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.

Occupational Health and Safety Essay Example | Topics and Well Written Essays - 1500 words

Occupational Health and Safety - Essay Example There is no standard as to what elements or factors should be present for workplace or working conditions to be considered safe. The Contributory Negligence Doctrine puts the entire blame on the employee and frees the employer of any responsibility on the mishap that occurred. The relationship between the employers and the workers is one where their goals and the means of attaining them are segregated or are on totally opposite fields. There is no interdependence and cooperation in reaching a common goal. Employers are mainly concerned with production and are not involved in matters concerning the conditions and welfare of their workers or employees. This doctrine held on to the notion that employees are totally and solely responsible for their actions and management is a separate entity which is only accountable to itself and to the costs and profits of the business. Being a separate entity, employers are in no way part of the workers personal and individual concerns, even wile in the workplace or within the premises of the company structure, other than the giving of wage for service rendered. The basis of the relationship is only grounded on the exchange of services for wages. This doctrine's main assumption is that if employees, prior to their acceptance of the job or prior to the commencement of their duties, are aware of the hazards involved in the job or of the presence of hazards in the workplace then they have accepted these hazards as part of the employment conditions. They cannot therefore sue their employees in the event that an accident happens, because their acceptance of the job meant that they have accepted the hazards that go with it. The court based this doctrine on the theory that if an employee sees that there are hazards involved in the job before even accepting the work, he would demand for a higher wage because of the possibility of getting injured. The employer on the other hand, as a reaction to this demand, would either do something to remove the risk or would pay the additional salary. This doctrine reflects again a boxed relationship between the employee and employer where the concern lies in the exchange of service for money. The concern does not extend to the physical or emotional welfare of the employee while working for the company. There is no initiative on the part of the employer in providing safe conditions for the workers. The reaction of eliminating the risk factors is just a response to the issue of additional wage demanded by the worker. The basis of this reaction again is the financial standing of the company or the cost that they would have to incur. It is in no way to afford additional benefits to workers like safe working conditions. The burden of protecting oneself from work hazards is again on the shoulders of the workers. By demanding for additional compensation in exchange for a future possibility of an accident occurring while at work, the worker will free the employer of any liability. C. Fellow-Servant Doctrine The basic idea of this doctrine is that an employee cannot seek compensation from the employer for damages if the accident was caused, either entirely or in part, by a co-worker. This doctrine is regarded as an extension of the

Roisin as a Secular Western Woman in the Film by Ken Loach Research Paper

Roisin as a Secular Western Woman in the Film by Ken Loach - Research Paper Example As the film begins, Casim is shown working as a disc jockey in a club, playing Arabic music. In this scene, the crowd primarily consisting of young British-Pakistanis is depicted dancing wildly to the music. This crowd contravenes the common precept of Islam as a largely conservative religion. It is also fairly unconventional for a Muslim to work as a deejay as Casim does. This scene clearly illustrates the extensive influence that secular western values have had on Islam, and especially on second-generation Muslims. It is evident that these young adults are not devout adherents of Islam and its traditions, like their parents. This lack of complete devotion could be attributed to their intermingling with other cultures and desire to be accepted in a rather diverse society (Ernst 5). Another scene focusing on religion in Ae Fond Kiss is that of Tahara delivering a speech in front of students during what appears to be a class debate (02:48-04:21). The debate evidently revolves around t he West’s unified crusade against global terrorism, as shown on the whiteboard. Tahara presents a strong argument stating that she defies the universal definition of terrorism as provided by the West since it fails to account for the many people subjected to terror in daily circumstances. Most importantly, Tahara says that she rejects the manner in which the West simplifies Muslims. The speech draws one’s attention to the stereotypes held by Westerners for Muslims. It also shows how absurd it is to generalize Muslims and link all of them to terrorism, yet they are as diverse as other religions.

SOC 111 LS1 Essay Example | Topics and Well Written Essays - 500 words

SOC 111 LS1 - Essay Example   Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   There was an individual who was a very close business associate with my father who I will identify as Mr. X. For reasons unbeknownst to me, Mr. X was as excellent sales associate and had a very successful professional career; however it is the case that this individual had a very task oriented/problem solving orientation when it came to personal matters. I knew Mr. X personally and (Successful as he may be) had a lot of difficulties in his social life and in general terms he was not a pleasant person to be around in social circumstances. Despite these problems Mr. X had been happily married until his wife suffered a brain aneurysm and passed away quite suddenly. Newly widowed, Mr. X had a great deal of difficulty in dealing with his grief and began to see much of his personal life spiraling out of control. As it is the case that most issues in Mr. X’s professional life were viewed as being a task oriented it could be the case that h e looked at his grief as a problem that he was trying to solve. It comes as no surprise that there was no solution to Mr. X’s Grief, and it was the case that he started to see his professional life start to decline as well, and around this time Mr. X was began battling with problematic drinking. On the advice of his work colleagues (Including my father), Mr. X started seeing a therapist. As I highlighted earlier, Mr. X always had a task oriented personality and by being active in his routines (Typically work routines) Mr. X on a personal level was in general terms happier. Mr.X was simply unable to handle the problem of his grief, and by failing in this aspect of his life it started to negatively affect other parts of his life and he was on track to seeing his life spiral out of control. The advice of the therapist was to simply not view his grief as some sort of failure on his behalf and from a stregnths based perspective his

A Tale of Two Hearts in Charlotte Brontes Jane Eyre :: Jane Eyre Essays

A TALE OF TWO HEARTS While an artist uses a variety of colors and brushes to create a portrait, Charlotte Bronte used contrasting characters and their vivid personalities to create a masterpiece of her own.   In her novel Jane Eyre, Bronte uses narration and her characters to portray the struggle between a society’s Victorian realism and the people’s repressed urges of Romanticism.   In order to discern between the Victorian and Romantic themes, Bronte selects certain characters to portray the perfect stereotype of each theme.   Mademoiselle Celine Varens is the model of the Romantic attitude.   Varens a â€Å"French opera-dancer† found herself as the â€Å"grande passion† of Mr. Rochester.   The amour between Rochester and Varens started in a â€Å"complete establishment of servants, a carriage, cashmere, diamonds, dentells, etc.† and ended with Rochester â€Å"finding her out† with another man.   Varens’ irrationality did not only affect Rochester, but also her child: â€Å"she abandoned her child and ran away with a musician or singer.†Ã‚   Celine Varens, a woman in a daring profession, led a life of passion, freedom and irresponsibility.   Her life was ballad of adventure idolized by Romantics but frowned upon by society.   Mrs. Reed is the perfect representative of Victorian realism.   She had all t he visual attributes found in a Victorian styled lady.   She possessed gentry as the mistress of Gateshead Hall and her material wealth was made obvious by the luxuries found in her home –â€Å"a bed supported on massive pillows of mahogany, hung with curtains of damask†Ã¢â‚¬â€and in her children â€Å"in their Muslim frocks and scarlet sashes.†Ã‚   Besides wealth and gentility, Mrs. Reed also maintained Victorian characteristics of insularity and censoriousness.   Ã¢â‚¬Å"Eliza, John and Georgiana were now clustered round their mama in the drawing room: she lay reclined on the sofa by the fireplace and her darlings about her†¦Ã¢â‚¬  Mrs. Reed literally maintains insularity – snobbishly creating an island of her and her children, detaching themselves from Jane.   Lastly Mrs. Reed exercised censoriousness towards Jane on a continual basis until Jane was left with â€Å"a habitual mood of humiliation, self doubt, forlorn depression.†Ã‚   Jane’s state is the result of the Victorian need of moral severity, which was expressed by blame and disapproval.   Bronte uses Varens and Reed to paint the contrast between the Romantics controlled by emotion, freedom and imagination and the Victorians who exhibit middle-class stuffiness and pompous conservatism. But any author can capture the essence of two societies and illustrate the opposites in two opposing characters.

Social Smoking

One potentially important factor is social influence (Van den Putte, Yzer, & Brunsting, 2005), as this has been shown to be a significant predictor of the uptake of smoking (Kobus, 2003; Mayhem, Flay, & Mott, 2000). An important model which explicitly takes into account social influence and the role of the social environment is the theory of planned behaviour (TPB; Ajzen, 1991). This theory proposes that people’s intentions to behave in particular ways are informed by three main factors: their personal attitude towards the behaviour; their perceptions of social pressure from significant others to perform the behaviour, or subjective norms; and the amount of control they believe they have over performing the behaviour, or perceived behavioural control. In the smoking domain, TPB variables have been shown to predict both quitting intentions (Abrams & Biener, 1992; Droomers, Schrijvers, & Mackenbach, 2004; Godin, Valois, Lepage, & Desharnais, 1992; Norman, Conner, & Bell, 1999) and actual quitting (Godin et al. , 1992; Norman et al. , 1999), as well as the uptake of smoking among adolescents (Wilkinson & Abraham, 2004). Of primary interest to the present study is the role of subjective norms. Out of the three main TPB variables, norms have generally been shown to have the weakest effect on intentions (Armitage & Conner, 2001; Godin & Kok, 1996). However, it has been argued that this is due to the poor measurement and inconsistent conceptualisation of norms (Armitage & Conner, 2001) or the lack of variation of norms within a culture at any point in time. Research by Wiium, Torsheim, and Wold (2006) demonstrated that different kinds of norms differentially influence intentions and behaviour, and argued that the assessment of different kinds of norms in the TPB model can both extend the concept of ‘norm’ and improve its predictive power. In the present study we distinguish between norms from significant others (i. e. erceptions of what significant others believe about smoking) and societal norms (i. e. perceptions of what society in general believes about smoking). In this respect, we depart from previous smoking research that has treated these kinds of norms as two components of a higher order social norm (e. g. Hammond, Fong, Zanna, Thrasher, & Borland, 2006). We argue that it is important to distinguish between these two sources of normative influence, as individuals’ perceptions of the broader social desirability of smoking may differ from their perceptions of what their significant others believe. This distinction is particularly important when examining cultures that have quite different normative environments regarding smoking. In some countries, such as Australia and the USA, smoking has become a socially undesirable behaviour. This has occurred, at least partially, through decades of communication about the harms of smoking and a range of tobacco control policies, including the reduced capacity of tobacco companies to promote their products, health warnings on cigarette packs, and restrictions on where smoking is permitted. However, the social undesirability of smoking is not a global phenomenon. Some countries, such as Malaysia, have had a comparatively tobacco-friendly environment, with a relative lack of strongly enforced tobacco control policies and a higher prevalence of smoking than in many Western countries, at least among men. Nevertheless, individual Malaysian smokers’ families and close social networks may still disapprove of smoking. Thus, it is of interest to examine the relative influence of these two potentially opposing smoking norms on quitting intentions in different countries.

Gun Control And The United States - 957 Words

One of the most debated topics in the world today is the conflicting belief on whether people should or should not own and use guns. Gun control is generally defined as â€Å"laws or policies that regulate the manufacture, sale, transfer, possession, modification, or use of firearms† (Gopink, 2012). The views and opinions of this situation vary across the world. Some territories set strict rules and difficult procedures to obtain weapons while others allow easy access. People are usually very opinionated about this subject, causing debates and conflicting reactions. Gun control is one of the most controversial topics with numerous approaches to how it should be handled. The United States alone has â€Å"88.8 guns per 100 people, or about 270,000,000 guns† (Cornell, 2015). This is the highest total number of guns per country in the entire world. 22 percent of Americans â€Å"own one or more gun† (Cornell, 2015). These statistics are overwhelming to some people, w hile others see it as completely normal, or even excellent. Many laws have been passed to regulate this procedure, and citizens often cast their vote for officials solely based off of their opinion on gun control and the way weapons should be handled. All in all, the statistics are debated due to the fact that no one can agree on this questionable matter. One of the leading viewpoints on gun control is that citizens of the United States should give up their guns and that only military should be given the privilege of operating aShow MoreRelatedGun Control Of The United States1698 Words   |  7 Pagesshootings that has happened throughout the Unites States has created a great divide among Americans on what should our nation do to prevent further shootings from happening. Many people believe that forcing new laws on how people purchase weapons should require background checks. 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Life becomes dangerous and we need to be able to protect your family by yourself, your business, your property. Therefore so many people thinking about to buys guns and to have guns at home. In addition, the gun is freedom. We live in a free country