Transient Analysis of a Modified Differentiated Vacation Queueing System for Energy-Saving in WiMAX

A modified differentiated vacation queueing system with a close-down period and impatient customers is investigated in this research paper. The proposed model can be applied to study the energy management mechanisms of WiMAX and tethered high altitude platform (HAP) systems. In this system, the WiMAX mobile station (MS) switches to a close-down period for a random duration at the end of the busy period. At the end of the close-down period, if the system is non-empty, the MS switches to a functional state. Otherwise, the MS takes an ordinary vacation. The MS switches to a working vacation (WV) if the system is empty at the end of the ordinary vacation period. Jobs arriving during the WV are served at a slower service rate. Jobs may become impatient in any state of the system except during the regular busy period. Explicit expressions for the transient and steady-state probabilities of this system are obtained using continued fraction and confluent hypergeometric functions. Furthermore, performance indices such as mean, variance, average abandonment rate, and system throughput are computed. Finally, a cost-profit analysis and graphical illustrations are provided.