Time dependent of M/M/c/N an with discouragement arrivals and retention of impatient customers
البيومي, Ù. (2019). Time dependent of M/M/c/N an with discouragement arrivals and retention of impatient customers. EKB Journal Management System, 22(1), 27-43. doi: 10.21608/jsfc.2019.244578
مهدي البيومي. "Time dependent of M/M/c/N an with discouragement arrivals and retention of impatient customers". EKB Journal Management System, 22, 1, 2019, 27-43. doi: 10.21608/jsfc.2019.244578
البيومي, Ù. (2019). 'Time dependent of M/M/c/N an with discouragement arrivals and retention of impatient customers', EKB Journal Management System, 22(1), pp. 27-43. doi: 10.21608/jsfc.2019.244578
البيومي, Ù. Time dependent of M/M/c/N an with discouragement arrivals and retention of impatient customers. EKB Journal Management System, 2019; 22(1): 27-43. doi: 10.21608/jsfc.2019.244578

Time dependent of M/M/c/N an with discouragement arrivals and retention of impatient customers

المجلة العلمية لقطاع کليات التجارة بجامعة الأزهر
Article 3, Volume 22, Issue 1, June 2019, Page 27-43  XML PDF (155.58 K)
Document Type: المقالة الأصلية
DOI: 10.21608/jsfc.2019.244578
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Author
مهدي البيومي email
کلية التجارة بنات بالدقهلية - جامعة الأزهر - طريق النصر - أمام قاعة المؤتمرات - مدينة نصر - القاهرة الرقم البريدي / 11751
Abstract
In this paper, the matrix technique is employed to attain transient solution of a finite capacity multi-servers Markovian queue having discouraged arrivals, retention and reneging of reneged customers. We consider the cases where both service times and the inter-arrival follow the exponential distribution. The time dependent solution of the system is expressed by using the eigenvalues of a symmetric tridiagonal matrix. As a reneged customer can be preserved in a lot of cases by utilizing definite convincing mechanisms to keep on queue for completion of service, it follows that a reneged customer can keep hold of the queuing system with chance. Otherwise, customer may leave the queue without getting a service with probability (+=1). Laplace transforms of governing equations system are expressed in matrix forms. Moreover, employing the characteristics of symmetric tridiagonal matrices, and the steady state probabilities are gained. Finally, some queuing models are derived as special cases of this system.
Keywords
Reneging; retention of reneged customers; transient solution; Discouraged arrivals
References
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