Kuyruk modelleri ve endüstriyel sistemlerde bir uygulama
Queuning models and an application in industrial systems
- Tez No: 66763
- Danışmanlar: DOÇ. DR. ALPASLAN FIĞLALI
- Tez Türü: Yüksek Lisans
- Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Endüstri Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Endüstri Mühendisliği Bilim Dalı
- Sayfa Sayısı: 72
Özet
ÖZET Üretim şekilleri karmaşıklaştıkça, endüstriyel sistemler içindeki "kuyruk yapılarfnın daha sıklaştığını ve çok çeşitli biçimler aldığını görmekteyiz. Günümüz rekabet koşullarında, temel hedeflerden biri de mal ve hizmetlerin daha hızlı ve etkin şekilde üretimini sağlamaktır. Üretim araçlarının kapasitelerinin artırılması ve bundan daha önemlisi, kapasitenin etkin kullanımının sağlanmasıyla, endüstriyel sistemler içindeki kuyruk yapılarının performansı artırılabilinmektedir. Bir kuyruk modelinde, bekleme hattı durumu şu şekilde meydana gelir: Bir müşteri alana gelir; bir bekleme hattına (kuyruğa) katılır. Servisçi. bekleme hattından bir müşteri seçer. Servisin tamamlanmasından sonra yeni bir müşterinin seçilmesiyle proses tekrarlanır. Servis görmüş müşterinin ayrılması ve yenisinin servise alınması arasında zaman kaybedilmediği farzedilir. Bir kuyruk sistemi şu faktörlere bağlıdır: 1. Aradarada gelen iki müşterinin gelişlerarası sürelerinin dağılımı (Eksponansiyel. Erlang. Gamma, Genel dağılım vs.). 2. Müşterilerin gördüğü servis süresi dağılımı (Eksponansiyel, Erlang, Gamma. Genel dağılım vs.). 3. Bekleme hattının dizaynı (servisçiler seri, paralel ya da şebeke halinde dizilebilirler). 4. Servis için seçilen müşterilerin önceliği (FCFS: ilk giren ilk servis görür; LCFS: son giren ilk servis görür; SIRO: rassal servis önceliği). 5. Kuyrukta bekleyen müşteri sayısı kısıtı (sonlu: bekleme alanı kısıtlı sayıda müşteri alabilir; sonsuz: bekleme alanı, gelen tüm müşterileri alabilecek büyüklüktedir). 6. Müşteri kaynağı türü (sonlu: örneğin, atölyede, tamir için bekleyen makinalar; sonsuz: örneğin, vapur gişelerinde bilet almak için bekleyen yolcular). 7. Müşterilerin insan olması halinde, gösterdiği davranışlar (manevracı, engel olucu, vazgeçici). Çalışmada öncelikle kuyruk sistemleri teorik açıdan ele alınmış ve bu sistemlerle ilgili temel ölçüler çıkarılmıştır. Daha sonra da, örnek olarak seçilen bir endüstriyel sisteme kuyruk modeli uygulanmıştır. Hesaplamalar sonucunda elde edilen bilgilerle de, sitemin performansına ait yorumlar getirilmiştir. IX
Özet (Çeviri)
SUMMARY QUEUING MODELS AND AN APPLICATION IN INDUSTRIAL SYSTEMS Think back over your week and consider how much time you spent waiting in line- at the supermarket. in traffic, at the post office. Every moment you spent waiting for some type of service you were part of a queue. But queues are not always this obvious and they do not have to involve people. A suit waiting to be dry-cleaned is part of a queue; and a lawsuit waiting to be heard in court is part of a queue. A queue is a group of people, tasks, or objects waiting to be served. Waiting is the essence of queuing. Though we are most aware of our own waiting time, queuing is foremost a problem for industry and government. The success of any organization depends on maximizing the utilization of its resources. Every minute that an employee spends waiting for another department and every minute that a job spends waiting to be processed is money wasted. The success of any organization also depends on attracting and keeping customers. Every minute that a customer spends waiting to be served translates into lost business and lost revenue. The best way to understand how a queue operates is to examine the characteristics of the basic queuing elements. Here are some of the things to consider. Customer: The arrival process depicts the timing of a customer arrivals at a queue. Do customers arrive independently of each other, or do they arrive in groups? Do customers arrive at a fairly constant rate, or is there some pattern to their arrivals (for example, a“rush hour”)? Is the arrival process predictable or random? Do different types of customers arrive at different times of the day? In addition to understanding customer arrivals, one should also understand customer reneging, balking, and jockeying. Reneging is the act of leaving a queue before being served; balking is the act of not joining a queue upon arrival. Conceptually, the two concepts are same. The only difference is the timing of when the customer leaves (either immediately in the case of balking or later in the case of reneging). Jockeying is the act of swiching from one queue to another. Reneging, balking, and jockeying are three of the most difficult aspects of a queuing system to measure because the customer may never be recorded by the system. How long must a queue be before customers renege? Are some types of customers more likely to renege than others?.. Will a customer that reneges come back or never return? If the customer returns, when will that be?Server: The service process represents the time taken to serve customers, commonly referred to as the service time. Is the service time constant, or does it vary from customer to customer? Are customers served in bulk, as atraffic signal? Does the service time depend on the type of customer, and can it be predicted in advance?.. Does the service time depend on the server or the time of they? Is there any way to shorten the service time by improving server efficiency? A second important aspect of the server is its configuration. How many servers are there? Which servers work in paraleli, performing identical tasks, and which perform in series, performing different tasks? What are the rules governing how customers move from server to server'.' Queue: The queue discipline specifies the order in which customers in the queue are served. Are customers served on a first-come, first-served (FCFS) basis, or perhaps on a last-come, first-served (LCFS) basis? Do different customers receive different priority, and if so. what is the system for assigning priority? Is service for a customer ever interrupted to serve another with higher priority? A second important characteristic of the queue is its general organization. Is there a single queue that feeds all servers, separate queues at each server, or some variation of the two? Is there a limit on the total number of customers in the queue? What is the system for keeping track of customers and ensuring orderliness? These are some of the key questions to ask in assessing in queuing system. Many of these aspects can be changed in order to improve the performance of the system: others are beyond control. Regardless, understanding these aspects is the first step toward improving a queuing system's performance. This study's name is“Queue Models and an Application at Industrial Systems”. Firstly, queue systems are investigated theoretically. Then, queue model is applied an industrial system that is determined as an example. It is said that an queue model depends on a certain number of factors. These are: 1. Arrivals distribution (single or bulk arrivals). 2. Service-time distributions (single or bulk service). 3. Design of service facility (series, parallel, or network stations) 4. Service discipline (FCFS, LCFS. SIRO) and service priority. 5. Queue size (finite or infinite). 6. Human behavior (jockeying, balking, and reneging). A notation that is particularly suited for summarizing the main characteristics of queues has been universally standardized in the following format: (a/b/c) : (d/e/f) The symbols a, b. c, d, e, and f stand for basic elements of the model as follows: XIa s arrivals distribution b 3 service time (or departures) distribution e s number of parallel servers (e = 1. 2 so) d = service discipline (e.g.. FCFS. IXTS, SIRO e = maximum number allowed in system (in queue + in service) f = size of calling source ?t The standard notation replaces the symbols a and b for arrivals and departures by the following codes: M = Poisson (or Markovian) arrival or departure distribution (or equivalently exponential interarrival or / service-time distribution) D = constant or deterministic interarrival or service time Eu= Erlangian or gamma distribution of interarrival or service time distribution with parameter k GI = general independent distribution of arrivals (or interarrival time) G = General distribution of departures (or service time) The ultimate objective of analyzing queuing situations is to develop measures of performance for evaluating the real systems. However since any queuing system operates as a function of time, we must decide in advance whether we are interested in analyzing the system under transient or steady-state (the state that arrival rate smaller than service rate) conditions. Transient conditions prevail when the behavior of the system continues to depend on time. Thus the pure birth and death processes always operate under transient conditions. On the other hand, queues with combined arrivals and departures start under transient conditions and gradually reach steady state after a sufficiently large time has elapsed, provided that the parameters of the system permit reaching steady state. Although the basic equations of the various models that we develop here can be used to study the transient behavior, our analysis will concentrate on the analysis of steady-state results. This conclusion is based on the assumption that most systems are normally designed to stay in operation for a long while. However, we must add also that transient-state analysis is quite complex mathematically and any venture into that area will take us far afield. Under steady state conditions we shall be interested in determining the following basic measures of performance: pn = (steady-state) probability of n customers in system Ls = expected number of customers in system Lq = expected number of customers in queue Ws s expected waiting time in system (in queue + in service) Wq s expected waiting time in queue The Poisson distribution plays an important role in the development of queuing models because it describes many real-life situations. Naturally, statistical methods xiiexist that arc designed to test the hypothesis that a given set of data follows a certain probability distribution. The best known of these is the chi-square test of goodness of fit. It is based on a comparison between observed and theoretical distribution being tested. The details of the method are given in the statistic books but there are two crude rules that can give us an idea about whether the arrivals or departures of a real-life situation follow the Poisson distribution: 1. If the queuing situation is already in existence, observe the operation for a while. Do successive arrivals (departures) appear to occur randomly, or is there a pattern of arrivals (departures)? If they are random, there is a good chance that the process may follow the Poisson distribution. 2. Gather observations about the number of arrivals (departures) of customers by recording the number of customers arriving (departing) during appropriate equal time intervals (e.g. hourly). After gathering a“sufficient”amount of data, compute the mean and variance. If the distribution is Poisson. its sample mean and variance will be“approximately”equal (barring, of course, sampling error). This is a unique property of the Poisson among all commonly known discrete distributions. In this study, the inputs of application show that arrival and service distributions don't fit Poisson distribution. The general distribution is accepted using the certain means and variances of interarrival and service time distributions. There are not only a server in a queuing system. There are queuing networks that contain servers more than one. Queuing networks occur when the service process, for reasons of efficiency, is divided into separate tasks. Consequently, queuing networks require the coordinated effort of two or more servers The most important concept in queuing networks is that of the bottleneck. In most queuing networks, queuing delays are greatly influenced by the performance of one or more bottleneck servers. To improve the performance of the entire system, one most identify the bottlenecks and improve their performance. The bottleneck will be an important concept in each of the two basic types of network service: serial service and parallel service. With parallel service, tasks are performed simultaneously by different servers. For instance, in a job shop, a lathing operation might be performed on a component at the same time as a drilling operation on another. Of course, many networks contain both serial and parallel elements. The complexity of queuing networks makes it extremely difficult to develop analytical models of their stochastic behavior. It is not, however, difficult to develop graphical models of their deterministic behavior under varying levels of demand. Models are also provided for estimating the throughput (that is output rate) of the queuing network, an important measure of system performance. In the simplest type of queuing network, queues and servers are organized in a series, and every customer passes through the entire series in the exact same sequence. In production this is sometimes called a flow shop. XlllIn this study, the application contains a queuing model that has two serial servers. The two serial servers do not operate independently of each other because the arrival of customers at the second server is tied to the service of customers at the first server. More generally, one server's departure process dictates the next server's arrival process. This statement is the crux of the issue. Bottleneck server, for queues in series, offering continuous service, the server (or servers) with the smallest service capacity. At the application of this study, the bottleneck situations were examined on condition that varying server's capacities. The significance of the bottleneck in queues with series, is that it alone determines how much time customers spend in the system. Time in the system can only be reduced by increasing the service capacity of a bottleneck server. If there is more than one bottleneck in a series queue, all of the bottleneck capacities must be increased. Increasing the capacity of nonbottleneck servers will not decrease time in system. In this study, queuing model has been applied an industrial system in order to do the theory clear. Application has been made about two different and consecutive processes in Assan Alüminyum Tesisleri. Assan Alüminyum that is the leader society of the metal industry has been producing flat aluminium products since 1987. The examined processes are Cold Milling (Soğuk Hadde) and Stretching-Straighten Line (Gerdirme-Düzeltme Hattı). The observation was made at these processes between March Ist - April 10th thus the interarrival times were determined. Service times are based on time study. Firstly, the distributions of the interarrival and service times has been determined. Because of the mains and standard deviations aren't equally, these distributions haven't Markovian characteristics. Also, arrivals and departures of the products don't fit the real life situation. The distributions have been accepted General Distribution based on the certain mains and variances. Using the inputs, the parameters of the system (X, u., Lq, Ls, Wq, Ws...etc.) have been determined that belong to observation time. Then, the bottleneck and non steady- state conditions have been searched changing the inputs. XIV
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