Reliability analysis of a retrial queueing systems with collisions, impatient customers, and catastrophic breakdowns

摘要

A lot of different real-life systems can be modeled by retrial queuing (RQ) models. In this paper, RQ-systems are considered. The single server system is non-reliable, non-deterministic system failures might occur. This is a finite source system. In applications, it is more realistic, and there is no stability problem. One of the first considered system operational characteristics is the collision or the conflict of customers. When a job is under service at the server, and a new job comes, they will collide. In this case, both jobs will transport to a virtual waiting room, called orbit. The customers retry their requests from the orbit. The retrial times are random. Server failures might happen, the server might go down. While the server is down state, the new requests are transported to the orbit, or the source is blocked, that is, no customer can enter into the system. The second system characteristic is the impatient property of the customers. The customers stay in the orbit and waiting for their service. After a non-deterministic time-interval, a customer gives up retrying and leaves the system. These customers will be lost from the system, they remain unserved. This is the impatient characteristic. The third system characteristic is the catastrophic breakdown. It means, that in case of a negative event, all of the customers at the server and in the orbit leave the system, and take their places in the source. The novelty of this paper is to investigate the phenomenon of the catastrophic breakdown in a collision environment with impatient customers. This impatient property results, that the recursive algorithm for the time-independent probabilities can not be formulated. MOSEL-2 tool can be used for solving the system equations and calculating the system performance measures. These measures are, for example, the average sojourn time and other reliability metrics. The main goal is to investigate the effect of the impatient property under catastrophic breakdown. Numerical results are presented graphically, as well.