Kuyruk modellerinin yapısal olarak incelenmesi ve Atatürk Hava Limanı sistemi üzerinde bir simulasyon uygulaması

Abstract

ÖZET `Kuyruk modellerinin yapısal olarak incelenmesi ve Atatürk Hava Limanı Sistemi üzerinde bir simulasyon uygulaması` adlı bu çalışma 4 bölümden oluşmaktadır. Bölüm l'de kuyruk teorisinin oluşmasına neden olan toplumsal hayattan örneklere yer verilerek kuyruk sistemlerinin incelenmesinde kullanılan simulasyon ve analitik tekniklerinden bahsedilmiştir. Daha sonra bu tekniklerin uygulanacağı `Atatürk Hava Limanı Sistemi` (ATHLS) ile ilgili araştırma problemi tesbit edilmiş içerik ve kısıt yönleri bakımından tanıtılmaya çalışılmıştır. Bölüm 2'de kuyruk teorisinden bahsedilerek bazı kuyruk modelleri yapısal olarak incelenmiş ve konu ile ilgili formüller irdelenmiştir. Bölüm 3'de sistem, model ve simulasyon kavramlarına yer verilerek açıklanmaya çalışılmıştır. Bölüm 4' de ilk olarak Atatürk Hava Limanı Sistemi tanıtılmış daha sonra bu sistemden derlenen datalar analize hazırlanmıştır. Analiz tekniklerinin, hazırlanan datalara uygulanmasıyla; ATHLS'ne gelen uçakların arka ar kaya geliş sürelerinin istatistiksel dağılımının üstel dağılıma uyduğu? Sistem performansı için simulasyon tekniğinin, analitik tekniğe göre gerçeği daha iyi yansıttığı, ATHLS'de kuyrukta bekleme ile servis sağlama maliyetlerinin bugünkü verilere göre dengede olduğu; Sistem için kurulmuş olan simulasyon modelinin genelde bütün kuyruk sis temlerine uygulanabilir olacağı sonuçları elde edilmiştir. - vıı -

SUMMARY STRUCTURAL ANALYSIS OF EQUEING MODELS AND A SIMULATION APPLICATION TO THE ATATÜRK AIRPORT SYSTEM This study, whose title is given above, consists of four chapters. The content of each chapter is summarized below. The first chapter points out to the importance of 'queueing` as one of the causes of human beings' settling in groups and illustrates various examples of queueing in our present world. With these examples it tries to emphasize ideas concerning the optimality between the cost of time wasted waiting at the queues and the cost of service. The theory of queueing is started to develop when the problem of waiting on queue was begun to investigate through mathematical analysis. The fundamental queueing theory can be divided into two mathematical studies. One of these studies deals with special distributions from which mathematical formulae are obtained while the other one deals with classical, experimental or hypothetical distributions which are analysed by simulation methods. The importance of studying queueing theory is emphasized because queueing causes disturbance in daily life in many ways. Again in this part it has been stated that queueing is an economical problem and the concepts of 'queueing' and 'service1, which form the two components of the fundamentals of queueing theory, are emphasized. Towards the end of this chapter, the research problem concerning the Atatürk Airport System (ATHLS), which is the subject of this research, is described. The second chapter, titled 'Queueing Theory', introduces queueing systems. Telephone queues, which were first handled by a Danish electrical engineer E.K.Erlang in 1909 are mentioned. The main elements of this queueing system are depicted in figure 2.1. The six main characteristics of a queueing system are as folio w s : - vxii -1- Input or arrival distribution. 2- Output or departure distribution. 3- Service channels. 4- Service discipline. 5- Maximum number of customers allowed in the system. 6- Calling source. The following characteristics of queueing process are also given in this part: the arrival process, queueing configuration, queueing discipline, service discipline and service possibility; and the basic service structures are illustrated in figure 2.2. In this study, the queueing models are classified as follows: (a / b / c) : (d / e / f) In this notation: represents the arrival or interarrival distribution represents the departure or service time distribution represents the number of parallel service channels represents the service discipline represents the maximum number of customers allowed in the system represents the calling source Usually, the following conventional codes are used to replace symbols a and Instead of symbols `a` and `b` M- Poisson arrival or departure distributions (or an equivalent exponential interarrival or service time distribution). D- Deterministic interarrival or service time distribution. E- Erlangian or Gamma interarrival or service time distribution. GI- General independent variables. G- General distribution of departure or service times. - xx -Instead of symbol `d` FIFO- First input, first output. LIFO- Last input, first output. SIRO- Service in random order. GD- General service discipline. c- Any positive number. e- Number of customers in the system. F- Number of customers in the calling source. The formulae for Chi-Square goodness of fit test for determining the distributions used in defining the arrival and service structure in queueing models and the formulae for the statistical distributions that are obtained as a result of application of this test are explained. D x' (Chi-Square Test) 2) p(x=x) - f(x) = -X t (>x=0,l,2, ) (Poisson distribution) 3) f(x)=/ Xe -Xx > 0 X' < 0 (Negative exponential distribution) In order to emphasize the queueing optimation, service level and the cost of waiting time is illustrated in figure 2.3; service level and cost of service supply is illustrated in figure 2.4; and the total cost of service supply is illustrated in figure 2.5. As a result of analysing structurally the single channel model M/M/l, the following formulae have been given: Ex A pected number of customers in the system L = - - r ]i - A Expected number of customers in the queue L = -777-^ - - r- v q M(y-X) - x -Average waiting time per customer in the system W = y-X Waiting time per customer in the queue W = q M(u-A) and the following formulae have been given multiple channel model M/M/c : for the P0=l / n=0 n'. V i,x c t cVl c'. V ^cU-X J] T _ ^ q ` (c-d: x u p. (t) (cU-X) 2 'o L = L + A q u L W = -9- q x w = w + - q p And an example is included for each formula. Chapter 3 deals with simulation, system and model concepts and defines simulation, mentions simulation types and gives an example for each simulation model. Chapter 4 introduces the Atatürk Airport System, which is the subject of this research problem and mentions different ways in which the landing, service beginning and take off times of planes that land, receive service and take off in this system are entered in the control tower register forms. Then it mentions how the data collected from the Atatürk Airport System (ATHLS) is prepared for analysis. It also exylains that the data prepared for analysis is illustrated as in Appendix A and mentions the simulation and analytic methods which will be applied to the performance and analyses obtained form the ATHLS system. Then the ATHLS performance and analysis results that are determined by the application of these two techniques seperately are compared and the following conclusions and suggestions are stated: - xi -1- It has definitely been proved that the periods formed by successive arrival times- of the planes landing at ATHLS display a negative exponential distribution and thus the probability of the number of planes arriving at the system matches with poisson distribution. Any statistical study on the ATHLS can make use of this conclusion. 2- It has also been illustrated in a real system that in analysing and estimating the performance of queueing systems, for which it is impossible to set up an exact analytic model, simulation technique estimates the real situation better. 3- According to the most recent data, in ATHLS- where approximately 0.15 of the capacity is used, considering the 0.40 server idle time percentage, we can conclude that the reason why the planes that seem to be waiting for service wait is not due to full runways and overloaded service; there must be some other reason. And thus it is possible to understand the optimality of the cost of planes' waiting at the queue and the cost of service supply. 4- The simulation system model (İ.T.Ü. IBM 4381) which is set up for this time consuming research whose results are summarized in a few pages is a system that can be used in estimating and analysing the performance of various queueing systems. - xn -