Comparison of buffer usage utilizing single and multiple servers in network systems with power-tail distributions

Date of Completion

January 1997


Computer Science




We present the results of a parametric study of the buffer size needed to prevent overflow or loss in single and multiple server systems where data arrivals or service times are "bursty", "self-similar", or "fractal". Such erratic behavior can be caused (or adequately described) by renewal processes whose interarrival distributions are power-tail (or Pareto, or Levy, or "long-tail") with infinite variance. Power tail distribution functions behave as $1-F(x)\Rightarrow1/x\sp{\alpha}$ for large x. We show that power tails can cause problems for intermediate values of the utilization parameter, $\rho,$ and become very serious (beyond the usual $1/(1-\rho)$ factor) when $\rho$ is close to 1, and/or when $\alpha$ approaches 1. For systems with a power-tail arrival distribution and multiple servers (PT/M/C), we gain no performance increase by utilizing multiple exponential servers. However, for systems with a Poisson arrival rate and power-tail service times (M/PT/C), the improvement by using multiple, slower servers over a single faster one can be great indeed. ^