Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application

Models To Estimate Arrival Counts And Staffing Requirements In Nonstationary Queueing Systems Applied To Long Distance Road Races

We examine the problem of staffing refreshment stations at a long distance road race. A race is modeled as a mixed queueing network in which the required number of servers at each service station has to be estimated. Two models to represent the progress of runners along a long distance road race course are developed. One model is a single-class model that allows a road race manager to staff service stations assuming the runners are identical to those in some historical dataset. Another model is a multi-class simulation model that allows a road race manager to simulate a race of any number of runners, classified based on their running pace into different runner classes. Both the single-class model and the multi-class model include estimates for the rates at which the runners arrive at specified locations along the course. The arrival rates, combined with assumed service rates, allow us to base staffing decisions on the Erlang loss formula or a lesser known staffing rule that gives a lower bound for the required number of servers. We develop a staffing strategy that we call the Peak Arrival Staffing Bound (PASB), which is based on this staffing bound. The PASB and the Erlang loss formula are implemented in the single-class model and the multi-class simulation model. By way of numerical experiments, we find that the PASB is numerically stable and can be used to get staffing results regardless of the traffic intensity. This finding is in contrast to the Erlang loss formula, which is known to become numerically unstable and overflows when the traffic intensity exceeds 171. We compare numerical results of the PASB and the Erlang loss formula with a blocking probability level of 5% and find that when iii the traffic intensity is high, staffing results based on the PASB are more conservative than staffing results based on the Erlang loss formula. As the traffic intensity gets lower, we find that staffing results based on the PASB are similar to staffing results based on the Erlang loss formula. These findings suggest that the PASB can be a valuable tool to aid race directors in making staffing decisions for races of all traffic intensitie

Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application

Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application.Queueing Sojourn time Feedback Blood testing