Browsing by Author "Tsoukatos, K.P."
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Item Heavy Traffic Analysis for a Multiplexer Driven by M|GI|Input Processes(1996) Tsoukatos, K.P.; Makowski, Armand M.; ISRWe study the heavy traffic regime of a multiplexer driven by correlated inputs, namely the M|GI|input processes of Cox. We distinguish between M|GI|processes exhibiting short or long- range dependence, identifying for each case the appropriate heavy traffic scaling that results in non-degenerate limits. As expected, the limits we obtain for short-range dependent inputs involve the standard Brownian motion. Of particular interest though are our conclusions for the long-range dependent case: The normalized queue length can be expressed as a function not of a fractional Brownian motion, but of some other stable non -- Gaussian self-similar process. Thus, the M|GI|processes serve as an example demonstrating that, within long-range dependence, fractional Brownian motion does not assume the ubiquitous role that its counterpart, standard Brownian motion, plays in the short-range dependence setup, and that modeling possibilities attracted to non -- Gaussian limits are not so hard to come by.Item Heavy Traffic Limits Associated with M|GI|Input Processes(1997) Tsoukatos, K.P.; Makowski, Armand M.; ISR; CSHCNWe study the heavy traffic regime of a discrete-time queue driven by correlated inputs, namely the M|GI|input processes of Cox. We distinguish between M|GI|processes with short- and long- range dependence, identifying for each case the appropriate heavy traffic scaling that results in non-degenerate limits. As expected, the limits we obtain for short-range dependent input involve the standard Brownian motion. Of particular interest are the conclusions for the long-range dependent case: The normalized queue length can be expressed as a function not of a fractional Brownian motion, but of an a-stable, 1/a self-similar independent increments levy process. The resulting buffer asymptotics in heavy traffic display a hyperbolic decay, of power 1 - a. Thus M|GI|processes already demonstrate that, within long-range dependence, fractional Brownian motion does not necessarily assume the ubliquitous role that standard Brownian motion plays in the short-range dependence setup.