Atraumatic Restorative Treatment for Dental Caries

Atraumatic Restorative Treatment for Dental Caries Atraumatic restorative treatment for the management of dental caries: A Review Abstract: Atraumatic restorative treatment is a method of minimal caries intervention that uses only hand instruments. Over the past few years, there has been an increase in the number of studies reporting on various aspects of the Atraumatic Restorative Treatment and it is over three decades ART has been introduced, so this was considered an appropriate time for a systematic review on ART. Objective of this review article was to assess the effectiveness of ART in management of dental caries. All randomized or quasi-randomized control trials on ART were included. Intervention with adhesive restorative material such as GIC with different viscosity was evaluated. Primary outcomes measures such as pain relief, patient discomfort, anxiety and durability of restoration was assessed. Studies showed survival rates ranging from 66% to 76% at 6 year for single surface restorations ART approach provided higher survival percentages for single surface restorations and it causes less pain and dis comfort. Key words: Atraumatic restorative treatment, Survival, Deciduous teeth, Permanent teeth Introduction: Dental caries is one of the most prevalent oral diseases of public health concern. It affects almost all individuals irrespective of age, sex, occupation, religion, castes etc in developed as well as developing countries. It varies greatly among countries, even within a country and from region to region and there are several reasons for this problem like changes in food habits, poverty, lack of facilities especially to underprivileged section of the society, etc. WHO objective of â€Å"Health for All† still remains a dream, particularly in the underprivileged population of the world. Also, there has been a radical change in the methods of treatment of dental disease. We have seen a change in approach of treatment by the dentist, starting with extraction, then conservation of tooth structure and now stress is being laid on preventive dentistry. But the underprivileged population have not benefited from these developments that have brought about improved oral health in the indus trialized world. Realizing the magnitude of this problem, particularly lack of oral health care in below poverty line segment of society, JE Frencken embarked on simplistic approach of removing caries with hand instruments and filling up the ‘cavity’. This approach is termed as Atraumatic Restorative Treatment.[1] ART was first discovered in Tanzania in mid 1980s to suit the needs of the developing countries by JE Frencken Later, in Zimbabwe, the experiment was repeated by his team in larger school population group. WHO endorsed the ART procedure for the underprivileged population on world health day in April 7, 1994.[2] The idea of ART is strongly supported by the modern scientific approach to controlling caries maximal prevention, minimal invasiveness and minimal cavity preparation.[3] Different studies have been investigating the various aspects of ART approach in the past and still continue to increase. Most of the studies have investigated the survival of ART restoration and sealants. As ART approach is being utilized all over the world since more than 25 years, there is a need to carry out a systematic investigation about the survival and effectiveness of ART restorations. So the present systematic review focuses on the effectiveness of ART in management of dental caries in deciduous and permanent teeth. Materials and Methods We attempted to identify all relevant studies. Detailed search strategies were developed for each database to be searched and it was carried out in the Medline, Embase, Hinari, k-hub. All randomized controlled trials or quasi-randomized controlled trials were included. Non-randomized controlled trials were excluded. Studies with Dentate participants, regardless of the age and sex, with a history of dental (coronal) caries who have undergone restorative treatment using either conventional restorative or ART approaches were included. Studies in which evaluators were calibrated and independent, Survival result more than 1 year were included. Interventions were adhesive restorative materials, such as GICs with different viscosities, placed with the ’true’ Atraumatic Restorative Treatment (ART) approach, including Interim therapeutic restoration (ITR) with hand instruments, compared with different restorative materials, such as amalgam, placed with conventional cavity prepar ation methods. Studies on modified ART approaches, Survival results Selection of Studies All records identified by the searches printed off and checked on the basis of title first, then by abstract or keywords or both. Records that obviously irrelevant were discarded and the full text of all remaining records were obtained. The full reports obtained from all the electronic and other methods of searching assessed independently by two review authors to establish whether the studies meet the inclusion criteria or not, using an inclusion criteria form, which previously prepared and pilot tested. Where resolution was not possible, a third review author consulted. If more than one publication of a trial was identified, all publications were reviewed and the paper with the first publication date included as a primary version. All studies meeting the inclusion criteria then underwent data extraction and a quality assessment. Types of Outcome Measures Primary Outcome Measure Pain relief, i.e. freedom from symptoms of pain and sensitivity as reported and experienced by the patient. Patient discomfort during the procedure measured by physiological measurement or behavioral observation. Patient’s anxiety and stress after treatment. Durability of restoration survival time of restoration (in months) from the time of placement. Secondary outcome measures Defects of restorative materials such as wear, fracture and staining (color changes) of restoration. Restoration failure, e.g. replaced restorations. Marginal integrity of restoration. Secondary caries. Results Pain, Anxiety and Discomfort: Five studies were reported on pain out of which three studies suggested that ART was found to be less painful.[4,5,6] In a study conducted by Rahimtoola S et al[7] pain was reported when ART technique was used but was significantly less than the conventional restorative technique. While in one study there was no significant difference in the pain levels of children treated using conventional restorative treatment, atraumatic restorative treatment or ultraconservative treatment but it was observed that when conventional restorative treatment was used, more children neededlocal anesthesia.[8] One study showed that the levels of dental anxiety were less in patients treated with ART as compared to conventional restorative treatment.[9]The studies from Topaloglu et al[10] and de Menezes Abreu et al[11] reported no difference in the levels of dental anxiety. ART technique has a potential to cause less discomfort to the patient and to less invasive to the dental tissue than conventional approach. The patient’s acceptance of ART was verified by Mickenautsch et al[12] who observed that both children and adults receiving ART restorations responded positively to the treatment. Study conducted by Schriks MC[13] and Van Amerongen WE[14] stated that children treated according to the ART approach using hand instruments alone experience less discomfort than those treated using rotary instrument. Similar findings were reported by ECM Lo CJ Holmgren also.[5] A summary of these studies outcomes is presented in Table1. TABLE 1: Overview of studies having assessed dental pain, anxiety and discomfort between the ART and the traditional treatment approach Comparison Age Operator background Variable measured Conclusion ART vs rotary Instruments[7] 6–16 years old Dentists Pain: -Questions: Did you feel any pain during treatment? ART caused less pain ART vs rotary Instruments[8] 4–7 years old Pedodontist specialist Pain: -Wong–Baker FACES Pain Rating Scale ART caused less pain ART vs rotary instruments vs ultraconservative treatment[4] 6–7 years old Pedodontist specialist Pain: -Wong–Baker FACES Pain Rating Scale -No difference in levels of pain among treatments -Local anaesthesia was more frequent given in the rotary instrument group ART vs rotary instruments ART vs ART with Carisolv [10] 6–7 years old Pedodontist specialist Anxiety: -Venham Picture Test No difference in levels of anxiety between treatments ART vs rotary Instruments[9] Children and adults Dentists and dental therapists Anxiety: -Childrens fear survey schedule -Corahs dental anxiety scale Both children and adults treated with the ART were less dental-anxious ART vs rotary instruments vs ultraconservative treatment[11] 6–7 years old Pedodontist specialist Anxiety: -Facial Image Scale No difference in levels of anxiety among treatments ART vs rotary Instruments[13] 6-year-old children Dental students and dentists Discomfort: -Heart rate and modified Venham index (observations) ART caused less discomfort Durability of Restoration Various studies showed that survival rates were lower with increasing period of time.[15,16] Frencken JE[15] assessed the survival of ART restoration after first, second and third year evaluation interval and found that the survival rate of one surface ART restoration were higher in first year compared to second and third year. Lo ECM[16] Suggested that cumulative survival rates of the large restoration were lower, being 77% and 46% after 3 and 6 year respectively. There were no statistically significant differences in cumulative survival percentages of the evaluated ART restorations between single and multiple-surface restorations at 1-year (p=0.137) and 2-year (p=0.377) evaluations. But at the 10-year evaluation, the survival rate for single-surface restorations (65.2%) was 2.1 times higher than that for the multiple surface restorations (30.6%). This difference was statistically significant (p=0.009).[17] Secondary Outcome Measures: Defects of restorative materials wear and fracture of restoration: Studies conducted by Lo ECM[16] and Frencken JE[18] showed that most of the restoration were in good condition and had only minor defects and wear which did not warrant further treatment. Secondary caries Increment of secondary caries was found to be maximum in a study conducted by Zanata RL[17] while other studies showed no statically significant difference.[18,19] Operator effect. Frencken JE [18] et al observed an operator effect for single surface ART restorations. It was observed in one study that experienced operators place better ART restoration than inexperienced operators.[15] Marginal Integrity of Restoration: In a study the restorations that were evaluated with the USPHS criteria at the 5-year examination, unacceptable marginal integrity, either a crevice extending to the enamel–dentine junction or the restoration being fractured was found in 9% of the small and 21% of the large restorations.[18] While in another study, 63.6% of the ART restorations were assessed as ‘good’, 15% as having a ‘slight marginal defect’ at 3years.[19] Restoration Failure Failure occurred in 24% of the small restorations and 41% of the large restorations. The large restorations had a higher relative risk of failure, 5.87, compared with the small restorations.[16] Failures were related to unacceptable marginal defects and total loss of restoration. Frencken JE [18] reported failure of total 28 ART restorations placed in 25 students during the 3 year period. While same author in another study reported 106 ART restoration failures from total of 487 ART single surface posterior restorations.[15] Discussion: The ART approach seems to be an economic and effective method for improving the oral health not only of people in developing but also of those in industrialized countries (Frencken and Holmgren 2004).[1] It may be considered as a safe and conservative alternative for conventional restorative dental treatment, particularly for Class I (occlusal) dental cavities. Pr imary outcome measures: Pain, Discomfort and Anxiety: The originators of the ART approach noticed that the technique had a potential to cause less discomfort to the patient and to be less invasive to the dental tissues than the conventional approach. The patients acceptance of ART was verified by Mickenautsch and Rudolph[12], who observed that both children and adults receiving ART restorations responded very positively to the treatment. Dentists also seemed to approve the â€Å"new† approach. Among the main reasons given were those related to the patients comfort: the reduced use of local anesthetic and absence of the noisy drill and suction.[20] Some suggested that ART as found to be less painful and cause less dental anxiety. The reasons could be contributed to the operator’s level of specialization and /or skills in handling anxious children. The studies from Topaloglu et al [10] and de Menezes Abreu et al [4,11] in which no difference in levels of dental anxiety and dental pain were observed, were performed by pediatric dentists. In the studies that favored ART [7,8,13] all operators, but the one from de Menezes Abreu et al, [8] were non-pediatric dentists (general practitioners, dental therapists or dental students). However, the latter study had included children younger than 6 years, and all those given the conventional treatment received local anesthesia and the restorations were performed under rubber dam isolation. It is not unrealistic to argue that age and the use of the needle and that of rubber dam might have influenced childrens perception of pain. In light of all these aspects, it can be hypothesized th at the behavior management provided by a pediatric dentist may overcome much of the discomfort that a child can feel independent of the restorative treatment approach. Durability of Restoration: The survival percentages of single surface non occlusal posterior ART restoration were significantly higher than for comparable amalgam restoration 4.4, 5.3 and 6.3 years. Although it is known that non occlusal glass ionomer restoration survive long but significant lower survival results for non occlusal amalgam than for comparable ART glass ionomer restorations were observed.[15] The cumulative survival rate of ART single surface restoration remained high throughout the study 92.7% (SE 3.0%) over 2 years and65.2%(SE 7.3%) up to 10 years. These rates are in the line with the results of other investigations, which reported survival rates ranging from 66% to 76% at 6 year for single surface restorations. The cumulative success of 65.2% observed in this study could be considered even better due to the longer period of clinical service. The survival rates of multiple surface restorations (class II) decreased significantly from 2 to 10 years. After 2 years, the survival rates between single and multiple surface restorations were similar. These results are consistent with those of Cefaly and Farag which observed similar survival rates for class 1 and class II restoration after 1 and 5 years, respectively. However, a statistical difference was apparent over the 10 year evaluation period (65.2Ãâ€"30.6% success rates for single and multiple surface restorations, respe ctively).[17] Secondary outcome measures: Defects of restorative material such as Wear, Fracture and Staining of Restoration: The annual wear rate of the high strength glass–ionomer material used in their study was rather stable at around 20-25 m after the first year and this did not increase much with time or size of the restoration. This rate is very satisfactory and may help to alleviate some of the concerns of earlier reviews on ART. The use of an adhesive material in ART restorations also makes repair of restorations with gross defects and wear possible and total replacement may not be necessary.[15] Reasons for minor defects and wear can be explained by the fact that firm finger pressure was applied over the restorative material to ensure good penetration of glass ionomer into the pits and fissures, as recently demonstrated.[18] Secondary caries: It has been shown that caries left in occlusal enamel lesions had either not progressed at all or only progressed slightly under clinically ‘intact’ as well as ‘sometimes intact’ sealants after 3 years. In contrast, caries had progressed under sealants that were ‘never intact’.[18] No ART restoration failed because of carious lesion development only. Restorations failed because of a combination of dentine carious lesions and mechanical defects.[17] This pattern of failure was also observed by Frencken et al[15] but contrasts with the study of Prakki et al[21] which observed no caries even in those teeth whose ART restorations were missing. Operator effect: An operator effect has been cited in a number of ART studies.[18,22,23] Although all operators (dentists and dental therapists) in the studies referred to above had followed a training course on ART, the operator effect seems to indicate that in order to perform quality ART restorations, the operating dental personnel requires skill, diligence and comprehension. An ART training course of a couple of days may be too short for some qualified dentists and dental therapists.[15] The operators’ greater experience in applying ART and the use of a high-viscous glass ionomer in the study may explain the higher results.[18] Failure of Restoration: The finding that failures of ART restorations placed in the same child were correlated suggests that some factors related to the individual subjects such as diet, occlusion, and caries risk may influence restoration survival.[16] The predominant reasons for ART restorations to fail were unacceptable defects at the margin and re restoration.[15] Almost half of the failures were related both to the physical characteristics of the glass ionomer used and to the operators’ handling of the material. Few failures were due to excessive wear. The other half of the failures were considered to be operator related. The exact reasons for the unacceptable marginal defects were unknown. However, it can be speculated that improper mixing of glass ionomer, providing a mixture that was either too dry or too wet, was one of the reasons. Another reason could be the difficulty in inserting the material into the depths of deep and small preparations. Subsurface voids produced during insertion may have resulted in later fracture of the surface layer under pressure.[18] Compared to conventional treatment approaches, ART is still very young. Despite this, much progress has been made in researching various aspects of the ART approach. More experience in the actual technique of cleaning carious cavities with hand instruments has been gained and newer, physically stronger glass ionomers have been marketed as a result of its existence. These developments have most probably led to the higher survival results of ART restorations in permanent teeth in the more recent compared to the early studies. Conclusion: ART technique has proved to be less painful and causes less discomfort to the patients with high survival rate in both in primary and permanent teeth. This technique has the potential to make oral health care more available to a larger part of the world’s population than before. The greater part of the world’s population has no access to restorative dental care. ART should be taken seriously by the dental profession and educational courses should be organized before the approach is used in the clinic.

Socialization Essay -- Sociology Society Behavior Essays Papers

Socialization Socialization is the process by which culture is learned; also called enculturation. During socialization individuals internalize a culture's social controls, along with values and norms about right and wrong. Socialization is a complex process that involves many individuals, groups, and social institutions. AGENTS OF SOCIALIZATION There are four main agents of socialization family, school, peer groups (friends and collogues), and mass media. The family is the single most important agent of socialization because the family is the first and most continuous social world for infants and children. The family provides the child's initial social identity in terms of race, religion, social class, and gender. In time, all these elements become part of the child's self-concept. The family is responsible for the child's social foundation and role in society and plays a vital role of teaching children skills, values and beliefs. Research indicates that children brought up in a loving environment tend to be happy and well-adjusted The school has the responsibility for instilling in children the information, skills, and values that society deems important for social life. School teaches children the basics of the three R's, as well as honesty, dependability, interpersonal interaction, discipline, and punctuality. Schools socialize children into gender roles and gender differences continue through college. Schools introduce a formal system of evaluation by using grades and report cards whereas the family provides a more intimate relationship with the child. The peer group is composed of status equals, which are children of the same age, similar interests, and general social status. Social position in the f... ... expected to complete all the work and even more than your job description indicates so that you can prepare yourself for future advancement in the field. Your final grade in school takes into consideration all the work, test grades, as well as your positive attitude toward the professor, fellow students and the work. The use of the grading system teaches students that personal achievement and competition are important. The annual review on the job reflects all the positive things you learned during your college years from punctuality to dedication to the completion of assigned tasks, rapport with co-workers, honesty, and also respect for employer and co-worker. Just as your final reward for your college experience is good grades, the final reward for your annual performance is an excellent report on your year's work and a salary increase/and or promotion. Socialization Essay -- Sociology Society Behavior Essays Papers Socialization Socialization is the process by which culture is learned; also called enculturation. During socialization individuals internalize a culture's social controls, along with values and norms about right and wrong. Socialization is a complex process that involves many individuals, groups, and social institutions. AGENTS OF SOCIALIZATION There are four main agents of socialization family, school, peer groups (friends and collogues), and mass media. The family is the single most important agent of socialization because the family is the first and most continuous social world for infants and children. The family provides the child's initial social identity in terms of race, religion, social class, and gender. In time, all these elements become part of the child's self-concept. The family is responsible for the child's social foundation and role in society and plays a vital role of teaching children skills, values and beliefs. Research indicates that children brought up in a loving environment tend to be happy and well-adjusted The school has the responsibility for instilling in children the information, skills, and values that society deems important for social life. School teaches children the basics of the three R's, as well as honesty, dependability, interpersonal interaction, discipline, and punctuality. Schools socialize children into gender roles and gender differences continue through college. Schools introduce a formal system of evaluation by using grades and report cards whereas the family provides a more intimate relationship with the child. The peer group is composed of status equals, which are children of the same age, similar interests, and general social status. Social position in the f... ... expected to complete all the work and even more than your job description indicates so that you can prepare yourself for future advancement in the field. Your final grade in school takes into consideration all the work, test grades, as well as your positive attitude toward the professor, fellow students and the work. The use of the grading system teaches students that personal achievement and competition are important. The annual review on the job reflects all the positive things you learned during your college years from punctuality to dedication to the completion of assigned tasks, rapport with co-workers, honesty, and also respect for employer and co-worker. Just as your final reward for your college experience is good grades, the final reward for your annual performance is an excellent report on your year's work and a salary increase/and or promotion.

Acquiring Personal Freedom Essay -- Narrative Memoir Essays

Acquiring Personal Freedom On a cold January day, a performance broke all barriers. The crowd erupted as the curtains opened to reveal the silhouette of a rock legend. The music initiated moves that seemed to defy explanation. Long, sensuous legs captured the audience as they moved with lightning speed while voluptuous red lips seemed to pour lyrics like a fountain. Some people were in shock about who was performing, while some mystified by how the artist seemed to control the stage. The singer was creating questions with every gyration during the unstoppable performance. No one, including me, could believe what was happening on stage. How someone’s attitude can change over a small amount of time. When I entered high school, I was very self-conscience about what I did and how I acted. This mental approach really dampened my creative side and it kept me from doing a lot of things I find fun now. By the middle of my sophomore year, I was ready to do something that would stir things up a bit and get the big wheels turning. Winterfest was only a week away and I, along with the rest of the school, was ready for a little break from the monotonous everyday routine. There was a competition scheduled for Thursday which was between different â€Å"air guitar† performances. I had been to a concert earlier in the year and saw Tina Turner perform one of her most famous songs, â€Å"Proud Mary.† To my mind, the idea of dressing like Tina Turner and performing on stage was absurd. I thought about it for a few days and decided that this could be something that might break the self-conscience chains holding my spirit down. I knew it would be hard and some people might think it a little overboard, but there was only one way to fin... ...ual attire rather than the leather mini-skirt. A glint in my eye seemed to light the way out of the dim-lit bathroom. Today, when confronted with a challenge, I just look back at this experience to help me through it. After I performed in front of the school in a skirt and high heels, some things seem minuscule. By overpowering my self-conscience feelings, I am now able to do things without caring how people might view me. I have noticed that my newly gained social confidence helps me through everything from interviews to relationships. On a cold January day, a performance broke all barriers blocking me from my goals. I did something I had never done and discovered that what others thought would not control my life any longer. On that day, my spirit escaped the bounding chains and set my big wheels in motion with no sign of stopping anytime soon.

George Orwell’s Animal Farm :: Animal Farm Essays

What is George Orwell’s message in Animal Farm, and how does he use two of the animal characters in the novel to present his political views? In this book George Orwell has tried to put a political view into the story. This political view is that Communist ideas can not work without using excessive power, also that political systems can easily be corrupted by power-hungry people. George Orwell uses animals in this clever allegory to represent humans. Two main characters of ‘Animal Farm’ are Napoleon and Boxer. Napoleon acts like a dictator and leads the farm and animals. He has power over the animals so they have no freedom, so much so, that they can’t rebel against him if they wanted to. Boxer an idealistic follower for Napoleon; he will sacrifice anything for the farm and the other animals. Boxer believes everything that he is told by Napoleon and cannot see that Napoleon is a corrupt leader. As soon as Old Major had died Napoleon took his place as the leader of the Animals, and so he controlled them after the rebellion against humans. At first he was a fair leader and treated the animals kindly, or so they thought. â€Å"The pigs did not actually work, but directed and supervised the others.† This shows that the pigs were lazy and demanding from the beginning when they started to run the farm, and it wasn’t that they grew power-hungry, they already were. The animals started to realise that the pigs were not doing any work. The majority thought there must be an excellent reason for them not doing any work. â€Å"We pigs are the brain-workers. The whole management and organization of the farm depends on us† After hearing this, the animals understood that they were there to do the hard work, but they thought that was because they couldn’t run the farm as well as the pigs. They did not mind lying to the animals and not doing any work while the other animals are. Napoleon knew that there was a chance that the animals might rebel against him so when 9 puppies were born on the farm he took them to train as his bodyguards. â€Å"As soon as they were weaned, Napoleon took them away from their mothers†¦Ã¢â‚¬  After the animals knew what he was doing, even if they did disagree with what he was doing could not do anything about it even if the wanted to either because they were not strong enough or that they were to scared. So this meant that Napoleon could do whatever he wanted to, just like a dictator. The only animal threatening Napoleon’s place in power was Snowball, so

Fair Teacher Pay Association :: Argumentative Persuasive Education Papers

Fair Teacher Pay Association Factà ³There is a shortage of qualified graduates of professional teacher preparation programs entering the teaching profession in the United States. Factà ³More than 80% of the employing jurisdictions in the United States have been forced to hire unlicensed, untrained, unprepared teachers because there are not enough licensed graduates of teacher preparation programs to fill the need. Factà ³The overwhelming response from college students to the question of why they wonà ­t enter the teaching profession is that "teacher pay is too low". Factà ³The average national salary for a beginning teacher for the 1998-1999 academic year was $25,735 , far less than the salary for other college graduates. Would you want to be a teacher?? Dear Mr. & Mrs. Doe: Do you care about the quality of your childrenà ­s education? Weà ­re sure you do, just like most hard working Americans. Think about it. Our childrenà ­s education is their future, and their future is our nationà ­s future. This future is determined by our childrenà ­s teachers. A lack of teachers and, more importantly, a lack of GOOD teachers is a big problem in our schools today. We, the members of the Fair Teacher Pay Association (FTPA), believe this injustice must be brought to the attention of all. In addition to informing the public, we want to do things to change the current system. This letter and informaional packet will briefly inform you of the facts you need to know on this subject. We often hear people say things such as: Teachers work form 9 to 3, less than bankers. Teachers work 9 months, and then get the summers off. Teachers themselves say: Teaching is the only job where you work three times per day. First you teach a full day, then you work at school in the afternoon, and then you take work home to do at night. The average teacher works a minimum of 8 hours and 37 minutes each day. 8:37 multiplied by an average school year of 180 days is 1551 hours a year. That is the minimum required for their daily tasks. Teachers also have supplementary tasks that they must complete on an irregular basis. These tasks such as pre and post school year activities, meetings, and continuing education add up to an average minimum of 318 hours per year. This adds up to a grand total of 1869 hours per year! Check out these statistics: - A teacher works a minimum of 1,869 hours per year to perform his/her

Ancient Cassiterides

Ancient geography The Cassiterides, meaning Tin Islands (from the Greek word for tin: /Kassiteros), are an ancient geographical name of islands that were regarded as situated somewhere near the west coasts of Europe. The traditional assumption, ignoring Strabo, is that Cassiterides refer to Great Britain, based on the significant tin deposits in Cornwall. Herodotus (430 BC) had only dimly heard of the Cassiterides, â€Å"from which we are said to have our tin,† but did not discount the islands as legendary. 3] Later writers — Posidonius, Diodorus Siculus,[4] Strabo[5] and others — call them smallish islands off (â€Å"some way off,† Strabo says) the northwest coast of the Iberian Peninsula, which contained tin mines or, according to Strabo, tin and lead mines. A passage in Diodorus derives the name rather from their nearness to the tin districts of Northwest Iberia. Ptolemy and Dionysios Periegetes mentioned them — the former as ten small islands i n Northwest Iberia far off the coast and arranged symbolically as a ring, and the latter in connection with the mythical Hesperides. Probably written in the first century BC, the verse Circumnavigation of the World, whose anonymous author is called the â€Å"Pseudo-Scymnus,† places two tin islands on the upper part of the Adriatic Sea and mentioned the marketplace Osor on the island of Cres, where extraordinary high-quality tin could be bought. [6][7] Pliny the Elder, on the other hand, represents the Cassiterides as fronting Celtiberia. At a time when geographical knowledge of the West was still scanty, and when the secrets of the tin-trade were still successfully guarded by the seamen of Gades and others who dealt in the metal, the Greeks knew only that tin came to them by sea from the far West, and the idea of tin-producing islands easily arose. Later, when the West was better explored, it was found that tin actually came from two regions: Northwest Iberia and Cornwall. Diodorus reports: â€Å"For there are many mines of tin in the country above Lusitania and on the islets which lie off Iberia out in the ocean and are called because of that fact the Cassiterides. † According to Diodorus tin also came from Britannia to Gaul and thence was brought overland to Massilia and Narbo. [8] Neither of these could be called small islands or described as off the Northwest coast of Iberia, and so the Greek and Roman geographers did not identify either as the Cassiterides. Instead, they became a third, ill-understood source of tin, conceived of as distinct from Iberia or Britain. Od najdawniejszych czasow Brytania znana byla ze swych zloz metali. Fenicjanie i Kartaginczycy sprowadzali stad glownie cyne (plumbum album). Jej glowne zloza wystepowaly w starozytnosci, podobnie jak dzis, na wybrzezu Kornwalii i wyspach stanowiacych jej przedluzenie, slynnych „Wyspach Cynowych† (insulae Cassiterides). W srodkowych rejonach wyspy obficie wystepuje zelazo, ktorego zloza powierzchniowe eksploatowali Brytowie, a z glebokich kopalni wydobywali je Rzymianie. Rzymianie tez rozpoczeli eksploatacje bogatych pokladow miedzi, ktore wystepuja glownie na terenie dzis. Kornwalii, Cardigenshire i Anglesey w poblizu Llandundo. Gory Walii byly natomiast terenami zlotodajnymi kopano tam tez srebro. Tacyt mowi po prostu: „Brytania dostarcza zlota, srebra i innych metali, ktore sa nagroda za zwyciestwo. †Ã‚   Wyobraznie rzymskich najezdzcow rozbudzaly tez inne legendarne bogactwa wyspy, o ktorych opowiada niezastapiony Tacyt: „Ocean rodzi perly lecz nieco sine i blade. †

Queuing Theory

Waiting Line Models ? ? ? ? ? ? ? ? The Structure of a Waiting Line System Queuing Systems Queuing System Input Characteristics Queuing System Operating Characteristics Analytical Formulas Single-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times Multiple-Channel Waiting Line Model with Poisson Arrivals and Exponential Service Times Economic Analysis of Waiting Lines Slide 1 Structure of a Waiting Line System ? ? Queuing theory is the study of waiting lines. Four characteristics of a queuing system are: †¢the manner in which customers arrive †¢the time required for service the priority determining the order of service †¢the number and configuration of servers in the system. Slide 2 Structure of a Waiting Line System ? ? Distribution of Arrivals †¢Generally, the arrival of customers into the system is a random event. †¢Frequently the arrival pattern is modeled as a Poisson process. Distribution of Service Times †¢Service time i s also usually a random variable. †¢A distribution commonly used to describe service time is the exponential distribution. Slide 3 Structure of a Waiting Line System ? Queue Discipline †¢Most common queue discipline is first come, first served (FCFS). An elevator is an example of last come, first served (LCFS) queue discipline. †¢Other disciplines assign priorities to the waiting units and then serve the unit with the highest priority first. Slide 4 Structure of a Waiting Line System ? Single Service Channel Customer arrives ? Waiting line Multiple Service Channels System S1 Customer leaves System S1 Customer arrives Waiting line S2 Customer leaves S3 Slide 5 Examples of Internal Service Systems That Are Queueing Systems Type of System Customers Server(s) Secretarial services Employees Secretary Copying services Employees Copy machine Computer programming servicesEmployees Programmer Mainframe computer Employees Computer First-aid center Employees Nurse Faxing service s Employees Fax machine Materials-handling system Loads Materials-handling unit Maintenance system Machines Repair crew Inspection station Items Inspector Production system Jobs Machine Semiautomatic machines Machines Operator Tool crib Machine Clerk Slide 6 Examples of Transportation Service Systems That Are Queueing Systems Type of System Customers Server(s) Highway tollbooth Cars Cashier Truck loading dock Trucks Loading crew Port unloading area Ships Unloading crew Airplanes waiting to take off Airplanes RunwayAirplanes waiting to land Airplanes Runway Airline service People Airplane Taxicab service People Taxicab Elevator service People Elevator Fire department Fires Fire truck Parking lot Cars Parking space Ambulance service People Ambulance Slide 7 Queuing Systems ? ? ? ? A three part code of the form A/B/k is used to describe various queuing systems. A identifies the arrival distribution, B the service (departure) distribution and k the number of channels for the system. Sym bols used for the arrival and service processes are: M – Markov distributions (Poisson/exponential), D – Deterministic (constant) and G – General istribution (with a known mean and variance). For example, M/M/k refers to a system in which arrivals occur according to a Poisson distribution, service times follow an exponential distribution and there are k servers working at identical service rates. Slide 8 Queuing System Input Characteristics = 1/? =  µ= 1/ µ = = the average arrival rate the average time between arrivals the average service rate for each server the average service time the standard deviation of the service time Slide 9 Queuing System Operating Characteristics P0 = Pn = Pw = Lq = probability the service facility is idle robability of n units in the system probability an arriving unit must wait for service average number of units in the queue awaiting service L = average number of units in the system Wq = average time a unit spends in the queu e awaiting service W = average time a unit spends in the system Slide 10 Analytical Formulas ? ? For nearly all queuing systems, there is a relationship between the average time a unit spends in the system or queue and the average number of units in the system or queue. These relationships, known as Little's flow equations are: L = ? W and Lq = ? Wq Slide 11 Analytical Formulas ? ?When the queue discipline is FCFS, analytical formulas have been derived for several different queuing models including the following: †¢M/M/1 †¢M/M/k †¢M/G/1 †¢M/G/k with blocked customers cleared †¢M/M/1 with a finite calling population Analytical formulas are not available for all possible queuing systems. In this event, insights may be gained through a simulation of the system. Slide 12 M/M/1 Queuing System ? ? ? ? ? ? Single channel Poisson arrival-rate distribution Exponential service-time distribution Unlimited maximum queue length Infinite calling population Examples: †¢Single-window theatre ticket sales booth Single-scanner airport security station Slide 13 Notation for Single-Server Queueing Models ? ? = Mean arrival rate for customers = Expected number of arrivals per unit time 1/? = expected interarrival time ? m = Mean service rate (for a continuously busy server) = Expected number of service completions per unit time 1/m = expected service time ? r = the utilization factor = the average fraction of time that a server is busy serving customers = /? m Slide 14 ? Assumptions 1. Interarrival times have an exponential distribution with a mean of 1/?. 2. Service times have an exponential distribution with a ean of 1/m. 3. The queueing system has one server. †¢ The expected number of customers in the system is L = r? /? (1 –? r) = /? (m? – ? )? †¢ The expected waiting time in the system is W = (1 / ? )L = 1 / (m – ? ) †¢ The expected waiting time in the queue is Wq = W – 1/m = ? / [m(m – ? )] â⠂¬ ¢ The expected number of customers in the queue is Lq = ? Wq = ? 2 / [m(m – ? )] = r2 / (1 – r) Slide 15 ? The probability of having exactly n customers in the system is Pn = (1 – r)rn Thus, P0 = 1 – r P1 = (1 – r)r P2 = (1 – r)r2 : : ? The probability that the waiting time in the system exceeds t is P(W ; t) = e–m(1–r)t for t ? ? The probability that the waiting time in the queue exceeds t is P(Wq ; t) = re–m(1–r)t for t ? 0 Slide 16 Problem: ? Consider the situation where the mean arrival rate is one customer every 4 minutes and the mean service time is 2. 5 minutes. Calculate the following †¢Average no. of customer in the system †¢Average queue length †¢Average time a customer spends in the system †¢Average time a customer waits before being served. Slide 17 Problem: ? ? ? Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between one arrival an d the next. The length of a phone call is ssumed to be exponentially distributed with mean 3 minutes. What is the probability that a person arriving at the booth will have to wait? The telephone department will install a second booth when convinced that an arrival would expect to have to wait at least three minutes for the phone. By how much must the flow of arrivals be increased in order to justify a second booth? Slide 18 Example: SJJT, Inc. (A) ? M/M/1 Queuing System Joe Ferris is a stock trader on the floor of the New York Stock Exchange for the firm of Smith, Jones, Johnson, and Thomas, Inc. Stock transactions arrive at a mean rate of 20 per hour.Each order received by Joe requires an average of two minutes to process. Orders arrive at a mean rate of 20 per hour or one order every 3 minutes. Therefore, in a 15 minute interval the average number of orders arriving will be ? = 15/3 = 5. Slide 19 Example: SJJT, Inc. (A) ? Arrival Rate Distribution Question What is the probability that no orders are received within a 15-minute period? Answer P (x = 0) = (50e -5)/0! = e -5 = .0067 Slide 20 Example: SJJT, Inc. (A) ? Arrival Rate Distribution Question What is the probability that exactly 3 orders are received within a 15-minute period? Answer P (x = 3) = (53e -5)/3! 125(. 0067)/6 = . 1396 Slide 21 Example: SJJT, Inc. (A) ? Arrival Rate Distribution Question What is the probability that more than 6 orders arrive within a 15-minute period? Answer P (x ; 6) = 1 – P (x = 0) – P (x = 1) – P (x = 2) – P (x = 3) – P (x = 4) – P (x = 5) – P (x = 6) = 1 – . 762 = . 238 Slide 22 Example: SJJT, Inc. (A) ? Service Rate Distribution Question What is the mean service rate per hour? Answer Since Joe Ferris can process an order in an average time of 2 minutes (= 2/60 hr. ), then the mean service rate,  µ, is  µ = 1/(mean service time), or 60/2. m = 30/hr. Slide 23 Example: SJJT, Inc. (A) ?Service Time Distribution Ques tion What percentage of the orders will take less than one minute to process? Answer Since the units are expressed in hours, P (T ; 1 minute) = P (T ; 1/60 hour). Using the exponential distribution, P (T ; t ) = 1 – e- µt. Hence, P (T ; 1/60) = 1 – e-30(1/60) = 1 – . 6065 = . 3935 = 39. 35% Slide 24 Example: SJJT, Inc. (A) ? Service Time Distribution Question What percentage of the orders will be processed in exactly 3 minutes? Answer Since the exponential distribution is a continuous distribution, the probability a service time exactly equals any specific value is 0 . Slide 25Example: SJJT, Inc. (A) ? Service Time Distribution Question What percentage of the orders will require more than 3 minutes to process? Answer The percentage of orders requiring more than 3 minutes to process is: P (T ; 3/60) = e-30(3/60) = e -1. 5 = . 2231 = 22. 31% Slide 26 Example: SJJT, Inc. (A) ? Average Time in the System Question What is the average time an order must wait from th e time Joe receives the order until it is finished being processed (i. e. its turnaround time)? Answer This is an M/M/1 queue with ? = 20 per hour and m = 30 per hour. The average time an order waits in the system is: W = 1/( µ – ? ) 1/(30 – 20) = 1/10 hour or 6 minutes Slide 27 Example: SJJT, Inc. (A) ? Average Length of Queue Question What is the average number of orders Joe has waiting to be processed? Answer Average number of orders waiting in the queue is: Lq = ? 2/[ µ( µ – ? )] = (20)2/[(30)(30-20)] = 400/300 = 4/3 Slide 28 Example: SJJT, Inc. (A) ? Utilization Factor Question What percentage of the time is Joe processing orders? Answer The percentage of time Joe is processing orders is equivalent to the utilization factor, ? /m. Thus, the percentage of time he is processing orders is: ?/m = 20/30 = 2/3 or 66. 67% Slide 29 Example: SJJT, Inc. A) Solution ? 1 2 3 4 5 6 7 8 9 A B C D E F Poisson Arrival Rate Exponential Service Rate Operating Character istics Probability of no orders in system Average number of orders waiting Average number of orders in system Average time an order waits Average time an order is in system Probability an order must wait G ? m H 20 30 Po Lg L Wq W Pw 0. 333 1. 333 2. 000 0. 067 0. 100 0. 667 Slide 30 M/M/k Queuing System ? ? ? ? ? ? Multiple channels (with one central waiting line) Poisson arrival-rate distribution Exponential service-time distribution Unlimited maximum queue length Infinite calling population Examples: Four-teller transaction counter in bank †¢Two-clerk returns counter in retail store Slide 31 1 ? P? n ? m ? P0 , for (n ? k) ? n! ? ? n ? ? m ? P0 , for (n ? k) ? ? ? 1 n k ? 1 1 km ? ? ? ? n! ? m ? ? k! ? m ? km ? ? ? ? ? 1 ? k! k n ? k P? 0 P w ? n ? k ? 1 ? n ? 0 ? n 1 ? ? P(n ? k ) ? ?m? ? k! ? ? k km P0 , km ? ? k ?m ? ? m ? ? ? ? ? ? L? P0 ? 2 m (k ? 1)! (km ? ? ) W? L ? , Lq ? ,r ? km Lq ? 1 ? L? , Wq ? W ? ? m m ? Slide 32 General Operating Characteristics Little' s F low Equations : L (or W ? ) ? Lq (or Wq ? ) ? L ? ?W L q ? ?Wq W ? Wq ? 1 m Slide 33 Problem: ? ? ? ? ? ? ? ?A Tax consulting firm has four service stations (counters) in its office to receive people who have problems and complaints about their income, wealth and sales taxes. Arrivals average 80 persons in an 8 hour service day. Each tax advisor spends irregular amount of time servicing the arrivals which have been found to have an exponential distribution. The average service time is 20 minutes. Calculate the average no. of customers in the system, average no. of customers waiting to be serviced, average time a customer spend in the system, average waiting time for a customer in queue. Calculate how many hours each week does a tax advisor spend erforming his job? What is the probability that a customer has to wait before he gets service? What is the expected no. of idle tax advisors at any specified time? Slide 34 Example: SJJT, Inc. (B) ? M/M/2 Queuing System Smith, Jones, Joh nson, and Thomas, Inc. has begun a major advertising campaign which it believes will increase its business 50%. To handle the increased volume, the company has hired an additional floor trader, Fred Hanson, who works at the same speed as Joe Ferris. Note that the new arrival rate of orders, ? , is 50% higher than that of problem (A). Thus, ? = 1. 5(20) = 30 per hour. Slide 35Example: SJJT, Inc. (B) ? Sufficient Service Rate Question Why will Joe Ferris alone not be able to handle the increase in orders? Answer Since Joe Ferris processes orders at a mean rate of  µ = 30 per hour, then ? =  µ = 30 and the utilization factor is 1. This implies the queue of orders will grow infinitely large. Hence, Joe alone cannot handle this increase in demand. Slide 36 Example: SJJT, Inc. (B) ? Probability of n Units in System Question What is the probability that neither Joe nor Fred will be working on an order at any point in time? Slide 37 Example: SJJT, Inc. (B) ? Probability of n Units in Sy stem (continued)Answer Given that ? = 30,  µ = 30, k = 2 and (? / µ) = 1, the probability that neither Joe nor Fred will be working is: 1 P0 ? k ? 1 ( ? / m )n (? / m ) k km ? ( ) ? n! k! km ? ? n? 0 = 1/[(1 + (1/1! )(30/30)1] + [(1/2! )(1)2][2(30)/(2(30)-30)] = 1/(1 + 1 + 1) = 1/3 = .333 Slide 38 Example: SJJT, Inc. (B) ? Average Time in System Question What is the average turnaround time for an order with both Joe and Fred working? Slide 39 Example: SJJT, Inc. (B) ? Average Time in System (continued) Answer The average turnaround time is the average waiting time in the system, W. Lq = ? µ(? / µ)k (k-1)! (k µ – ? )2 P0 = (30)(30)(30/30)2 (1! ((2)(30)-30))2 (1/3) = 1/3 L = Lq + (? / µ) = 1/3 + (30/30) = 4/3 W = L/ (4/3)/30 = 4/90 hr. = 2. 67 min. Slide 40 Example: SJJT, Inc. (B) ? Average Length of Queue Question What is the average number of orders waiting to be filled with both Joe and Fred working? Answer The average number of orders waiting to be filled is Lq. This was calculated earlier as 1/3 . Slide 41 Example: SJJT, Inc. (B) ? Formula Spreadsheet 1 2 3 4 5 6 7 8 9 10 A B C D E F Number of Channels Mean Arrival Rate (Poisson) Mean Service Rate (Exponential ) Operating Characteristics Probability of no orders in system Average number of orders waitingAverage number of orders in system Average time (hrs) an order waits Average time (hrs) an order is in system Probability an order must wait G k ? m H 2 30 30 Po =Po(H1,H2,H3) Lg ## L =H6+H2/H3 Wq =H6/H2 W =H8+1/H3 Pw =H2/H3 Slide 42 Example: SJJT, Inc. (B) ? Spreadsheet Solution 1 2 3 4 5 6 7 8 9 10 A B C D E F Number of Channels Mean Arrival Rate (Poisson) Mean Service Rate (Exponential ) Operating Characteristics Probability of no orders in system Average number of orders waiting Average number of orders in system Average time (hrs) an order waits Average time (hrs) an order is in system Probability an order must waitG k ? m H 2 30 30 Po Lg L Wq W Pw 0. 333 0. 333 1. 333 0. 011 0. 044 1 . 000 Slide 43 Example: SJJT, Inc. (C) ? Economic Analysis of Queuing Systems The advertising campaign of Smith, Jones, Johnson and Thomas, Inc. (see problems (A) and (B)) was so successful that business actually doubled. The mean rate of stock orders arriving at the exchange is now 40 per hour and the company must decide how many floor traders to employ. Each floor trader hired can process an order in an average time of 2 minutes. Slide 44 Example: SJJT, Inc. (C) ? Economic Analysis of Queuing Systems Based on a number of factors the brokerage firm as determined the average waiting cost per minute for an order to be $. 50. Floor traders hired will earn $20 per hour in wages and benefits. Using this information compare the total hourly cost of hiring 2 traders with that of hiring 3 traders. Slide 45 Example: SJJT, Inc. (C) ? Economic Analysis of Waiting Lines Total Hourly Cost = (Total salary cost per hour) + (Total hourly cost for orders in the system) = ($20 per trader per hour) x (Number of traders) + ($30 waiting cost per hour) x (Average number of orders in the system) = 20k + 30L. Thus, L must be determined for k = 2 traders and for k = 3 traders with ? = 40/hr. nd m = 30/hr. (since the average service time is 2 minutes (1/30 hr. ). Slide 46 Example: SJJT, Inc. (C) ? Cost of Two Servers P0 ? 1 k ? 1 (? ? n? 0 / m )n ( ? / m ) k km ? ( ) n! k! km ? ? P0 = 1 / [1+(1/1! )(40/30)]+[(1/2! )(40/30)2(60/(60-40))] = 1 / [1 + (4/3) + (8/3)] = 1/5 Slide 47 Example: SJJT, Inc. (C) ? Cost of Two Servers (continued) Thus, Lq = ? µ(? / µ)k (k-1)! (k µ -? )2 P0 = (40)(30)(40/30)2 1! (60-40)2 (1/5) = 16/15 L = Lq + (? / µ) = 16/15 + 4/3 = 12/5 Total Cost = (20)(2) + 30(12/5) = $112. 00 per hour Slide 48 Example: SJJT, Inc. (C) ? Cost of Three Servers P0 ? 1 k ? 1 (? ? n? 0 / m )n ( ? / m ) k km ( ) n! k! km ? ? P0 = 1/[[1+(1/1! )(40/30)+(1/2! )(40/30)2]+ [(1/3! )(40/30)3(90/(90-40))] ] = 1 / [1 + 4/3 + 8/9 + 32/45] = 15/59 Slide 49 Example: SJJT, Inc. (C) ? Cost of Three Servers (continued) (30)(40)(40/30)3 Hence, Lq = (15/59) = 128/885 = . 1446 (2! )(3(30)-40)2 Thus, L = 128/885 + 40/30 = 1308/885 (= 1. 4780) Total Cost = (20)(3) + 30(1308/885) = $104. 35 per hour Slide 50 Example: SJJT, Inc. (C) ? System Cost Comparison 2 Traders 3 Traders Wage Cost/Hr $40. 00 60. 00 Waiting Cost/Hr $82. 00 44. 35 Total Cost/Hr $112. 00 104. 35 Thus, the cost of having 3 traders is less than that of 2 traders. Slide 51