An Introduction to Queuing Theory

An Introduction to Queuing Theory Queuing theory is the mathematical study of queuing, or waiting in lines. Queues contain customers (or â€Å"items†) such as people, objects, or information. Queues  form when there are limited resources for providing a service. For example, if there are 5 cash registers in a grocery store, queues will form if more than 5 customers wish to pay for their items at the same time. A basic queuing system consists of an arrival process (how customers arrive at the queue, how many customers are present in total), the queue itself, the service process for attending to those customers, and departures from the system. Mathematical queuing models are often used in software and business to determine the best way of using limited resources. Queueing models can answer questions such as: What is the probability that a customer will wait 10 minutes in line? What is the average waiting time per customer?   The following situations are examples of how queueing theory can be applied: Waiting in line at a bank or a storeWaiting for a customer service representative to answer a call after the call has been placed on holdWaiting for a train to comeWaiting for a computer to perform a task or respondWaiting for an automated car wash to clean a line of cars Characterizing a Queuing System Queuing models  analyze how customers (including people, objects, and information) receive a service. A queuing system contains: Arrival process. The arrival process is simply how customers arrive. They may come into a queue alone or in groups, and they may arrive at certain intervals or randomly.Behavior. How  do customers behave when they are in line? Some might be willing to wait for their place in the queue; others may become impatient and leave. Yet others might decide to rejoin the queue later, such as when they are put on hold with customer service and decide to call back in hopes of receiving faster service.  How customers are serviced. This includes the length of time a customer is serviced, the number of servers available to help the customers, whether customers are served one by one or in batches, and the order in which customers are serviced, also called service discipline.Service discipline refers to the rule by which the next customer is selected. Although many retail scenarios  employ the â€Å"first come, first served† rule, other situations may call for other types of service. For example, customers may be served in order of priority, or based on the number of items they need serviced (such as in an express lane in a grocery store). Sometimes, the  last customer to arrive will be served first (such s in the case in a stack of dirty dishes, where the one on top will be the first to be washed). Waiting room. The number of customers allowed to wait in the queue may be limited based on the space available. Mathematics of Queuing Theory Kendall’s notation is a shorthand notation that specifies the parameters of a basic queuing model. Kendall’s notation is written in the form A/S/c/B/N/D, where each of the letters stand for different parameters. The A term describes when customers arrive at the queue – in particular, the time between arrivals, or interarrival times. Mathematically, this parameter specifies the probability distribution that the interarrival times follow. One common probability distribution used for the A term is the Poisson distribution.The S term describes how long it takes for a customer to be serviced after it leaves the queue. Mathematically, this parameter specifies the probability distribution that these service times follow. The Poisson distribution is also commonly used for the S term.The c term specifies the number of servers in the queuing system. The model assumes that all servers in the system are identical, so they can all be described by the S term above.The B term specifies the total number of items that can be in the system, and includes items that are still in the queue and those that are being serviced. Though many systems in the real world have a limited capacity, the model is easier to analyze if this capacity is considered infinite. Consequently, if the capacity of a system is large enough, the system is commonly assumed to be infinite. The N term specifies the total number of potential customers – i.e., the number of customers that could ever enter the queueing system – which may be considered finite or infinite.The D term specifies the service discipline of the queuing system, such as first-come-first-served or last-in-first-out. Little’s law, which was first proven by mathematician John Little, states that the average number of items in a queue can be calculated by multiplying the average rate at which the items arrive in the system by the average amount of time they spend in it. In mathematical notation, the Littles law is: L ÃŽ »WL is the average number of items, ÃŽ » is the average arrival rate of the items in the queuing system, and W is the average amount of time the items spend in the queuing system.Little’s law assumes that the system is in a â€Å"steady state† – the mathematical variables characterizing the system do not change over time. Although Little’s law only needs three inputs, it is quite general and can be applied to many queuing systems, regardless of the types of items in the queue or the way items are processed in the queue. Little’s law can be useful in analyzing how a queue has performed over some time, or to quickly gauge how a queue is currently performing. For example: a shoebox company wants to figure out the average number of shoeboxes that are stored in a warehouse. The company knows that the average arrival rate of the boxes into the warehouse is 1,000 shoeboxes/year, and that the average time they spend in the warehouse is about 3 months, or  ¼ of a year. Thus, the average number of shoeboxes in the warehouse is given by (1000 shoeboxes/year) x ( ¼ year), or 250 shoeboxes. Key Takeaways Queuing theory is the mathematical study of queuing, or waiting in lines.Queues contain â€Å"customers† such as people, objects, or information. Queues form when there are limited resources for providing a service.Queuing theory can be applied to situations ranging from  waiting in line at the grocery store to waiting for a computer to perform a task. It is often used in software and business applications to determine the best way of using limited resources.Kendall’s notation can be used to specify the parameters of a queuing system.Little’s law is a simple but general expression that can provide a quick estimate of the average number of items in a queue. Sources Beasley, J. E. â€Å"Queuing theory.†Boxma, O. J. â€Å"Stochastic performance modelling.† 2008.Lilja, D. Measuring Computer Performance: A Practitioner’s Guide, 2005.Little, J., and Graves, S. â€Å"Chapter 5: Little’s law.† In Building Intuition: Insights from Basic Operations Management Models and Principles. Springer ScienceBusiness Media, 2008.Mulholland, B. â€Å"Little’s law: How to analyze your processes (with stealth bombers).† Process.st, 2017.

Contract Law Coursework Example | Topics and Well Written Essays - 1250 words

Contract Law - Coursework Example The two situations involve contracts that are governed by observance of There are therefore various legal principles that will govern the two situations to have involved formation of binding contracts. A contract is defined as an agreement made between two or more parties that is legally binding. Parties to a contract usually expect a win-win situation where they can both benefit from the contract. However the there is usually no certainty for both parties to attain this situation.2 One party may end up having a legal liability towards the other party. Any contract made whether in an attorney’s office or just written by the involved parties is valid and binding provided that the legal principles involved are understandable to both parties. The contract becomes valid on the acceptance of an offer, provided it is in compliance with the laws of the state. The first principle is the legal capacity which for many states the parties are expected to have attained the majority age of 18 years. The parties are as well expected to be in their sound mental capacity to understand the terms of the contract and consequences for non performance.3 The party representing a business organization is in a position to sign the contract thus binding the business to the contract.4 The second principle is the offer and acceptance. A contract comes to existence upon acceptance of the offer. A person may reject an offer and opt for a counter offer if they fail to agree to the terms allowed. Once accepted, offer can be revoked at any time. A contract is therefore formed on acceptance of offer or counteroffer by both parties. The third principle in formation of a legal contract is the exchange of value or consideration. This is the payment made for the performance of the contract. Consideration may be anything valuable for instance cash or goods and services. Where the consideration made is not stated

Network Infrastructure Planning Research Paper Example | Topics and Well Written Essays - 1000 words

Network Infrastructure Planning - Research Paper Example With these services, only the user interface of some application is presented on the client machine. All input from client machine is purposely redirected to the application server where all the processing happens. Terminal services is a very well in place technology to provide services to remote offices since organizations are finding ways to reduce the cost of ownership by centrally deploying and managing windows based applications and remotely administering window server 2003- based computers. The services allow centrally deployment and management of windows based applications. This has the advantage that a company can ensure that all the computers are running the current version of application software since the software is installed once on the server instead of installing on each and every machine. This has the advantage of reducing the cost of installation and maintenance of such applications since it’s done once on a machine. Also such services reduce application suppo rt since its being done from one central server. This ensures a cost effective way of installation and maintenance of services within the different four remote offices. The issue of mirroring all application to the headquarters is reduced since the headquarters have all the information about the application used remotely by the offices. Since installation services are done mainly from the headquarters, then the cost incurred due to licensing and other costs of installation are just incurred once from the headquarters. This saves a lot of operation costs due to the reduced licensing costs. Costs like disk space usage are greatly reduced since this is mainly incurred from the server which runs all the applications. The issue of security when accessing sensitive files is up to standard since all security matters about who accesses what is controlled from the headquarters. The following are ideal situations where terminal services are mainly applied:- Hosting Line-of-Business Applicatio ns If an organization or some groups within the organization normally uses some specialized software to do their specialized work, it is always a good idea to host their applications using a terminal server. This is an ideal area to apply Terminal server. Terminal server can be used in the following situations: Custom applications.  If business application is developed internally, what is commonly referred to as in-house or specifically for your organization, and specifically tends to require updating frequently, deployment of the application once on a terminal server can greatly reduce the costs. This is especially important if your environment is actually dispersed or when you are deploying terminal server to centrally serve different offices. Large central data pool.  Applications that tend to rely on access to a central data source often run well on a terminal server because huge amounts of data do not necessarily travel across users for access. Instead the whole data proces sing is done on the server. Only the keystrokes and some display information have to travel across the specified network, which allows one to use lower bandwidth connections. This is especially important if users of that data pool are remotely located, for example in an office branch with a sluggish connection to database server. Task workers.  In setups where security is an issue and you want workers to mainly access only applications they have rights to access in order to perform their jobs, centralization of the

UK Telecommunications Management of Interest Rates

UK Telecommunications Management of Interest Rates INTRODUCTION In business world today many companies are faced with the increase in volatility of financial markets which has lead to increase in financial price risk. Many companies are faced with exposure to financial risk which are caused by unanticipated exchange rate and interest rate movements. These unanticipated movement in exchange rate which is caused by international competition can results into large gain or loss if the risk is not managed properly. Exchange rate movement generate business risks which can vary the current foreign assets and liabilities and interest rate movement can have indirect impact on companys value on its future cash flows. Domestic and multinational companies who are faced with these kind of risks must assure that they control these risks otherwise if they are unmanaged then this can result into total failure of business. Financial Institutions have introduced different products to help companies in risk management. These products are Forward contracts on exchange rate, Futures contracts, Interest rate swaps and Options. Forward contract being the oldest product to be introduced to manage both foreign exchange and interest rate risks. 1.1 Problem statement Changes in business environment and increase in movement of interest rate and exchange rate has resulted into rise in financial risk exposure. These movements can affect not only companys profit but also companys survival in indirect way. Financial risks management has turn to be a significant area of pertain for UK corporations. Therefore this proposal attempt to find out how UK Telecommunications industry handle financial risks in an increasing business risk environment. Research aim and objectives Aim The main aim of the study is to determine how firms in UK Telecommunications industry manage interest rate and foreign exchange financial risks by looking into use of derivatives. 1.3 Research Objectives The primary objectives of the research will be; To determine how companies manage risk To determine whether derivatives are used or not To determine which derivatives are used and for what purpose Disclosure of financial instruments 1.4 Research Questions The following research questions will guide this research How companies manage risk? Are derivatives used or not used? Which derivatives are used and for what purpose? What are the disclosure of financial instruments? 2. LITERATURE REVIEW Derivatives are financial instruments whose values are deduced from some underlying assets or rate/price. Derivatives are now of paramount importance to the business world, with imaginary value of more than $200 trillion of these derivatives are being traded on coordinated and over the counter markets in 2004 (Bank for International Settlements, 2004). The financial products which are provided by FinanciaI Institution are options, futures contract, forward contract and interest rate swap. The common Interest rate derivative is Interest rate swaps and others are future contracts and interest rate options while for foreign exchange derivatives are forwards contracts, currency swaps, foreign exchange futures and options. Forward contract gives the owner the obligation to buy an asset at set price and maturity date as agreed in the contract. Future as like forward but in futures are public traded while forwards are private contracts. Unlike future and forward, options give the owner the right but not obligation to buy or sell an asset at a fixed price on or before specified date (Prevost et al, 2000). Derivatives are used to cut down cash flows and earnings volatility caused by changes in foreign currency exchange rates, commodity prices, interest rates and other risk factors (Barton J, 2000). Use of financial derivatives is widespread, especially among large publicly traded companies and is still increasing sharply. For example, in a study done by Guay and Kothari, (2003) based on annual reports information of 413 largest firms in the U.S revealed that 57% were using derivatives. In another study of 314 Fortune 500 firms showed that 72% were using derivatives (Barton J, 2001). Mallin et al. (2001) did survey analysis on the use of derivatives in risk management, he mailed questionnaire to 800 UK non financial firms listed on London stock exchange. Results showed that of 231 respondents 32% were applying at least one derivative instrument. Another researchers Bodnar et al (2003) studied derivative usage in managing risk to 167 non-financial Netherlands firms and revealed 84 usable responses which is 50.3%. In India a study was conducted to examine derivatives usage in managing foreign exchange risk to 640 companies which were faced with foreign exchange exposure and results showed that 70.4% of respondents used foreign exchange derivatives to manage risk (Anand and Kaushik 2007). Whilst many firms use derivatives in managing risk, misuse of it may result into major losses. This was proved by Karpinsky (1998) who revealed companies like Sumitomo Corporation lost $3,500 million in 1996 because of copper future. On the other hand El-Masry (2003) collected data from questionnaire mailed to 401 non financial companies listed on London stock exchange, 50% of respondents did not use derivatives because the risk exposure was not substational. Likewise suryey done by Bodnar et al (1995) revealed lower use of derivatives and the reason being low insignificant exposure. Regarding to mostly used derivatives to manage risk exposure, survey done by Marshall (1997) pointed that options, swaps and forwards were normally used to manage interest rate and foreign exchange risks. In El-Masry (2003) survey of UK non financial firms, results indicated that firms use options at 29.4%, forward/future at 23.7% and swaps 23.1%. 3.0. RESEARCH METHODOLOGY Research design This study will be conducted as a quantitative survey Sources of data The main source of data will be the annual reports of 10 companies in the UK telecommunications industry for the past three years. Documentary source Bell (1999) state documentary source involves the reading of relevant information from library source such as text books, journals, newspapers and internet. Secondary source will enable a researcher to conduct broad investigation and help confirm the reliability of the findings given that the findings may be subjective and this source will be used as well to cut down reliance on the annual reports as the main source of data used in the study. Sampling selection Selection of sample will be based on the public data information of the companies and the eligibility criteria will base on following factors; The company must be in the telecommunication services industry The company must be either a Domestic or a Multinational one which is exposed to financial risks as an outcome of international competition The company should be among of the listed London Stock Exchange companies Data analysis Data collected will be analysed using Statistical Package for Social Sciences (SPSS) and presented using frequency table. 4. CONCLUSION Measuring and managing financial risk exposure are crucial functions in cutting down companies vulnerabilities from major exchange and interest rate movements. Financial derivatives are very important in risk management of corporations 5. REFERENCE Anand m., Kaushik k. p., (2007).Management Motivations for Use of Foreign Currency Derivatives in India, IIML Working Paper Series. Bank for International Settlements. (2004). Triennial Central Bank Survey of Foreign Exchange and Derivatives Market Activity in 2004. http://www.bis.org/publ/rpfx05.htm. Barton, J. (2001). Does the Use of Financial Derivatives Affect Earnings Management Decisions? The Accounting Review, 76, 1-26. Bell, Judith. (1999). Doing your Research Project: A guide for first time researcher in Education: 3rd Edition Buckingham, Open University press.UK Bodnar g. m., de jong a., macrae v., (2003). The impact of Institutional Differences on Derivatives Usage: a Comparative Study of US and Dutch Firmsà ¢Ã¢â€š ¬?, European Financial Management vol. 9, No. 3, pp. 271-297. El-masry a.,(2003) A survey of derivatives use by UK non financial companies, Social science research network Manchester Business School pg.455. Grant, K. and Marshall, A. P. (1997), à ¢Ã¢â€š ¬Ã…“Large UK companies and derivativesà ¢Ã¢â€š ¬?, European Financial Management, vol. 3 no. 2, pp. 191-208. Guay W Kothari, S. P. (2003). How Much Do Firms Hedge with Derivatives? Journal of Financial Economics, 70, 423-461. Hentschel, L., Kothari, S. P. (2001). Are Corporations Reducing or Taking Risks with Derivatives. Journal of Financial and Quantitative Analysis, 36, 93-118. Mallin c.; Ow-yong k. and Reynolds m.,(2001) Derivatives usage in UK non-financial listed companies, The European Journal of Finance Vol. 7 (2001), pp. 63-91. Saunders, M., Lewis, P. Thornhill, A. (2007). Research Methods for Business Students. 4th Edition. Pearson Education Limited UK. Prevost, A. K., Rose, L. C., Miller, G. (2000). Derivatives Usage and Financial Risk Management in Large and Small Economies: A Comparative Analysis. Journal of Business Finance and Accounting, 27, 733-759.

Communications Persuasive Essay Essay

Specific purpose: I would like to persuade my audience that drug test screenings should be mandatory in order for welfare recipients to receive their money. Introduction Attention material: How many if you have jobs? How many if the people with jobs like to see a huge chunk of their check MIA due to state and federal taxes? And how many of you like knowing that that chuck of your check that’s missing could very well be going towards someone’s drug addiction? Thesis Statement: By enforcing a mandatory drug test to all welfare recipients, you ensure that hard working people’s tax dollars are being used the correct ways, and not being used to support a drug addiction, Preview: Today I will inform you on the pros of drug testing welfare recipients, how many states have already passed this law, how many states are trying to pass the law, the cons of the drug testing, and what we can do to out this plan into action. Body I. What benefits would drug testing welfare recipients have on our country? A. David Vitter of U.S. News Weekly states, by drug testing welfare recipients, it would ensure that all hardworking taxpayers’ money I’d going to get used in the correct and intended way. The nation is already in enough debt of more than $14 trillion, does it make much sense to be wasting tax money on illegal drugs and dishonest welfare recipients? That makes no sense at all! (Vitter, 2011) B. Enforcing drugs testing will also force drug users or addicts that are looking for financial assistance to get help before receiving money that would have been used to feed their ongoing addiction (Vitter, 2011) By coming up with a plan to make drug user go to rehabilitation centers and treating their addiction before they receive financial assistance from the government will cause people to either get better first, or not have the opportunity to take the tax money and waste it on illegal drugs anyway. ll. Where in the United States has this law been implemented? A. Many states have tried very hard to get the drug testing law put into place and used effectively but not all have succeeded. In fact only 7 of the 29 that have proposed the law have had it passed in their state. The states that have the law include Florida, Utah, Michigan, Tennessee, Arizona, Missouri, and Oklahoma. Many of the states that have Mercado 3 tried to get this law into effect include North Dakota, Arkansas, New Hampshire, Texas, Kansas, Maine, Wyoming, and Virginia (National, 2013) III. What are the possible cons to drug testing welfare recipients? A. Two Michigan mothers, both on welfare argue that the drug testing law in effect in their state is it if constitutional grounds. Tanya Marchwinski, one of these mothers states, â€Å"Just because we are lower income we are singled out. Makes me feel like I’m doing something wrong and I’m constantly being watched.† (Cannon, 1999) B. Many states that have tried passing the drug testing law have failed because it is deemed unconstitutional. Due to the simple fact that the state representatives cannot assume all welfare applicants or recipients are drug users or addicts. Being able to pass these laws would take the conditions being changed to drug testing only taking place if state representatives suspect drug use in a welfare applicant or recipient. IV. A proposal on welfare reform A. Domenick Basolo the president of Good for Society, proposes a structure somewhat like the â€Å"Three-Strikes Law† Strike 1- Failing the given drug test when applying for welfare follows in providing written documentation for agreeing to signing up for a rehabilitation program. Strike 2- Must submit random drug screening, and provide proof once a week to attending rehabilitation programs. Strike 3- YOU’RE OUT! The failure to adhere to the following conditions and opportunities given will result in loss of funds to recipient, and possible household search to rule in or out of potential child negligence (Basolo, 2013). Conclusion A. There are many opinions on the welfare reform and whether or not to require applicants and recipients for submit a drug test and pass the drug test to relieve funds. However not all ideas or opinions would be acceptable in this country, because most ideas are deemed unconstitutional. Nevertheless, it is very evident a reform in welfare is much needed. It’s just now about finding an acceptable way to reform it without creating controversy. Personally, as a hard working tax payer, I would like to know my tax dollars are going to the right things they’re intended for, not just to support a drug addict and at the same time neglect innocent children’s needs for daily life items.

Definition and Examples of Formal Prose Style

In composition, formal style is a broad term for speech or writing marked by an impersonal, objective, and precise use of language. A formal prose style is typically used in orations, scholarly books and articles, technical reports, research papers, and legal documents. Contrast with informal style  and colloquial style. In The Rhetorical Act (2015), Karlyn Kohrs Campbell et al. observe that formal prose is strictly  grammatical  and uses complex sentence structure and precise, often technical  vocabulary. Informal prose is  less strictly grammatical and uses short, simple sentences and ordinary, familiar words. Observations Whenever we speak or write, we make certain assumptions about what kind of language is appropriate to the situation at hand. Basically, this amounts to deciding how formal or informal to be. Rhetorical style ranges from the formality of a presidential address or scholarly article on the one hand to the informality of a radio or TV interview or a conversation—perhaps even a text or twitter message—with a friend on the other. Generally speaking, as style becomes more informal, it becomes more conversational or colloquial.(Karlyn Kohrs Campbell, Susan Schultz Huxman, and Thomas A. Burkholder, The Rhetorical Act: Thinking, Speaking and Writing Critically, 5th ed. Cengage, 2015)Formal and Informal StylesToday rhetoricians speak of formal and informal styles. The former is characterized by more advanced vocabulary, longer, more complex sentences, use of one instead of you, and is appropriate for more formal occasions such as lectures, scholarly papers, or ceremonial addresses . The informal style has feature such as contractions, the use of the first and second person pronouns I and you, simpler vocabulary, and shorter sentences. It is appropriate for informal essays and certain kinds of letters.(Winifred Bryan Horner, Rhetoric in the Classical Tradition. St. Martins, 1988)The tone is polite, but impersonal. The pronoun you isnt usually appropriate in formal writing.The language of formal writing doesnt include contractions, slang, or humor. It is often technical. In an attempt to avoid pronouns like I, you, and me, some writers overuse the passive voice, which makes their writing stuffy and indirect.Sentence structure includes lengthy sentences with complex subordination, long verb phrases, and the expletive pronouns it and there for subjects. Since the information content of formal, technical, or legal documents is high, both readers and writers expect the reading pace to be slower than in informal writing.Characteristics of a Formal Style- Formal styl e is characterized by long and complex sentences, a scholarly vocabulary, and a consistently serious tone. Grammatical rules are scrupulously observed, and the subject matter is substantial. The selection may include references to literary works or allusions to historical and classical figures. Absent are contractions, colloquial expressions, and an identified speaker, with impersonal one or the reader frequently used as the subject.(Fred Obrecht, Minimum Essentials of English, 2nd ed. Barrons, 1999)- These are some typical characteristics of formal style: Formal style is appropriate for official documents, computer documentation, scholarly articles and books, technical reports, or letters with a negative message.(Deborah Dumaine. Instant-Answer Guide to Business Writing. Writers Club Press, 2003)

Debris Clouds Visual Cues of a Tornado Touchdown

A  debris cloud forms when the wind speeds of a tornado pick up very heavy objects and swirl them around in a dense cloud around the base or the funnel cloud itself. One of the most dangerous parts of a  tornado  can be its debris cloud.   In fact, items such as trucks, tractors, cars, animals, and people can be swirled around in a debris cloud. Not all tornadoes produce heavy debris clouds and not all tornadoes have enough sustained winds to pull up large objects. Therefore, the primary component of most debris clouds is dust and small bits of debris. Debris Formation A tornados debris cloud actually starts to form even before the funnel descends from the thunderstorm cloud downward to the ground. As the funnel descends, dust and loose objects on the area directly underneath it at the Earths surface will begin rotating and may even lift several feet off of the ground and swing out hundreds of yards wide in response to the air movement above. After the funnel touches the ground and becomes a tornado,  the debris cloud travels along with the storm.   As the tornado travels along its path, its winds continue to carry nearby objects airborne. The size of the objects within  its debris cloud depend on the strength of the tornados winds. Usually, however, the debris cloud whirls around smaller objects and dirt particles while the funnel cloud carries larger debris pieces. This is why the debris cloud color is normally gray or black. It can take on other colors depending on what it picks up. Keeping Safe From Tornado Debris The majority of tornado injuries and deaths occur not because of storm winds, but because of debris. In fact, the three main tornado safety tips—get low and cover your head, wear a helmet, wear shoes—are all meant to reduce your risk of encountering debris. Take the duck and cover position: By getting as low to the ground as you can you reduce the chance of being struck by airborne objects and debris. Covering your head with your arms or a blanket provides an extra layer of defense.Wear  a helmet: Since 2011, many people have added a bike, motorcycle, or sports helmet to their tornado preparedness kit. As bizarre as it sounds, when you consider that the single largest cause of tornado deaths is head trauma it suddenly makes good sense.  Wear  shoes:  If a tornado strikes when youre at home, youll likely be barefoot or wearing socks, which means your feet will be defenseless as you navigate your way over litter and glass after the storm. This is why its a good idea to always include a pair of lightweight portable footwear in your safety kit. By observing the takeoff and landing points of storm debris, scientists are able to learn how the debris, and therefore, the storm, traveled.   Updated by Tiffany Means