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.

The First Of A New Historical Period - 820 Words

With the repeated financial crises that effected the global market economy in resent years, and with the realization that many of the practices, behaviors, and political decision that led to the economic crisis in the first place are still in place, one can only wonder if capitalism as an economic, social, and political structure is coming to an end as we know it? What makes this predication more realistic now than ever is the political changes that we are witnessing and the lack of social stability that is affecting every corner of the planet; it seems that the seeds of change were already planted, and now we are witnessing the early stages of a new historical period. However, a system, like capitalism, that became part of the very nature of how societies function and exist is hard to overcome. In addition, this unstable era is not the first for the capitalist system. In fact, lack of stability and conflict during WWII only allowed capitalist countries, such as the U.S. and Japan, t o emerge stronger, more dominant, and more hegemonic. Thus, why would this period of time could by any different from the previous crises that the capitalist system faced and overcame? These debates have dominated the political economy field in the recent years, and in this paper, I will attempt to cover some of the main argument in support of each of these points of view. Many argued that capitalism, as we know it, in all of it variations and models, has came to an end. Capitalism, as Marx hadShow MoreRelatedNew Historicism Is A Really Good Way For Analyze Texts And Show Correlation Between Ideas And Timelines1408 Words   |  6 PagesAp 2nd Period September 29, 2014 New Historicism New Historicism is a really good way to analyze texts and show correlation between ideas and timelines that are in the book. 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Solution Focused Therapy Free Essays

Social Work Department Faculty of Humanities University of Johannesburg Student Surname| Le Roux| Student Initials| C| Student First Name| Charlene| Student Number| 201170104| Assignment Title| Practice Model| Date of Submission| 15 March 2013| Course Title| B Social work| Lecturers Name| Prof. Adrian Van Breda| Course Code| SW2A11| Plagiarism Declaration| I, Charlene Le Roux 201170104, declare that this assignment is my own original work. Where secondary material has been used (either from a printed source or from the internet), this has been carefully acknowledged and referenced in accordance with departmental requirements. We will write a custom essay sample on Solution Focused Therapy or any similar topic only for you Order Now I understand what plagiarism is and aware of the department’s policy in this regard. | Name| Charlene Le Roux| Signature| | Index Page 1. 2. 3. 4. 5. 5. 15. 25. 35. 45. 55. 65. 767. 8. | Introduction History of Solution Focused TherapyUnderlying theoryKey principlesApplication to the PCPEngagementAssessmentPlanningImplementingEvaluationTerminationFollow-upCritical reflectionConclusionReference list| Page 334-55-66-116-77-88991010-11111213| 1. Introduction I have chosen to do the Solution focused therapy practice model (Hereafter referred to as SFT). I chose this model because I was interested in finding out more about how to use one’s own resources and strengths to empower oneself. My hardest issue with counseling is learning how to teach clients how to use their own resources instead of supplying it myself and also encouraging clients to come up with their own solutions and just giving them advice and my opinion. SFT discusses the different techniques one can use to ensure they are empowering their clients and not doing everything for them. 2. History The two founding theorists for SFT are Insoo Kim Berg and Steve De Shazer. Together they adapted existing theories to mold into a theory of their own. They strongly believed that true positive change lies within the client themselves and not in the relationship between the client and worker. Berg was the cofounder of a center in Milwaukee in 1978 whose intention was to launch the mental research institute and it used Brief Family therapy. This was an organization that made no profit and was used to serve the needs of people in surrounding areas and people and families that were poor or living in poverty (O’Connell, 2005). Four years later this became the home of SFT (Lee, 2011). De Shazer later worked in the center and was thoroughly trained in brief family therapy. According to Milton Erikson, brief therapy models were hugely influenced by the strengths perspective and social constructivism. The strengths perspective is about using one’s own strengths, assets and resources to come up for solutions that are best suited for them and their problem rather than simply providing everything for one’s client. It goes with the famous saying â€Å"Give a man a fish and he will eat for a day, but teach him how to fish and he will eat for a lifetime†. Berg and De Shazer developed this model by listening to and using the feedback of their clients. They created this model by observing therapy sessions to observe the techniques and skills the therapist used, by listening to the feedback of their clients about what was or was not working for them and by observing the progress of their own clients (Lee, 2011). 3. Underlying theory of practice model Social constructivism strongly influences SFT (O ‘Connell, 2005). This perspective states that human beings create their own reality through different linguistic means. In other words, we create our own realities through conversations and by our own view of the truth so therefore each person has a different meaning that has been created which in turn means that there is no ‘objective truth’ that is true in any situation. This all implies that each person’s problems are constructed by the way in which they talk. As a result of each person having their own linguistic style, there is no fixed meaning attached to a problem or a solution. In order for a person to see their created reality from another perspective, the therapist or practitioners main goal is to change the language the client uses. Practitioners encourage clients to use solution talk as opposed to problem talk. One thing that stands out from the social constructivist perspective is that the clients perception and experiences have main priority. This theory also takes into account the context in which the client lives and emphasizes that people do not exist in social isolation but rather are products of the interactions that surround them. The relationship between the practitioner and the client is of utmost importance in this perspective because it is within this relationship that a new style of language can be created for the client to build new realities. The systems theory is another perspective that influences solution focused therapy. The systems theory expects a practitioner to look at all the systems surrounding an individual so that the best interventions can be used. To understand the systems theory fully there are some terms that are the most important (Kirst-Ashman Hull, 2006). Every individual is viewed as the product of interactions between different micro systems in that individuals life and practitioners look at their clients as a person-in-environment where they are constantly interacting with the various systems around them. These systems function reciprocally and change in one system means there will be change in another. The systems approach is also dynamic. It is ever changing and evolving from one particular view to another yet maintains a relatively stable homeostasis. All systems are interrelated. The systems theory basically states that because no two client systems are alike, no two solutions will be alike either and therefore every problem needs a unique and suitable intervention (Kirst-Ashman Hull, 2006). Lastly, the strengths perspective has had an influence on SFT. The main view of the strengths perspective is that every individual, family or community has already got strengths, resources and assets that should be used in intervention strategies and it is the responsibility of the practitioner to uncover these different strengths. The strength perspective doesn’t see hard times such as traumatic experiences, struggles and sicknesses as demotivating experiences but rather as opportunities and challenges that can be overcome and in the end be used to the benefit of the client even if it is just a lesson that was learned. A worker should never limit their clients capacities and capabilities but rather believe in their goals and dreams and help them achieve it in any way that they can and another important aspect to remember here is that their goals and dreams can only be achieved if the client and worker work together to achieve these. One last thing that is important for people to know about the strengths perspective is that it believes that every environment also has strengths and that the client should always look for help in their own environments rather than other environments. 4. Key principles As seen above and as previously mentioned, SFT was founded by bringing many different theories together. In this section the main principles of SFT will be discussed. First and foremost, it is set on the notion that if something is not broken there is no need to fix it (O ‘Connell, 2005). In other words, workers should not look for problems where there are none. If a situation is working for a client the worker shouldn’t try fix it even if it is different to the way the worker thinks it should be working. This is a theory that believes in the strengths of clients and the fact that people are resilient and can bounce back from traumatic experiences with the right support and resources. It draws on the importance of people to emerge as stronger people after the traumas by relying on their own resources and coping methods that they themselves have learned (Van Breda, 2011). If the client’s way of solving a problem is working then the worker should encourage the client to do it more often and if a resolution is not working then there is no point in continuing to try it so the worker should encourage the client to stop that way and try to find another way of dealing with the problem. It should be kept as simple as possible so as not to confuse the client but rather to encourage them to find new and improved solutions to dealing with individual problems. This process of therapy should not be drawn out longer than necessary and should be to the point with as little intervention from the therapist as possible. This theory believes that one change ultimately brings about another change until all the required change has been achieved. Therefore, this theory does not seek to make big changes but rather a chain of smaller changes. Another reason why smaller changes are encourages is because it helps the client feel less intimidated as they would feel by implementing one big change at one time. As always with positive change, a worker needs to recognize it and praise the client for the change they themselves have implemented. Since language is such an important aspect in this theory, the worker should never assume that there is only one possible solution to a problem but the worker should be open-minded and should try using many different paths to try and find a suitable solution. Since this theory focuses on solutions rather than problems, the worker should not spend time analyzing the problems but should jump into finding solutions that will work for that specific client and their circumstances (Malherbe Greef, 2005). . Application to the PCP The planned change process is a set of stages that a social worker can follow and the stages overlap and flows into one another (Kirst-Ashman Hull, 2006). 5. 1Engagement â€Å"Engagement is when a social worker begins to establish communication and a relationship with other but also addressing the problem† (Kirst-Ashman Hull, 2009, p. 34). Engagement starts from the very first interaction a worker has with a client. The main goal of engagement is to build rapport by using different skills such as acceptance and warmth. It is very important that the worker does not judge their client at any stage and shows acceptance as acceptance is a necessary tool for change. Part of engagement in SFT is for the worker to help the change process along from the very beginning. Change needs to be spoken about and visualized. In the engagement stage it is important for rules and expectations to be set and this can be done by a means of contracting. Contracting is when the client and the worker discuss the roles, norms and expectations for sessions and this is where the boundaries are set for the client-worker relationship (Kirst-Ashman hull, 2006) Contracting also helps establish roles between the client and the worker which is important in the formal relationship so that boundaries can be set in place. Firstly, the worker needs to enquire about the â€Å"pre-session change†. Pre-session change is that happened in the clients life that pushed them to make the appointment in the first place. The worker can do this by asking questions like â€Å"Tell me more about why you are here today† or â€Å"What made you seek help? †. Giving compliments to the client eases their anxiety and affirms the belief that positive regard increases the chance of change for people (Rasheed, Rasheed Marley, 2011). 5. 2 Assessment â€Å"Assessment is differential, individualized and accurate identification and evaluation of problems, people and situations and of their interrelations to serve as a sound basis for differential helping interventions† (Siporin as cited in Kirst-Ashman Hull, 2009, p. 34). Assessment is usually when the worker assesses what the problems are that the client is facing but because SFT focuses on solutions the worker needs to change problem talk into solution talk and already start thinking about possible solutions to the problem. A worker using SFT needs to pay attention to detail and listen to the clients carefully during the assessment stage. Once the worker has heard the clients issues they need to respond empathically as this helps create empowerment for the client as well as lets the client know that the worker is paying attention and understanding the clients’ point of view. There are many different types of questions that should be used in the assessment stage of SFT. The miracle question is the first. The answer to this type of question is usually on the path of the fitted solution. This type of question helps the client vision their preferred future. These questions are asked to find out about the clients story, strengths and resources and their own expectations for the solution. This type of question would be something like â€Å"Imagine you were sleeping tonight and a miracle happens that solves the problem you came to speak to me about. When you wake up in the morning, what would be the change that would make you realize something must have happened to solve your problem? † a client could possibly reply with answers similar to this, â€Å"my children weren’t moody and crying, my husband and I were smiling and organized. We left on time for work and when we came home we had food on our plates and the children were playing. † Another type of question is an exception question. This type of question helps the worker to get an idea of the good times in a client’s life. It helps the client remember that there were times when they knew what to do nd how to do it in order for them to function normally. Helping a client remember times when they were managing better gives them hope that they can do it again. A worker would ask this question â€Å"can you think of a time in the past month, year or ever that you did not have this problem? What were you doing differently during those times that helped prevent the problem then? † (De Shazer as cited in Lee, 2011). Coping questions are also important questions when assessing and planning for implementation. This question is useful for clients who feel completely helpless because it can give ideas to solutions that could help serve their problems. This type of question helps the worker get to know more about the clients coping strategies. A coping question would be something along the lines of â€Å"wow, how have you managed to carry on during all of these hard times? † Lastly, scaling questions can be used. These questions can be used during the evaluation stage as well. This question helps the client track their own progress which helps them identify where they are at (Lee, 2011). This is a question that asks the clients to choose a number between 1 and 10 to determine their progress. A worker would ask a question like â€Å"from a scale of 1 to 10, 10 being the best, how are you feeling now compared to when we started? † (Nichols Schwartz, 2008). 5. 3 Planning â€Å"Planning specifies what should be done† (Kirst-Ashman Hull, 2009, p. 370. Planning in this theory goes hand in hand with assessment because in assessment the worker will not spend too much time focused on the problem but rather on already finding possible solutions. It is also important to remember that changes should be planned as small rather than one big change. 5. 4 Implementation Implementation is the actual doing of the plan. The Client and worker follow their plan to achieve their goals. Progress during implementation must be constantly monitored and assessed. Sometimes, new issues, situations and conditions require the plan to be changed† (Kirst-Ashman Hull, 2009, p. 40). The most important aspect to the implementation is the changes need to small so as to not overwhelm the client with major changes. When a small change is achieved, it leaves the client feeling empowered and motivated to start change in another dimension of their lives. It gives the client courage to try for new and bigger changes (Lee, 2011). The above mentioned questions can also be asked to stimulate change (Macdonald, 2011), therefore intervention starts during the assessment stage. Intervention by the worker should be limited ensuring that the changes will be as a result of the clients new ways of doing things while at the same time making sure the client gets a sense of independence rather than relying on the worker to do all the work. 5. 5 Evaluation â€Å"Each goal is evaluated in terms of the extent to which it has been achieved. The decision must be made about whether the case must be terminated or reassessed to establish new goals† (Kirst-Ashman Hull, 2009, p. 41). Evaluation in SFT basically combines all the above mentioned techniques. The worker uses the questions to find out how much change and progress has been made. Once the worker realizes what those changes are he or she points these out and celebrates together with the client for making these changes (Macdonald, 2011). The miracle question is used to monitor the progress and to keep the client in a positive frame of mind in order for them to continue progressing to their full potential. It is important for the worker and client to reflect to evaluate what has been improved and how. Evaluation in SFT does not necessarily only occur after implementation. The worker also evaluates the client at the beginning of every session to see what changes have been made and how the client is progressing. 5. 6 Termination â€Å"The worker/client relationship must eventually come to an end. Termination in Generalist Practice involves specific skills and techniques† (Kirst-Ashman Hull, 2009, p. 41). Termination begins from the very beginning in order to prepare clients for the ending of sessions. SFT is meant to be brief and not carry on for long periods of time. The worker needs to keep reminding the client that the therapy will not be long and the client should have the goals of finding new solutions quicker than in other types of therapy. In the last session, the client is asked to describe in detail what changes they experienced so the change can be maintained and the worker should point out what worked and what did not work in the clients’ progress. One way of knowing when a client is ready for termination is by asking them a scaling question (Macdonald, 2011). This is when a client answer from a scale of 1 to 10, 10 being the best level of functioning. If a client’s answer is 7 or higher then the client is ready to terminate. These types of questions can be â€Å"What would you rate your level of functioning as on a scale from 1 to 10, 10 being the best? † or â€Å"Consider that when we started you were on a level 3 scale of functioning, what would you rate your level as now between 1 and 10? †. It is important to remember that terminating with an open door policy is of benefit to this client. This means that even though the sessions are over, you let the client know they are always welcome back should they encounter any other problems but the worker can also encourage the client to come visit in a few months to let the worker know how everything is going. this makes the client feel important and valuable and is a positive way to terminate. 5. 7 Follow-up Although not a stage of the planned change process I do think it is important for a social worker to follow up with their clients to ensure that everything is still going alright. Following-up with a client also empowers them in a way because it makes them feel like they are still cared for and worried about and not like they were just forgotten by the social worker. Following up can be done in many different ways. A worker can request that the client comes back for one last session just to follow-up and ensure that everything is okay. It can also be done telephonically or via e-mail. If a client does not respond to the email or does not come in for the session it is the responsibility of the worker to find out what the reason is just to make sure the client is still on track. . Critical reflection There are some concerns surrounding SFT. One of the concerns is that it is so focused on solutions that it does not focus on curing the root cause of the problems. A therapist using this model could say that the deep rooted cause was in fact also just a form of the clients’ distortion of reality. This therapy also relies too much on the client. In some cases people may not understand that what they want is not what they need and clients sometimes need a counselor to give them a new view point to look at their situation from. For example a married couple may sometimes not know what it is they need and a worker can step in to give some ideas for solutions they can try instead of relying on the client to recognize what it is they really need. I would use this practice model if I could change a few things. I would focus more on the way a client is feeling about their problems because sometimes all somebody needs is someone to listen to their problems and not just think of solutions. Sometimes it is important to try and understand a client in a bit more of an informal way rather than strictly professional. It is important though to remember boundaries and that a client may never be friend with a worker as there may then be conflict of interest. Although there are holes in this model, there are also things I really like about SFT. It is good to focus on the positive things rather than continuously analyzing the negative to get to a solution. Focusing on a solution puts the client in the future and motivates them to get to that level of functioning. It is a model that can help clients succeed a lot quicker than other models. I also like the fact that SFT has specific types of questions that are direct because other models can sometimes take a long time just to assess the problem leaving the client feeling like there has been no progress over a period of time because the worker has just been assessing. With SFT the client will start to see changes quite soon and will feel empowered just by the questions that they will be asked. 7. Conclusion I like the idea of SFT because it focuses on strengths and it has always fascinated me to know how a client can use their own strengths. After researching this practice model I understand a lot more about how I can recognize what a client’s strengths are and how they can be used for solutions. It is a therapy that is direct and results can be seen soon after the first session. This therapy promotes the empowerment of people and is easy to follow in order to empower one’s own clients. It is a widely used therapy and has a high success rate. I am glad I have learned about this model because I can now apply it to my practice this year. Instead of focusing on my clients weaknesses (low self-esteem) we can focus on building confidence and not on what has caused the low self-esteem. This is great because often speaking about the causes can be re-traumatizing to the client when all they want to do is more forward instead of focus on the past. 8. Reference List Kirst-Ashman, K. K. , Hull, G. H. (2009). Understanding Generalist Practice (5thed. ). Belmont, CA: Brooks/Cole, Cengage Learning. Lee, M. Y. (2011). Solution-focused theory. In F. J. turner (Ed. ), Social work treatment: Interlocking theoretical approaches (5th ed. pp. 460-476). New York: Oxford University Press. Macdonald, A. (2011). Solution focused therapy. In R. Nelson-Jones (Ed. ), Theory and practice of counselling and therapy (5th ed. , pp. 371-391). Los Angeles, CA: Sage. Nichols, M. P. , Schwartz, R. C. (2008). Family therapy: concepts and methods (8th ed. ). Boston, MA: Pearson. O’Connell. B. (2005). Solution focused therapy (2nd ed. ). London : Sage Publications ltd. Rasheed, J. M. , Rasheed, M. N. , Marley, J. A. (2011). Family therapy: models and techniques. Los Angeles, CA: Sage. How to cite Solution Focused Therapy, Essay examples