Analysis of an SSP/G/1 system with multiple vacations and E-limited service discipline

Many researchers have studied variants of queueing systems with vacations. Most of them have dealt with M/G/1 systems and have explicitly analyzed some of their performance measures, such as queue length, waiting time, and so on. Recently, studies on queueing systems whose arrival processes are not Poissonian have appeared. The authors consider a single server queueing system with multiple vacations and E-limited service discipline, where messages arrive to the system according to a switched Poisson process. First, they consider the joint probability density functions of the queue length and the elapsed service time or the elapsed vacation time. The authors derive the equations for these pdf’s, which include a finite number of unknown values. Using Rouché’s theorem, they determine the values from boundary conditions. Finally, the authors derive the transform of the stationary queue length distribution explicitly.