OPTIMIZATION OF LOSS PROBABILITY FOR GI / M / 3/ 0 QUEUING SYSTEM WITH HETEROGENOUS SERVERS

Year 2010, Volume: 1 Issue: 1, 73 - 89, 29.07.2011

H. Okan İşgüder Umay Uzunoglu Kocer

Abstract

In this paper a queuing system with recurrent arrivals, three heterogeneous servers, and no waiting line is examined. In this system an arriving customer may choose any one of the free servers with equal probability. When all servers are busy, customers beyond the capacity of the system are lost.
These customers are called “lost customers”. The probability of losing a customer is computed for the queuing system, and it is shown that when the mean of the interarrival time distribution is fixed, loss probability is minimized by deterministic interarrival time distribution. This conclusion is supported by the simulation results.

Keywords

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Teorik Bilimler

Abstract

Bu çalışmada rekurrent girişli, bekleme yerinin olmadığı, 3 heterojen kanallı bir kuyruk modeli incelenmiştir. Bu sistemde gelen müşteri, boş olan kanallardan herhangi birisine eşit olasılıkla girer. Bütün kanallar dolu ise sistem kapasitesi aşıldığından, gelen müşteri hizmet almadan sistemden ayrılır. Bu tür müşterilere “kaybolan müşteri” denir. İncelenen kuyruk sisteminde müşterinin kaybolma olasılığı hesaplanmış ve ortalaması sabit olan gelişlerarası süre dağılımları içinden gelişlerarası süre dağılımı deterministik seçildiğilde kaybolma olasılığının minimum olduğu gösterilmiştir. Elde edilen sonuçlar bir simülasyon çalışmasıyla desteklenmiştir

Keywords

Deterministik dağılım, Heterojen servis birimi, Kaybolma olasılığı, LS dönüşümü, Kaybolan müşteri akımı, Optimizasyon

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