Analysis of a Multiple M/M/1/DV Queueing System with a Dual-Threshold Policy, Vacation Interruption and a Waiting Server

An M/M/1/DV queueing system with a dual-threshold policy, vacation interruption and a waiting server are analysed in this paper. Power-saving mechanisms (PSM) of WiMAX could be modelled using this model. In the investigated model, after transmitting all the data frames in the awake state, the server switches to the sleep state for some random duration of time T1. After the expiry of time T1, if no data frame is waiting for service, the server switches to another state called the listening state and activates a timer T2. Both the sleep state and the listening state can be interrupted when the system size reaches two predefined threshold values of k1 and k2, respectively. An explicit expression for a transient and steady-state solution is obtained for the investigated model. Furthermore, performance indices like the mean, variance of the system size, system size probabilities and system throughput are computed. Finally, cost–profit analysis and numerical illustrations are depicted to investigate system behaviour.