Transient Solution of Two –Class priority Queuing System with Balking and Catastrophes | ||
| Scientific Journal for Damietta Faculty of Science | ||
| Volume 13, Issue 2, 2023, Pages 84-94 PDF (541.93 K) | ||
| Document Type: Original articles | ||
| DOI: 10.21608/sjdfs.2023.175105.1067 | ||
| Authors | ||
| rehab G ElQady* 1; Ahmed Tarabia2; Ghadeer Alshreef3 | ||
| 1Al Baylouq, Aga, Dakahlia Governorate | ||
| 2Mathematics Department, Faculty of Science, Damietta University | ||
| 3Department of Mathematics, Faculty of Science, Damietta University | ||
| Abstract | ||
| The present paper investigates the transient solution of two- class priority queuing system with balking and catastrophes. We discuss priority queuing system with two-class priority (high and low) with balking and catastrophes where balking is for high class priority and catastrophes for all the system. We consider a single server queuing system serving two types of customers say class-1 and class-2, each having its own respective line and the arrival process for both types is state independent. A higher priority is assigned to class-1 and a low priority to class-2. Suppose that the service rule within each class is FIFO and the priority system is preemptive resumed, i.e. during the service of a low priority customer, if high priority customers joins the system, then the low priority customer’s service is interrupted and will be resumed again when there is no high priority customers in the system. On arrival a customer either decides to join the queue of the class-1 with probability one if the number of customers in the class-1 is less than a threshold value k. If there are k customers or more ahead of him, then he joins the queue with probability β and may balk with probability (1- β). The capacity of the system is infinite. When the system is idle or busy, catastrophes may occur at the service station according to Poisson process of rate .Whenever a catastrophe occurs at the busy. Moreover, we discuss some special cases. | ||
| Keywords | ||
| Queueing; Queue length; Generating function; Catastrophe | ||
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