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A maximum entropy framework based on Tsallis entropy is proposed to depictlong tail behavior of queue lengths in broadband networks. Queue lengthexpression as measured in terms of number of packets involves Hurwitz-zetafunction. When the entropy parameter q in Tsallis entropy is less than unity,the distribution of packets yields power law behavior. In the limit q tendingto unity, Tsallis entropy expression reduces to one due to Shannon andwell-known results of M/M/1 queuing system are recovered. Relationship betweenTsallis entropy parameter q and Hurst parameter H (measure of self-similarity)is postulated. A numerical procedure based on Newton-Raphson method is outlinedto compute Lagrange's parameter b. Various relationships between trafficintensity r and Lagrange's parameter b are examined using data generated frommean number of packets from storage model due to Norros. It is found that bestfit corresponds to r being a linear combination of decaying exponential andpower exponent in b for different values of entropy parameter q. Explicitexpression for the probability that queue size exceeds a certain value isderived and it is established that it asymptotically follows power law for qless than one. The system utilization shows an interesting behavior when theparameter r is varied. It attains lower values than that of M/M/1 system forsmaller values of r whereas situation reverses for higher values of r.

Long Tail Behavior of Queue Lengths in Broadband Networks: Tsallis Entropy Framework