Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption

Abstract

We consider a MAP/PH/1-type queueing system with server vacations as a model that is useful for the analysis of multiple access systems with polling discipline without transmission interruption. Vacation of the server corresponds to the service providing competitive information flows to the polling system. In this paper, we consider a vacation queueing model under pretty general assumptions about the probabilistic distributions describing the behavior of the system and the realistic assumption, in many real-world systems, that ongoing service cannot be terminated ahead of schedule. We derive the criterion of the stable operation of the system and the stationary distributions of the system states and the waiting time. An illustrative numerical example is presented.

A Review of Vacation Queueing Models in Different Framework

“…They performed a qualitative study of the model in steady-state through a number of system performance measures including the tail probabilities of the sojourn time for various scenarios. Very recently, Dudin et al [33] analyzed a single server MAP/PH/1-type queueing system with server vacations which is useful for the analysis of multiple access systems with pooling discipline without transmission interruption. Sakuma et al [110] considered an M/PH/1 queue with workloaddependent processing speed and vacations.…”