HİZMET SÜRESİ HİPO-ÜSTEL DAĞILIMA UYAN KUYRUK MODELİNDE, NEUTS’UN MATRİS-GEOMETRİK YÖNTEMİNİN SİMULASYON YARDIMI İLE ERGODİKLİK SONUÇLARI VE PERFORMANS ÖLÇÜLERİNİN ELDE EDİLMESİ

Year 2018, Volume: 3 Issue: 2, 61 - 77, 01.11.2018

Murat Sağır

Abstract

Bu çalışmada, varış süresi parametreli üstel dağılım ve hizmet içi HipoÜstel dağılım içeren bir kuyruk modeli incelendi. Müşteri sisteme geldiğinde, kuyrukta veya hizmet kanalında müşteri varsa, hizmet almak için kuyrukta beklemeye başlar ve müşterinin kaybolmasına izin verilmez. FIFO yönteminin kuyruk disiplini olarak kullanıldığı bu modelde, diyagram sistemde müşteri sayısını ve hizmet alan istemcinin hangi aşaması olduğunu gösteren geçiş hızı diyagramını gösterir. Buna göre, tridiagonal matris ve matris alt matrisleri inşa edilmiştir. ve matrisleri bu alt matrislerin yardımı ile hesaplanır. Neuts’un matrisi, bu matrislerin bir fonksiyonu olan sırası uygulanan yineleme tarafından elde edilir. Homojen doğrusal denklemler sisteminin çözümü için kararlı durumlu alt kümeler olan bu R matrisi olasılık vektörü , olarak hesaplanır. başlangıç değerine ve ’a bağlı olarak elde edilir. Sistem parametrelerinin gerçek olasılıkları, çözüm ve sayısal analizlerin normalleştirilmesi ile hesaplanır.

Keywords

Hipo-Üstel, Neuts’un Matris-Geometrik Yöntemi, Ergodiklik, Performans Ölçümleri

On Obtaining Of Ergodicity Results And Performance Measures Of Hypo-Exponential Distributed Queuing Model With Neuts Matrix-Geometric Method

Abstract

In this study, a queuing model with exponential distribution and inter-service hypo-exponential distribution with inter-arrival time parameter was studied. When the customer arrives in the system, if there are customers in the queue or service channels, they start to wait in the queue to get service, and the customer is not allowed to lose. In this model where FIFO method is used as queue discipline, the diagram shows the number of customers in the system and the transition rate diagram for the showing which phase the client receiving the service is. Accordingly, the tridiagonal matrix and the sub-matrices of the matrix are constructed. The matrices and are calculated with the help of these submatrices. Neuts' matrix is obtained by the iteration applied on the sequence which is defined as a function of these matrices. The probability vector from this matrix , which is the steady-state subvectors for the solution of the system of homogeneous linear equations, is computed as , are obtained based on the initial value and depending on . The actual probabilities of the system parameters are calculated by normalizing the solution and numerical analysis.

Keywords

Hypo-Exponential, Neuts Matrix-Geometric, Ergodicity, Perfomance Measure

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