Analytical and numerical estimates of the Weibull/M/1 and Weibull/Weibull/1 queues efficiency

At the present time network communication is an important issue where erratic human behavior plays a major role, so the problem of network server efficiency analysis comes up. However, traditional models with Poisson arrival jobs flow are not accurate enough for such cases, so G/M/1 or G/G/1 models with non-exponential distribution of inter-arrival times and either exponentially or non-exponentially distributed service time could be an alternative. Here we introduce the Weibull/M/1 and Weibull/Weibull/1 queues - single server queues where inter-arrival time follows Weibull distribution, and service time follows either exponential or Weibull distributions. We found approximate analytical and numerical efficiency estimates for these queuing systems.