Mathematical modelling and performance analysis of single server queuing system - eigenspectrum

Classical queuing theory is playing vital role to study and analyse the performance analysis of real-time servicing systems, production inventory and manufacturing systems, telecommunication systems, modern information and communication technology systems and computing sector. In recent decays, bounded and immeasurable queues have been intensively studied; due to its attractive mathematical features with wide spread applicability. Such a system describes units of work, e.g., particles or customers, arriving at a resource, that stay present for some random duration that is independent of other customers. The aim of this paper is to evaluate the performance measures with a single server queuing system. Mathematical model has been developed to study the probability live time of the server using algebraic eigenproperties. These models are indispensable in real-time systems, manufacturing and communication queuing systems, including wireless networks, mobility, and randomly arriving traffic.