An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times
This paper deals with a discrete-time $Geo/G/1$ retrial queueing system with probabilistic preemptive priority and balking customers, in which the server is subject to starting failures and replacements in the repair times may occur with some probability. If the server is found busy at an arrival ep...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-05-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/math.2020276/fulltext.html |
| _version_ | 1811325189655363584 |
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| author | Shaojun Lan Yinghui Tang |
| author_facet | Shaojun Lan Yinghui Tang |
| author_sort | Shaojun Lan |
| collection | DOAJ |
| description | This paper deals with a discrete-time $Geo/G/1$ retrial queueing system with probabilistic preemptive priority and balking customers, in which the server is subject to starting failures and replacements in the repair times may occur with some probability. If the server is found busy at an arrival epoch, the newly arriving customer either interrupts the customer in service to begin its own service with probability $p$ or enters the orbit with probability $1-p$. When an arriving customer (external or repeated) finds the server free, he must turn on the server. If the server is activated successfully, the customer receives service immediately. Otherwise, the server undergoes a repair process. If an external arrival finds that the server is under repair, he decides either to join the orbit with probability $q$ or leaves the system completely (balking) with probability $1-q$. Applying the supplementary variable method and the generating function technique, we analyze the Markov chain underlying the considered queueing model and derive the stationary distributions under different system states, the generating functions for the number of customers in the orbit and in the system, as well as some crucial performance measures in steady state. Especially, some corresponding results under special cases are directly obtained by setting appropriate parameter values. Further, some numerical examples are provided to examine the effect of various system parameters on queueing characteristics. Finally, an operating cost function is formulated to discuss numerically a cost optimization problem. |
| first_indexed | 2024-04-13T14:28:48Z |
| format | Article |
| id | doaj.art-b4a8c9930dc141a9b79d72c00aa77741 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T14:28:48Z |
| publishDate | 2020-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b4a8c9930dc141a9b79d72c00aa777412022-12-22T02:43:15ZengAIMS PressAIMS Mathematics2473-69882020-05-01554322434410.3934/math.2020276An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair timesShaojun Lan0Yinghui Tang11 School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, Sichuan, China2 School of Fundamental Education, Sichuan Normal University, Chengdu, 610066, Sichuan, ChinaThis paper deals with a discrete-time $Geo/G/1$ retrial queueing system with probabilistic preemptive priority and balking customers, in which the server is subject to starting failures and replacements in the repair times may occur with some probability. If the server is found busy at an arrival epoch, the newly arriving customer either interrupts the customer in service to begin its own service with probability $p$ or enters the orbit with probability $1-p$. When an arriving customer (external or repeated) finds the server free, he must turn on the server. If the server is activated successfully, the customer receives service immediately. Otherwise, the server undergoes a repair process. If an external arrival finds that the server is under repair, he decides either to join the orbit with probability $q$ or leaves the system completely (balking) with probability $1-q$. Applying the supplementary variable method and the generating function technique, we analyze the Markov chain underlying the considered queueing model and derive the stationary distributions under different system states, the generating functions for the number of customers in the orbit and in the system, as well as some crucial performance measures in steady state. Especially, some corresponding results under special cases are directly obtained by setting appropriate parameter values. Further, some numerical examples are provided to examine the effect of various system parameters on queueing characteristics. Finally, an operating cost function is formulated to discuss numerically a cost optimization problem.https://www.aimspress.com/article/10.3934/math.2020276/fulltext.htmldiscrete-time retrial queueprobabilistic preemptive prioritybalking customersstarting failuresreplacement |
| spellingShingle | Shaojun Lan Yinghui Tang An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times AIMS Mathematics discrete-time retrial queue probabilistic preemptive priority balking customers starting failures replacement |
| title | An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times |
| title_full | An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times |
| title_fullStr | An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times |
| title_full_unstemmed | An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times |
| title_short | An unreliable discrete-time retrial queue with probabilistic preemptive priority, balking customers and replacements of repair times |
| title_sort | unreliable discrete time retrial queue with probabilistic preemptive priority balking customers and replacements of repair times |
| topic | discrete-time retrial queue probabilistic preemptive priority balking customers starting failures replacement |
| url | https://www.aimspress.com/article/10.3934/math.2020276/fulltext.html |
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