Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System

Erdinç YÜCESOY; Vedat SAĞLAM

doi:https://doi.org/10.53570/jnt.938304

Makale detayları

Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System

Yazarlar:

Erdinç YÜCESOY | Vedat SAĞLAM

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Olasılıklar ve uygulamalı matematik | Matematik

Dergi:

Journal of New Theory 2021 Issue 35, pp.91-102

Belge Tipi:

Makale

Yayın Tarihi:

6/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000490313

Sıklık:

Üç Aylık

pISSN:

2149-1402

DOI:

https://doi.org/10.53570/jnt.938304

Özet:

 

In this paper, a new blocked tandem queueing model is given and analysed. The arrival process to this queueing model is Poisson with parameter λ. There is one service unit at the first stage of the system, and the service time of this unit is exponentially distributed with μ1μ1μ_1 parameter. There are two parallel service units at the second stage, and the service time of these service units are exponentially distributed with parameters μ2μ2μ_2 and μ3μ3μ_3. No queue is allowed at the first stage of the system. Upon completing service at the first stage, a customer proceeds to the second stage if at least one of the service units at the second stage is available. If both service units at the second stage are busy, the customer blocks the service unit at the first stage, which results in loss. The most important measure of performance of this queueing system is the loss probability πlossπlossπ_{loss}. First of all, the state probabilities of the system are obtained and then using these probabilities, the steady-state distribution of the system is obtained. Transition probabilities of the system are calculated by using steady-state probabilities, and finally an equation is obtained for πlossπlossπ_{loss} in terms of transition probabilities. Furthermore, another measure of performance, the mean number of customers, is obtained in terms of transition probabilities. Since the Equation for πlossπlossπ_{loss} is very complex, a numerical method is used to calculate the minimum πlossπlossπ_{loss} probabilities. After numerical optimal πlossπlossπ_{loss} calculations, a simulation of the queueing system is done, and it is seen that the obtained numerical πlossπlossπ_{loss} values tend to simulation results.

Makale detayları

Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System

Yazarlar: Erdinç YÜCESOY | Vedat SAĞLAM

Yayıncı: Tokat Gaziosmanpasa University

Ana Başlıklar: Olasılıklar ve uygulamalı matematik | Matematik

Dergi: Journal of New Theory 2021 Issue 35, pp.91-102

Belge Tipi: Makale

Yayın Tarihi: 6/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000490313

Sıklık: Üç Aylık

pISSN: 2149-1402

DOI: https://doi.org/10.53570/jnt.938304

Sayı

Yazarlar:

Erdinç YÜCESOY | Vedat SAĞLAM

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Olasılıklar ve uygulamalı matematik | Matematik

Dergi:

Journal of New Theory 2021 Issue 35, pp.91-102

Belge Tipi:

Makale

Yayın Tarihi:

6/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000490313

Sıklık:

Üç Aylık

pISSN:

2149-1402

DOI:

https://doi.org/10.53570/jnt.938304