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Time Dependent of an M / M / C / N with Discouragement Arrivals and Retention of Impatient Customers

المصدر: المجلة العلمية لقطاع كليات التجارة
الناشر: جامعة الأزهر - كلية التجارة
المؤلف الرئيسي: El – Paoumy, M.S. (Author)
المجلد/العدد: ع22
محكمة: نعم
الدولة: مصر
التاريخ الميلادي: 2019
التاريخ الهجري: 1441
الشهر: يونية
الصفحات: 27 - 43
DOI: 10.21608/jsfc.2019.244578
ISSN: 2636-3674
رقم MD: 1301210
نوع المحتوى: بحوث ومقالات
اللغة: الإنجليزية
قواعد المعلومات: EcoLink
مواضيع:
كلمات المؤلف المفتاحية:
Reneging | Retention of Reneged Customers | Transient Solution | Discouraged Arrivals
رابط المحتوى:
صورة الغلاف QR قانون
حفظ في:
المستخلص: 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 chanceq. Otherwise, customer may leave the queue without getting a service with probability p (p +q =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.

ISSN: 2636-3674

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