ms per request, or request wth servce tme 80ms, the total servce demand at the database server remans the same, that s, 80ms. hus the average demand at a resource s the product of average servce tme at that resource and the vst count at that resource. he symbol D s used to denote average demand. hus at each resource n the system the average demand s: D V S.6 Summary of Notaton able summarzes the notaton we wll be usng n the rest of ths document. able : Notaton Symbol D N R S V X Z Descrpton Average Demand Average Number n System Average Response me Average Servce me Vst ount hroughput Average hnk me 4

6 2. Lttle s Law Lttle s Law, named after John D.. Lttle, states that the average number n a work conservng system equals the product of the system throughput and the average response tme. In ths secton, the proof for Lttle s Law wll be worked out, and extended to end-user systems. he smplcty and hgh applcablty of ths law has resulted n t beng wdely used n performance modellng. 2. Lttle s Law for any system he technque used n the proof s operatonal analyss. Let us observe arrvals and departures n a system. As shown n Fgure 3, let A(t) be the total number of arrvals up to tme t, and D(t) be the total number of departures up to tme t. Note that A(t) and D(t) are both non-decreasng functons. We also assume that each of them can be ncreased only n steps of unt. In other words, the probablty of two or more arrvals at exactly the same tme and of two or more departures at exactly the same tme s zero. hs s not a lmtaton snce we model two smultaneous arrvals as comng n at tme t and tme t+t, where t s an nfntesmally small nterval of tme. Snce the system s work conservng we cannot have more departures than arrvals, and hence D(t) A(t). By defnton of number n the system at any pont n tme t, N(t) (see Secton.4) we have N(t) = A(t) D(t) Fgure 3: Arrvals and Departures n a Work onservng System We are nterested n determnng the average number n the system, whch from Secton.4 s gven by: N 0 N( t) dt he ntegral of N(t) s the area under the functon, or the area between the functons A(t) and D(t), as shown n Fgure 4. 5

7 Fgure 4: Area Between Arrvals and Departures he shaded area n Fgure 4 s the sum of areas of the rectangles shown. Each rectangle s of heght (snce we assumed that no two arrvals or no two departures happen at exactly the same nstant of tme). he wdth of any rectangle s the dfference between the tme of the th departure, d and the tme of the th arrval, a. If the system has the same sequence of departures as the sequence of arrvals, or n other words t s a frst-come-frst-serve (FFS) system then d a s the response of tme job, denoted by R. We wll proceed wth the FFS assumpton and then prove the law can be extended for any other sequence of departures. We now have the area of rectangle as x R = R. herefore the average number n the system s: N 0 N( t) dt = R Here s the number of completons up to tme. In realty, equaton () wll hold for the lmt snce we are not consderng partal response tme of any request beng served at tme. herefore, we need to assume that the nterval of tme s large enough compared to ndvdual response tmes. We can rewrte equaton () by dvdng and multplyng wth to get: () R R (2) From Sectons.3 and.2, we can see that the frst term on the rght hand sde s the system throughput and the second term s the average response tme. We therefore have: R ombnng equatons () and (3) we get: X R (3) 6

8 N = X R Lttle s Law (4) o prove Lttle s Law we had assumed FFS sequencng n the system. Let s now show that Lttle s Law apples for any type of sequencng. he key to Lttle s Law s equaton () n whch we have assumed that the shaded area n Fgure 4 s the sum of the response tmes. Whle ths s true for FFS, why does t hold for any sequence of departures? Even f the sequence of departures s not FFS, there wll be a one-to-one parng between arrvals and departures. Fgure 5 shows a sample mappng of arrvals to departures. Fgure 5: Sample mappng of arrvals to departures Now let us renumber the departures as per ther arrval sequence. If we order the enttes n ther sequence of arrvals, then let d denote the departure tme of the th entty. hus d s the departure tme of the frst entty, whch by Fgure 5, s nothng but d 2, as per the one s to one mappng of arrvals and departures. Fgure 6, shows the departure tmes of Fgure 5 renumbered as per the arrval sequence of enttes. Fgure 6: Renumberng of departures By ths renumberng we therefore have response tme of entty as (d a ): R = (d a ) (5) omng back to the area of the shaded regon n Fgure 4, we see that the area s the sum of areas of rectangles each of heght and wdth (d a ): 0 N( t) dt ( d a ) (6) 7

9 he summaton on the rght hand sde can be expressed as: ( d a ) d a d ' a ( d ' a ) (7) ombnng equatons (6), (7), and (5) we get 0 ' N( t) dt ( d a ) ( d a ) R (8) On account of equaton (8), we have equaton () holdng for any sequence of departures, and thus Lttle s Law holds for any sequence of departures. o summarze, we have just proved that average number n a system s the product of the system throughput and the average response tme. N = X R 2.2 Lttle s Law for end-user systems onsder ths: f we have an I system wth,000 concurrent users, and average response tme of 2 seconds, then can we say that by Lttle s Law the system throughput s 000/2 = 500 requests/sec? hs wll not be correct snce there may not be,000 requests n the system. o extend Lttle s Law to end-user systems, consder Fgure 7, whch shows a system whose response tme s of nterest, as well as the end-users of the system who have an average thnk tme Z. Fgure 7: End-User System In Fgure 7, we consder an extended system shown by the dashed lne, whch ncludes the end-users. We have a total of N users n the extended system, each ether thnkng or watng for a response. hus, the total number n ths system s N. he response tme of ths extended system s the sum of the thnk tme and the response tme of the system. Lttle s Law must hold for the extended system as well. We therefore have for end-user systems: N = X (R + Z) (0) 8

10 For the example we started ths subsecton wth, f we have average thnk tme as 8 seconds, then we wll get the throughput as 000/(2+8) = 50 requests/sec. Another smple way to prove Lttle s Law for end-user systems or closed systems s as follows. he cycle tme for a sngle user s (R+Z). herefore the throughput per user s /(R+Z) and therefore the throughput for N users s N/(R+Z). In performance modellng when we look at a sngle resource or subsystem n solaton, we can vew t as an open system and use N = X R, to get the average queue sze or number n that subsystem or resource. hs s also true for very large systems lke google.com where t s mpossble to estmate the number of users, but t s possble to estmate the rate of access, whch means we can treat t as an open system. However, whenever we deal wth a fxed number of users then the closed system model works best. 3. Bottleneck Law and hroughput and Response me Bounds onsder an end-user system as llustrated n Fgure 8. An entty requestng servces of the system vsts several resources, wth a certan vst count and average servce tme. he crcles n the system denote resources, and the tuples shown next to the crcles specfy the vst count and average servce tme at the resources. Fgure 8: Vst ounts and Servce mes As defned n Secton.5, the average demand at a resource s the product of the vst count and the servce tme. For the purpose of our analyss we can equate Fgure 8 to Fgure 9, whch shows the system as a ppelne of resources each havng servce tme equal to demand. In other words, nstead of specfyng that a resource s vsted V tmes wth an average servce tme of S, we specfy that the resource s vsted once wth average demand of D. For the purpose of the bounds derved n ths secton, ths translaton works approprately. 9

11 Fgure 9: Ppelne of demands If we consder any ppelned system such as the one n Fgure 9, the maxmum throughput of the system cannot exceed the throughput at the slowest stage of the ppelne. In the example n Fgure 9, the maxmum throughput of the system s /5. Let the maxmum average demand n the system, across all resources, be denoted by D max : D max{ D } We therefore have the upper bound for system throughput as: max max X () D We refer to ths upper bound on throughput as the Bottleneck Law. In smpler terms you can go faster than the slowest stage n your system. he upper bound holds, regardless of the system workload. When the system saturates ths, the upper bound becomes an equalty. By defnton D max depends on vst counts and servce tmes. D max can be reduced by optmzng the software desgn and mplementaton to reduce servce tmes, or by usng faster PUs or dsks to reduce servce tmes, or by ncreasng the number of resources at a servce centre to reduce the vst count per resource, or by changng the archtecture of the system to reduce vst counts. For example, f database vst counts are hgh, one can ether ncrease the number of PUs or dsks, or ntroduce cachng at the applcaton server n order to reduce the vst counts. From Lttle s Law n equaton (0) we get: N R Z (2) X 0

12 Applyng the upper bound () to equaton (2) we get a lower bound on average response tme: R NDmax Z (3) Bounds () and (3) become equaltes upon system saturaton (unless the system s not work conservng and thrashes after a certan load). We wll see applcatons of these bounds n the next secton. he reader may refer to Lazowska et al. (see bblography at the end of ths chapter) for detaled analyss of bounds ncludng upper bounds on response tme and lower bounds on throughput, as well as bounds on balanced systems. 4. Examples on Lttle s Law and Bottleneck Law A number of real lfe examples on the usage of Lttle s Law and the bounds we have derved n ths chapter are presented n other sectons of ths ste. o sharpen the understandng of the law and the termnology ntroduced n ths secton we present several examples below and also encourage the reader to solve the exercses at the end of ths document. Example : A call centre for a credt card company wshes to plan on the number of employees t should have. he call centre receves 20,000 calls per day whch s expected to grow to 30,000 per day over next 6 months. 75% of the calls occur durng a peak 3 hour perod. he average duraton of a call s 5 mnutes. he call centre would lke ts employees to be 70% utlzed n attendng to calls. What s the number of employees that they should plan for, over the next 6 months? he peak throughput durng next 6 months wll be: X = 75% x 30,000 / 3 hours = 7,500 calls per hour = 25 calls per mnute If the average duraton of a call s 5 mnutes, then the cycle tme at 70% utlzaton per employee s: = 5 mnutes / 0.7 = 7. mnutes herefore average number of employees requred s gven by Lttle s Law: N = X = 25 x 7. = 888 employees Example 2: XYZ.com has wtnessed a surge n ts web ste traffc. It currently servces a maxmum throughput 5 mllon http hts per day across a farm of 0 web servers, each havng 2 PUs. hey have ordered another 5 web servers of 2 PUs each. What wll be the http vst count per PU? What s the throughput that can be servced by the 5 servers, assumng full scalablty at the web ter? Wth 5 more servers comng n, the total number of servers becomes 5 and the total number of PUs becomes 30. An http request can be servced by any of the 30 PUs and hence the http vst count per PU s / 30. Earler the http vst

13 count per PU was / 20. herefore the demand at the web server has come down n proporton to the vst count, that s, by 2/3 rd. herefore the throughput ncreases from 5 mllon hts per day to 5 mllon x 3 / 2 (nversely proportonal to demand) = 7.5 mllon hts per day. Example 3: XYZ.com has now started usng ts ste for revenue generaton. Wth the upgraded set of 5 web servers t servces mllon busness transactons per day. Each busness transacton makes an average of 7.5 http calls and 0 database calls. Assume that 25% of the busness transactons occur n peak one hour wndow and are unformly spread wthn the peak hour. What s the maxmum demand possble at the database server? If the database PU average servce tme per database call s 5 mllseconds, then what s the mnmum number of PUs requred at the database? Peak throughput s: X = 0.25 x mllon / hour = 0.25 mllon busness transactons per hour = 70 busness transactons per second o servce 70 busness transactons per second, the maxmum demand has to be: D max / 70 = 4.3 mllseconds herefore demand at the database ter has to be less than 4.3 mllseconds snce D max s the maxmum demand across all resources. Usng the defnton of demand we get: D database = V database S database 4.3 mllseconds Gven that average servce tme per database call S database s 5 mllseconds we get V database x V database 4.3 / 5 = 2.9 Now let s consder the vst count at the database ter per PU. We have 0 database calls per busness transacton. herefore vst count per database PU s: V database = 0 / (number of database PUs) 2.9 herefore we get: Number of database PUs 0/2.9 herefore there must be a mnmum of 4 PUs at the database. Example 4: In the prevous example, the average servce tme at the database was 5 mllseconds. Assume that for the above throughput ( mllon busness transactons per day) the database PU utlzaton durng peak hours s 90%. By how much should the average servce tme be reduced to brng the database PU utlzaton down to 70%? As can be seen from the exercses secton (Exercse 3), usng Lttle s Law one can derve the followng: 2

14 U = X S Where U s the utlzaton of the resource, X s the throughput, and S the average servce tme at the resource. We are targetng the same throughput of mllon busness transactons per day but now wsh to reduce the utlzaton. Usng ths relatonshp t s clear that average servce tme s drectly proportonal to utlzaton. hus the new average servce tme per database call should be: S = 0.7 / 0.9 x old servce tme = 0.7 / 0.9 x 5 = 3.9 mllseconds Useful Readng Lttle s Law s named after ts nventor and frst appeared n Lttle, J. D.. A Proof of the Queung Formula L = λ W. Operatons Research, 9, (96). It has been wdely used n a number of research papers n manufacturng, computer archtecture, and networks. he bounds for average response tme and throughput, as well as further readng on queueng networks s provded n Lazowska et al. Quanttatve Systems Performance. Prentce Hall, 984. hs book s wdely referenced n the lterature. Snce t s out of prnt t has now been made avalable electroncally from Exercses. A request for proposal (RFP) states that the soluton to be delvered must servce 72,000 transactons per hour, wth 2,000 concurrent users. What s the average cycle tme per user? 2. A web server access log fle (n extended format) shows a throughput of 5,000 hts per mnute wth an average response tme of 200 mllseconds. What s the average number of actve concurrent sessons at the web server? 3. onsder a subsystem wth a number of dentcal resources, for example a PU subsystem or a dsk subsystem. Any request wll undergo a servce tme and a wat tme (f the resources are busy). Now focus only on the resource tself and not the queue for the resource. As shown n the fgure below, draw the system boundary around the resources and apply Lttle s Law. Now prove that utlzaton of the resource U = X S, where X s the (sub)system throughput and S s the average servce tme at the resource. Note that for multple resources at the subsystem U can be more than one. For example, f an 8 PU server s 70% utlzed then U s 5.6 (that s, 0.7 x 8). 3

15 Average Servce me S hroughput X 4. You need to plan on network bandwdth for a large bank that has hundreds of branches all over the country. All branches connect to a central data centre over a wde area network (WAN). Branches come n flavours of small branches (5 users), medum branches (0 users), and large branches (20 users). Assume all users to be statstcally dentcal. he bank s peak throughput at the data centre s 00 transactons per second and there are a total of 5,000 users across all branches. he bank wants an average of second network delay between the branch and the data centre. a. What s the throughput n transactons per second at small, medum, and large branches? b. What s the (applcaton level) bandwdth requred for small, medum, and large branches f the network payload s 4KB per transacton? c. If the average response tme target n the data centre s second, what s the thnk tme per user? Answers to exercses. 00 seconds By Lttle s Law average number n resource subsystem s throughput tmes average response tme n subsystem. Average response tme wthn the resource (outsde of queueng) s average servce tme by defnton. Average number n resource subsystem dvded by number of resources s the percentage utlzaton of the subsystem. Hence U = X S. 4. a) Small branch 0. tps, medum branch 0.2 tps, large branch 0.4 tps b) 3.2Kbps, 6.4Kbps, and 2.8Kbps c) 48 seconds 4

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).

benefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ). REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or

More information

Communication Networks II Contents

Communication Networks II Contents 8 / 1 -- Communcaton Networs II (Görg) -- www.comnets.un-bremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP

More information

An Alternative Way to Measure Private Equity Performance

An Alternative Way to Measure Private Equity Performance An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate

More information

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING

ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 610-519-4390,

More information

Simple Interest Loans (Section 5.1) :

Simple Interest Loans (Section 5.1) : Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part

More information

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)

1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP) 6.3 / -- Communcaton Networks II (Görg) SS20 -- www.comnets.un-bremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes

More information

Lecture 3: Force of Interest, Real Interest Rate, Annuity

Lecture 3: Force of Interest, Real Interest Rate, Annuity Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annuty-mmedate, and ts present value Study annuty-due, and

More information

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur

Module 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..

More information

Section 5.4 Annuities, Present Value, and Amortization

Section 5.4 Annuities, Present Value, and Amortization Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today

More information

Recurrence. 1 Definitions and main statements

Recurrence. 1 Definitions and main statements Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.

More information

Graph Theory and Cayley s Formula

Graph Theory and Cayley s Formula Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll

More information

DEFINING %COMPLETE IN MICROSOFT PROJECT

DEFINING %COMPLETE IN MICROSOFT PROJECT CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMI-SP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,

More information

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error

Intra-year Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error Intra-year Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor

More information

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy

Answer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy 4.02 Quz Solutons Fall 2004 Multple-Choce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multple-choce questons. For each queston, only one of the answers s correct.

More information

Section 5.3 Annuities, Future Value, and Sinking Funds

Section 5.3 Annuities, Future Value, and Sinking Funds Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme

More information

Analysis of Energy-Conserving Access Protocols for Wireless Identification Networks

Analysis of Energy-Conserving Access Protocols for Wireless Identification Networks From the Proceedngs of Internatonal Conference on Telecommuncaton Systems (ITC-97), March 2-23, 1997. 1 Analyss of Energy-Conservng Access Protocols for Wreless Identfcaton etworks Imrch Chlamtac a, Chara

More information

The OC Curve of Attribute Acceptance Plans

The OC Curve of Attribute Acceptance Plans The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4

More information

Project Networks With Mixed-Time Constraints

Project Networks With Mixed-Time Constraints Project Networs Wth Mxed-Tme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa

More information

Calculation of Sampling Weights

Calculation of Sampling Weights Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a two-stage stratfed cluster desgn. 1 The frst stage conssted of a sample

More information

Section B9: Zener Diodes

Section B9: Zener Diodes Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peak-nverse

More information

FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals

FINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant

More information

7.5. Present Value of an Annuity. Investigate

7.5. Present Value of an Annuity. Investigate 7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on

More information

To manage leave, meeting institutional requirements and treating individual staff members fairly and consistently.

To manage leave, meeting institutional requirements and treating individual staff members fairly and consistently. Corporate Polces & Procedures Human Resources - Document CPP216 Leave Management Frst Produced: Current Verson: Past Revsons: Revew Cycle: Apples From: 09/09/09 26/10/12 09/09/09 3 years Immedately Authorsaton:

More information

9.1 The Cumulative Sum Control Chart

9.1 The Cumulative Sum Control Chart Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s

More information

Performance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application

Performance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdo-dong,

More information

The Application of Fractional Brownian Motion in Option Pricing

The Application of Fractional Brownian Motion in Option Pricing Vol. 0, No. (05), pp. 73-8 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qng-xn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com

More information

An Overview of Financial Mathematics

An Overview of Financial Mathematics An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take

More information

Chapter 4 Financial Markets

Chapter 4 Financial Markets Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that

More information

Reporting Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (including SME Corporate), Sovereign and Bank Instruction Guide

Reporting Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (including SME Corporate), Sovereign and Bank Instruction Guide Reportng Forms ARF 113.0A, ARF 113.0B, ARF 113.0C and ARF 113.0D FIRB Corporate (ncludng SME Corporate), Soveregn and Bank Instructon Gude Ths nstructon gude s desgned to assst n the completon of the FIRB

More information

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol

CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL

More information

Using Series to Analyze Financial Situations: Present Value

Using Series to Analyze Financial Situations: Present Value 2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated

More information

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis

The Development of Web Log Mining Based on Improve-K-Means Clustering Analysis The Development of Web Log Mnng Based on Improve-K-Means Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.

More information

Time Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money

Time Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6 - The Time Value of Money. The Time Value of Money Ch. 6 - The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21- Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important

More information

VRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT-09105, Phone: (370-5) 2127472, Fax: (370-5) 276 1380, Email: info@teltonika.

VRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT-09105, Phone: (370-5) 2127472, Fax: (370-5) 276 1380, Email: info@teltonika. VRT012 User s gude V0.1 Thank you for purchasng our product. We hope ths user-frendly devce wll be helpful n realsng your deas and brngng comfort to your lfe. Please take few mnutes to read ths manual

More information

Financial Mathemetics

Financial Mathemetics Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,

More information

Activity Scheduling for Cost-Time Investment Optimization in Project Management

Activity Scheduling for Cost-Time Investment Optimization in Project Management PROJECT MANAGEMENT 4 th Internatonal Conference on Industral Engneerng and Industral Management XIV Congreso de Ingenería de Organzacón Donosta- San Sebastán, September 8 th -10 th 010 Actvty Schedulng

More information

Traffic State Estimation in the Traffic Management Center of Berlin

Traffic State Estimation in the Traffic Management Center of Berlin Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D-763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,

More information

1 Approximation Algorithms

1 Approximation Algorithms CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons

More information

Time Value of Money Module

Time Value of Money Module Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the

More information

Abstract # 015-0399 Working Capital Exposure: A Methodology to Control Economic Performance in Production Environment Projects

Abstract # 015-0399 Working Capital Exposure: A Methodology to Control Economic Performance in Production Environment Projects Abstract # 015-0399 Workng Captal Exposure: A Methodology to Control Economc Performance n Producton Envronment Projects Dego F. Manotas. School of Industral Engneerng and Statstcs, Unversdad del Valle.

More information

1 Example 1: Axis-aligned rectangles

1 Example 1: Axis-aligned rectangles COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture # 6 Scrbe: Aaron Schld February 21, 2013 Last class, we dscussed an analogue for Occam s Razor for nfnte hypothess spaces that, n conjuncton

More information

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS

INVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMA-HDR NETWORKS 21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech-2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS

More information

Finite Math Chapter 10: Study Guide and Solution to Problems

Finite Math Chapter 10: Study Guide and Solution to Problems Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount

More information

Lossless Data Compression

Lossless Data Compression Lossless Data Compresson Lecture : Unquely Decodable and Instantaneous Codes Sam Rowes September 5, 005 Let s focus on the lossless data compresson problem for now, and not worry about nosy channel codng

More information

Introduction: Analysis of Electronic Circuits

Introduction: Analysis of Electronic Circuits /30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,

More information

Chapter 7. Random-Variate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 Random-Variate Generation

Chapter 7. Random-Variate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 Random-Variate Generation Chapter 7 Random-Varate Generaton 7. Contents Inverse-transform Technque Acceptance-Rejecton Technque Specal Propertes 7. Purpose & Overvew Develop understandng of generatng samples from a specfed dstrbuton

More information

Ameriprise Financial Services, Inc. or RiverSource Life Insurance Company Account Registration

Ameriprise Financial Services, Inc. or RiverSource Life Insurance Company Account Registration CED0105200808 Amerprse Fnancal Servces, Inc. 70400 Amerprse Fnancal Center Mnneapols, MN 55474 Incomng Account Transfer/Exchange/ Drect Rollover (Qualfed Plans Only) for Amerprse certfcates, Columba mutual

More information

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier

Lesson 2 Chapter Two Three Phase Uncontrolled Rectifier Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.

More information

Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.

Lecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression. Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook

More information

Luby s Alg. for Maximal Independent Sets using Pairwise Independence

Luby s Alg. for Maximal Independent Sets using Pairwise Independence Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent

More information

Multivariate EWMA Control Chart

Multivariate EWMA Control Chart Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant

More information

1. Measuring association using correlation and regression

1. Measuring association using correlation and regression How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a

More information

CHAPTER 14 MORE ABOUT REGRESSION

CHAPTER 14 MORE ABOUT REGRESSION CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp

More information

Generator Warm-Up Characteristics

Generator Warm-Up Characteristics NO. REV. NO. : ; ~ Generator Warm-Up Characterstcs PAGE OF Ths document descrbes the warm-up process of the SNAP-27 Generator Assembly after the sotope capsule s nserted. Several nqures have recently been

More information

Basic Queueing Theory M/M/* Queues. Introduction

Basic Queueing Theory M/M/* Queues. Introduction Basc Queueng Theory M/M/* Queues These sldes are created by Dr. Yh Huang of George Mason Unversty. Students regstered n Dr. Huang's courses at GMU can ake a sngle achne-readable copy and prnt a sngle copy

More information

RequIn, a tool for fast web traffic inference

RequIn, a tool for fast web traffic inference RequIn, a tool for fast web traffc nference Olver aul, Jean Etenne Kba GET/INT, LOR Department 9 rue Charles Fourer 90 Evry, France Olver.aul@nt-evry.fr, Jean-Etenne.Kba@nt-evry.fr Abstract As networked

More information

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6)

Passive Filters. References: Barbow (pp 265-275), Hayes & Horowitz (pp 32-60), Rizzoni (Chap. 6) Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called

More information

I. SCOPE, APPLICABILITY AND PARAMETERS Scope

I. SCOPE, APPLICABILITY AND PARAMETERS Scope D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable

More information

Efficient Striping Techniques for Variable Bit Rate Continuous Media File Servers æ

Efficient Striping Techniques for Variable Bit Rate Continuous Media File Servers æ Effcent Strpng Technques for Varable Bt Rate Contnuous Meda Fle Servers æ Prashant J. Shenoy Harrck M. Vn Department of Computer Scence, Department of Computer Scences, Unversty of Massachusetts at Amherst

More information

Lecture 2: Single Layer Perceptrons Kevin Swingler

Lecture 2: Single Layer Perceptrons Kevin Swingler Lecture 2: Sngle Layer Perceptrons Kevn Sngler kms@cs.str.ac.uk Recap: McCulloch-Ptts Neuron Ths vastly smplfed model of real neurons s also knon as a Threshold Logc Unt: W 2 A Y 3 n W n. A set of synapses

More information

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT

APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedo-cho

More information

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts

Power-of-Two Policies for Single- Warehouse Multi-Retailer Inventory Systems with Order Frequency Discounts Power-of-wo Polces for Sngle- Warehouse Mult-Retaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)

More information

A Replication-Based and Fault Tolerant Allocation Algorithm for Cloud Computing

A Replication-Based and Fault Tolerant Allocation Algorithm for Cloud Computing A Replcaton-Based and Fault Tolerant Allocaton Algorthm for Cloud Computng Tork Altameem Dept of Computer Scence, RCC, Kng Saud Unversty, PO Box: 28095 11437 Ryadh-Saud Araba Abstract The very large nfrastructure

More information

Section C2: BJT Structure and Operational Modes

Section C2: BJT Structure and Operational Modes Secton 2: JT Structure and Operatonal Modes Recall that the semconductor dode s smply a pn juncton. Dependng on how the juncton s based, current may easly flow between the dode termnals (forward bas, v

More information

Stress test for measuring insurance risks in non-life insurance

Stress test for measuring insurance risks in non-life insurance PROMEMORIA Datum June 01 Fnansnspektonen Författare Bengt von Bahr, Younes Elonq and Erk Elvers Stress test for measurng nsurance rsks n non-lfe nsurance Summary Ths memo descrbes stress testng of nsurance

More information

Performance Analysis and Comparison of QoS Provisioning Mechanisms for CBR Traffic in Noisy IEEE 802.11e WLANs Environments

Performance Analysis and Comparison of QoS Provisioning Mechanisms for CBR Traffic in Noisy IEEE 802.11e WLANs Environments Tamkang Journal of Scence and Engneerng, Vol. 12, No. 2, pp. 143149 (2008) 143 Performance Analyss and Comparson of QoS Provsonng Mechansms for CBR Traffc n Nosy IEEE 802.11e WLANs Envronments Der-Junn

More information

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services

An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsn-yng Wu b a Professor (Management Scence), Natonal Chao

More information

Brigid Mullany, Ph.D University of North Carolina, Charlotte

Brigid Mullany, Ph.D University of North Carolina, Charlotte Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte

More information

Conferencing protocols and Petri net analysis

Conferencing protocols and Petri net analysis Conferencng protocols and Petr net analyss E. ANTONIDAKIS Department of Electroncs, Technologcal Educatonal Insttute of Crete, GREECE ena@chana.tecrete.gr Abstract: Durng a computer conference, users desre

More information

1. Math 210 Finite Mathematics

1. Math 210 Finite Mathematics 1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210

More information

Nonlinear data mapping by neural networks

Nonlinear data mapping by neural networks Nonlnear data mappng by neural networks R.P.W. Dun Delft Unversty of Technology, Netherlands Abstract A revew s gven of the use of neural networks for nonlnear mappng of hgh dmensonal data on lower dmensonal

More information

Enabling P2P One-view Multi-party Video Conferencing

Enabling P2P One-view Multi-party Video Conferencing Enablng P2P One-vew Mult-party Vdeo Conferencng Yongxang Zhao, Yong Lu, Changja Chen, and JanYn Zhang Abstract Mult-Party Vdeo Conferencng (MPVC) facltates realtme group nteracton between users. Whle P2P

More information

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek

THE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo

More information

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic

Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange

More information

PAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of Illinois-Urbana Champaign

PAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of Illinois-Urbana Champaign PAS: A Packet Accountng System to Lmt the Effects of DoS & DDoS Debsh Fesehaye & Klara Naherstedt Unversty of Illnos-Urbana Champagn DoS and DDoS DDoS attacks are ncreasng threats to our dgtal world. Exstng

More information

Nasdaq Iceland Bond Indices 01 April 2015

Nasdaq Iceland Bond Indices 01 April 2015 Nasdaq Iceland Bond Indces 01 Aprl 2015 -Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes

More information

Hollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA )

Hollinger Canadian Publishing Holdings Co. ( HCPH ) proceeding under the Companies Creditors Arrangement Act ( CCAA ) February 17, 2011 Andrew J. Hatnay ahatnay@kmlaw.ca Dear Sr/Madam: Re: Re: Hollnger Canadan Publshng Holdngs Co. ( HCPH ) proceedng under the Companes Credtors Arrangement Act ( CCAA ) Update on CCAA Proceedngs

More information

Efficient Project Portfolio as a tool for Enterprise Risk Management

Efficient Project Portfolio as a tool for Enterprise Risk Management Effcent Proect Portfolo as a tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company January 5, 27 Effcent Proect Portfolo as a tool for Enterprse

More information

Cloud Auto-Scaling with Deadline and Budget Constraints

Cloud Auto-Scaling with Deadline and Budget Constraints Prelmnary verson. Fnal verson appears In Proceedngs of 11th ACM/IEEE Internatonal Conference on Grd Computng (Grd 21). Oct 25-28, 21. Brussels, Belgum. Cloud Auto-Scalng wth Deadlne and Budget Constrants

More information

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits

Linear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.

More information

A Design Method of High-availability and Low-optical-loss Optical Aggregation Network Architecture

A Design Method of High-availability and Low-optical-loss Optical Aggregation Network Architecture A Desgn Method of Hgh-avalablty and Low-optcal-loss Optcal Aggregaton Network Archtecture Takehro Sato, Kuntaka Ashzawa, Kazumasa Tokuhash, Dasuke Ish, Satoru Okamoto and Naoak Yamanaka Dept. of Informaton

More information

CHULMLEIGH ACADEMY TRUST INDUCTION AND DEVELOPMENT OF DIRECTORS POLICY

CHULMLEIGH ACADEMY TRUST INDUCTION AND DEVELOPMENT OF DIRECTORS POLICY CHULMLEIGH ACADEMY TRUST INDUCTION AND DEVELOPMENT OF DIRECTORS POLICY Adopted by BoD:30 May 2012 Polcy Statement The Drectors of Chulmlegh Academy Trust beleve all Drectors brng an equally valued range

More information

AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE

AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE AN APPOINTMENT ORDER OUTPATIENT SCHEDULING SYSTEM THAT IMPROVES OUTPATIENT EXPERIENCE Yu-L Huang Industral Engneerng Department New Mexco State Unversty Las Cruces, New Mexco 88003, U.S.A. Abstract Patent

More information

Multiple discount and forward curves

Multiple discount and forward curves Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of

More information

End-to-end measurements of GPRS-EDGE networks have

End-to-end measurements of GPRS-EDGE networks have End-to-end measurements over GPRS-EDGE networks Juan Andrés Negrera Facultad de Ingenería, Unversdad de la Repúblca Montevdeo, Uruguay Javer Perera Facultad de Ingenería, Unversdad de la Repúblca Montevdeo,

More information

RESEARCH DISCUSSION PAPER

RESEARCH DISCUSSION PAPER Reserve Bank of Australa RESEARCH DISCUSSION PAPER Competton Between Payment Systems George Gardner and Andrew Stone RDP 2009-02 COMPETITION BETWEEN PAYMENT SYSTEMS George Gardner and Andrew Stone Research

More information

A FASTER EXTERNAL SORTING ALGORITHM USING NO ADDITIONAL DISK SPACE

A FASTER EXTERNAL SORTING ALGORITHM USING NO ADDITIONAL DISK SPACE 47 A FASTER EXTERAL SORTIG ALGORITHM USIG O ADDITIOAL DISK SPACE Md. Rafqul Islam +, Mohd. oor Md. Sap ++, Md. Sumon Sarker +, Sk. Razbul Islam + + Computer Scence and Engneerng Dscplne, Khulna Unversty,

More information

Vasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio

Vasicek s Model of Distribution of Losses in a Large, Homogeneous Portfolio Vascek s Model of Dstrbuton of Losses n a Large, Homogeneous Portfolo Stephen M Schaefer London Busness School Credt Rsk Electve Summer 2012 Vascek s Model Important method for calculatng dstrbuton of

More information

Fault tolerance in cloud technologies presented as a service

Fault tolerance in cloud technologies presented as a service Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance

More information

Small pots lump sum payment instruction

Small pots lump sum payment instruction For customers Small pots lump sum payment nstructon Please read these notes before completng ths nstructon About ths nstructon Use ths nstructon f you re an ndvdual wth Aegon Retrement Choces Self Invested

More information

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN

EE201 Circuit Theory I 2015 Spring. Dr. Yılmaz KALKAN EE201 Crcut Theory I 2015 Sprng Dr. Yılmaz KALKAN 1. Basc Concepts (Chapter 1 of Nlsson - 3 Hrs.) Introducton, Current and Voltage, Power and Energy 2. Basc Laws (Chapter 2&3 of Nlsson - 6 Hrs.) Voltage

More information

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:

SPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background: SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and

More information

where the coordinates are related to those in the old frame as follows.

where the coordinates are related to those in the old frame as follows. Chapter 2 - Cartesan Vectors and Tensors: Ther Algebra Defnton of a vector Examples of vectors Scalar multplcaton Addton of vectors coplanar vectors Unt vectors A bass of non-coplanar vectors Scalar product

More information

Rapid Estimation Method for Data Capacity and Spectrum Efficiency in Cellular Networks

Rapid Estimation Method for Data Capacity and Spectrum Efficiency in Cellular Networks Rapd Estmaton ethod for Data Capacty and Spectrum Effcency n Cellular Networs C.F. Ball, E. Humburg, K. Ivanov, R. üllner Semens AG, Communcatons oble Networs unch, Germany carsten.ball@semens.com Abstract

More information

What is Candidate Sampling

What is Candidate Sampling What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble

More information

MAC Layer Service Time Distribution of a Fixed Priority Real Time Scheduler over 802.11

MAC Layer Service Time Distribution of a Fixed Priority Real Time Scheduler over 802.11 Internatonal Journal of Software Engneerng and Its Applcatons Vol., No., Aprl, 008 MAC Layer Servce Tme Dstrbuton of a Fxed Prorty Real Tme Scheduler over 80. Inès El Korb Ecole Natonale des Scences de

More information

Canon NTSC Help Desk Documentation

Canon NTSC Help Desk Documentation Canon NTSC Help Desk Documentaton READ THIS BEFORE PROCEEDING Before revewng ths documentaton, Canon Busness Solutons, Inc. ( CBS ) hereby refers you, the customer or customer s representatve or agent

More information

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression

A Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy S-curve Regression Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy S-curve Regresson Cheng-Wu Chen, Morrs H. L. Wang and Tng-Ya Hseh Department of Cvl Engneerng, Natonal Central Unversty,

More information

Proactive Secret Sharing Or: How to Cope With Perpetual Leakage

Proactive Secret Sharing Or: How to Cope With Perpetual Leakage Proactve Secret Sharng Or: How to Cope Wth Perpetual Leakage Paper by Amr Herzberg Stanslaw Jareck Hugo Krawczyk Mot Yung Presentaton by Davd Zage What s Secret Sharng Basc Idea ((2, 2)-threshold scheme):

More information

Open Access A Load Balancing Strategy with Bandwidth Constraint in Cloud Computing. Jing Deng 1,*, Ping Guo 2, Qi Li 3, Haizhu Chen 1

Open Access A Load Balancing Strategy with Bandwidth Constraint in Cloud Computing. Jing Deng 1,*, Ping Guo 2, Qi Li 3, Haizhu Chen 1 Send Orders for Reprnts to reprnts@benthamscence.ae The Open Cybernetcs & Systemcs Journal, 2014, 8, 115-121 115 Open Access A Load Balancng Strategy wth Bandwdth Constrant n Cloud Computng Jng Deng 1,*,

More information