Institute of Mathematics > Departments > Stochastic models in engineering science > Public relations > Queueing system with control

In the previous section "Design of queuieng systems" it was shown in an analytical example how performance parameters of a queuing system, such as the average number of customers in the system, can be influenced by the basic design.

In this section we will show by simulation that the service process can be improved significantly by small control measures of the operating strategy. Therefore three different operating models were generated for simulation. They can be described in detail as follows:

- There are two parallel servers. Upon arrival, customers are evenly distributed (i.e. 50% per queue) on the queues, regardless of how many customers are already in the queue. This model is referred to as the uncontrolled standard case.
- As in the model a) here also two parallel servers are available. Customers are however divided on the principle of the shortest queue, that is, an incoming customer is assigned to the queue with the least waiting customers. This model will be referred to as model with control.
- There is only one queue and one operator, but this operator works at double speed. This model is the reference model, which was the best model in the previous section.

A simulation run was started with the same parameters as in the previous section and was ran until the various systems have approached their steady states sufficiently. A comparison in terms of average number of customers in the system, mean waiting time and mean variance of the waiting time clearly shows that the uncontrolled system can improve its performance by adding a simple control mechanism. These dramatic improvements can easily be interpreted based on the course of the variance over the time. By the improving measures equally large queues arise and thus uniform waiting times apper. The variance of the waiting time decreases significantly. Both servers are busy constantly to 90% in the steady state of the system.