Transient Analysis of a finite capacity Markovian queuing system with feedback, discouraged arrivals and retention of reneged customers | ||
| المجلة العلمية لقطاع کليات التجارة بجامعة الأزهر | ||
| Article 9, Volume 16, Issue 2, 2016, Pages 1-13 PDF (415.43 K) | ||
| Document Type: المقالة الأصلية | ||
| DOI: 10.21608/jsfc.2016.39233 | ||
| Author | ||
| M.S . El – Paoumy | ||
| Department of Statistics, Faculty of Commerce, Al-Azhar University, Girls' Branch, Dkhlia , Egypt | ||
| Abstract | ||
| This paper analyze a finite capacity Markovian feedback queue with discouraged arrivals, reneging and retention of reneged customers in which the inter-arrival and service times follow exponential distribution. The transient solution of the system, with results in terms of the eigenvalues of a symmetric tri-diagonal matrix. Feedback in queuing literature represents customer dissatisfaction because of inappropriate quality of service. In case of feedback, after getting partial or incomplete service, customer retries for service . After the completion of service , each customer may rejoin the system as a feedback customer for receiving another regular service with probability 1 or he can leave the system with probability 1 q ( 1 1 q 1 ). A reneged customer can be retained in many cases by employing certain convincing mechanisms to stay in queue for completion of service. Thus, a reneged customer can be retained in the queuing system with probability 2 q or he may leave the queue without receiving service with probability 2 ( 2 2 q 1 ). Expressing the Laplace transforms of the system of governing equations in matrix form and using the properties of symmetric tri-diagonal matrices, the steady state probabilities are derived and some important queuing models are derived as special cases of this model. | ||
Highlights | ||
Transient Analysis of a finite capacity Markovian queuing system | ||
| Keywords | ||
| Transient Analysis of a finite capacity Markovian queuing system feedback; discouraged arrivals retention of reneged customers | ||
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