On inference concerning time-dependent queue performance: The M/G/1 example (Q914269)

The paper deals with easily-computed approximations to the finite-time expected waiting time for an M/G/1 system starting from an empty state. Both unsaturated \((\rho <1)\) and saturated \((\rho >1)\) conditions are considered. Numerical evidence is presented to indicate that the quality of the approximations is usefully good, especially when ease of computation is an issue. Further, the methodology is adapted to assess expected waiting times when inference must be made from a random sample of service times, and the decision is made to do so nonparametrically, i.e. without fitting a specific function. The results appear reasonable and potentially useful, and are not burdensome to obtain. The methodology investigated can also be applied to a variety of queueing models that are close siblings of M/G/1: priority and breakdowns and ``vacations'' being examples.