STABILITY AND STRUCTURAL-PROPERTIES OF STOCHASTIC STORAGE NETWORKS

We establish stability, monotonicity, concavity and subadditivity prop erties for open stochastic storage networks in which the driving proce ss has stationary increments. A principal example is a stochastic flui d network in which the external inputs are random but all internal how s are deterministic. For the general model, the multi-dimensional cont ent process is tight under the natural stability condition. The multi- dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content proces s is monotone in its initial conditions. Hence, when any content proce ss with non-zero initial conditions hits the origin, it couples with t he content process starting at the origin. However, in general, a tigh t content process need not hit the origin.