A framework based on maximization of Tsallis entropy constrained by fractional moments is proposed to model queue length distribution of number of packets in network traffic exhibiting long-range behavior. For appropriate range of the Tsallis entropy parameter q, it is found that the first moment of number of packets may not exist Based on Euler summation formula, explicit expressions for mean queue length and buffer overflow probability exhibiting power law behavior are obtained. It is shown that in the limiting case as q tends to 1, one recovers the asymptotic results for buffer overflow probability depicting Weibull-like tail.