In this article, we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the (Formula presented.) -queue that can be modeled as a QSF process on a two-dimensional state space. In addition, we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queue, their mean sojourn time and the variance as a function of (Formula presented.) for fixed mean arrival rate.
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- Ocean Engineering
- Management Science and Operations Research
- Coxian interarrival times
- QSF process
- successively lumpable