Mean Queue Size in a Queue With Discrete Autoregressive Gaussian Process Arrivals of Order P

The class of Gaussian processes is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space, or time and space. The popularity of such processes stems primarily from two essential properties. First, a Gaussian process is completely determined by its mean and covariance functions. This property facilitates model fitting as only the firstand second-order moments of the process require specification. Second, solving the prediction problem is relatively straightforward. The best predictor of a Gaussian process at an unobserved location is a linear function of the observed values and, in many cases; these functions can be computed rather quickly using recursive formulas. We consider a discrete time dual server queuing system queuing networks with negative customers, signals, triggers where they arrive Gaussian process of order p (DAR(P)/D/s, and the service time of a customer is one slot. In contrast with the normal positive customers, negative customers arriving to a non-empty queue remove and work from the queue For this queuing system, we give an expression for the mean queue size. Further we propose approximation methods for the mean queue size which is based on matrix method.