Internet-type queues with power-tailed interarrival times and computational methods for their analysis

Internet traffic flows have often been characterized as having power-tailed (long-tailed, fat-tailed, heavy-tailed) packet interarrival times or servi ce requirements. In this work, we focus on the development of complete and computationally efficient steady-state solutions of queues with power-taile d interarrival times when the service times are assumed exponential. The cl assical method for obtaining the steady-state probabilities and delay-time distributions for the G/M/1 (G/M/c) queue requires solving a root-finding p roblem involving the Laplace-Stieltjes transform of the interarrival-time d istribution function. Then the exponential service assumption is combined w ith the derived geometric arrival-point probabilities to get both the limit ing general-time state and delay distributions. However, in situations wher e there is a power tail, the interarrival transform is typically quite comp licated and never analytically tractable. In addition, it is possible that there is only a degenerate steady-state system-size probability distributio n. Thus, an alternative approach to obtaining a steady-state solution is ty pically needed when power-tailed interarrivals are present. We exploit the exponentiality of the steady-state delay distributions for the G/M/1 and G/ M/c queues, using level-crossings and a transform approximation method, to develop an alternative root-finding problem when there are power-tailed int erarrival times. Extensive computational results are given.