Abstract: In a random service system, people focus on decreasing system's cost and improving service rates. Based on the above purpose, this paper introduces the threshold and vacation interruption strategies into a discrete time GI/Geo/1 working vacation queue. Firstly, the two-dimensional embedded Markov chain before customers arrival instant is established, its transition probability matrix of GI/M/1-type is obtained. Secondly, the stationary queue length distribution is derived by the matrix analysis method, and the expected queue length and mean sojourn time are expressed. Finally, numerical analysis for the performance indices of the system are presented using the Matlab software, which shows that the expected queue length and sojourn time are both increasing with the increase of a threshold but decreasing with the increase of working vacation rates. It is expected that the results obtained here would provide some useful information for the research of SVC systems and wireless networks.

Key words: threshold, GI/Geo/1, multiple working vacations, matrix analysis