Power law characteristics and loss probability: finite buffer queueing systems

Analytical framework based on maximum Tsallis entropy is proposed for studying finite buffer queueing system when information about fractional moment of queue size and utilization is available. The framework enables us to obtain closed form expressions for queue length distribution and loss probability for generalized M/M/1/N system when input to the system possesses power law characteristics. It is shown that queue length distribution depicts power law as the number of units in the system becomes large. A new result for asymptotic loss probability exhibiting power law behavior is derived.