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

#### Erdinç YÜCESOY [1] , Vedat SAĞLAM [2]

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 $μ_1$ parameter. There are two parallel service units at the second stage, and the service time of these service units are exponentially distributed with parameters $μ_2$ and $μ_3$. 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 $π_{loss}$. 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 $π_{loss}$ 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 $π_{loss}$ is very complex, a numerical method is used to calculate the minimum $π_{loss}$ probabilities. After numerical optimal $π_{loss}$ calculations, a simulation of the queueing system is done, and it is seen that the obtained numerical $π_{loss}$ values tend to simulation results.
Stochastic processes, Markov chains, queueing theory, optimization, queue performance
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Primary Language en Mathematics, Mathematics, Applied Research Article Orcid: 0000-0002-1125-6840Author: Erdinç YÜCESOY (Primary Author)Institution: ORDU ÜNİVERSİTESİCountry: Turkey Orcid: 0000-0002-8586-1373Author: Vedat SAĞLAMInstitution: ONDOKUZ MAYIS ÜNİVERSİTESİCountry: Turkey Publication Date : June 30, 2021
 Bibtex @research article { jnt938304, journal = {Journal of New Theory}, issn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2021}, volume = {}, pages = {91 - 102}, doi = {10.53570/jnt.938304}, title = {Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System}, key = {cite}, author = {Yücesoy, Erdinç and Sağlam, Vedat} } APA Yücesoy, E , Sağlam, V . (2021). Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System . Journal of New Theory , (35) , 91-102 . DOI: 10.53570/jnt.938304 MLA Yücesoy, E , Sağlam, V . "Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System" . Journal of New Theory (2021 ): 91-102 Chicago Yücesoy, E , Sağlam, V . "Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System". Journal of New Theory (2021 ): 91-102 RIS TY - JOUR T1 - Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System AU - Erdinç Yücesoy , Vedat Sağlam Y1 - 2021 PY - 2021 N1 - doi: 10.53570/jnt.938304 DO - 10.53570/jnt.938304 T2 - Journal of New Theory JF - Journal JO - JOR SP - 91 EP - 102 VL - IS - 35 SN - 2149-1402- M3 - doi: 10.53570/jnt.938304 UR - https://doi.org/10.53570/jnt.938304 Y2 - 2021 ER - EndNote %0 Journal of New Theory Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System %A Erdinç Yücesoy , Vedat Sağlam %T Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System %D 2021 %J Journal of New Theory %P 2149-1402- %V %N 35 %R doi: 10.53570/jnt.938304 %U 10.53570/jnt.938304 ISNAD Yücesoy, Erdinç , Sağlam, Vedat . "Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System". Journal of New Theory / 35 (June 2021): 91-102 . https://doi.org/10.53570/jnt.938304 AMA Yücesoy E , Sağlam V . Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System. JNT. 2021; (35): 91-102. Vancouver Yücesoy E , Sağlam V . Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System. Journal of New Theory. 2021; (35): 91-102. IEEE E. Yücesoy and V. Sağlam , "Analysis and Simulation of a Two-Stage Blocked Tandem Queueing System", Journal of New Theory, no. 35, pp. 91-102, Jun. 2021, doi:10.53570/jnt.938304

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