Investigating a general service retrial queue with damaging and licensed units: an application in local area networks

Abstract

The idea behind queueing modeling of the proposed work originates from its applicability in various real life service systems. The performance indices obtained for the proposed model can be used to enhance the quality-of-service of many computer networks (LANs, etc.), Internet mail servers and radio communication. In these systems, packets or emails or calls are transmitted from various sources to its respective destination. During this transmission, it may be possible that a packet or an email or a call may be lost due to the effect of an unwanted unit such as ‘virus’ in computer system or ‘collision of packets’ in LANs and others. These unwanted units which force the service provider to collapse immediately are referred as ‘damaging unit’ in terms of queueing theory. This collapsed service provider is then sent for becoming renewed again by the technician present in the system, who makes it perfect after renewed process and the service provider resumes its service. The positive units (which are normal units) and the damaging units arrive to the system in Poisson fashion. We consider that the service provider furnish initial stage of compulsory service referred as ‘first stage service’ to each incoming unit while it furnish non-compulsory services (up to the number l) referred as ‘second stage service’ to only those who urge for the same. On the finish of each service or renewed process, the service provider may abandon the service system and go for break referred as vacation with a random vacation time distribution. Moreover, stochastic decomposition laws have been demonstrated for this proposed model. In addition, numerical experiments and sensitivity analysis are also carried out.