The diagram shows that if the number of arrivals increases from 350 arrivals per hour to 400 arrivals per hour (15 % increment), the waiting time increases from 24 seconds to 90 seconds (375 % increment) and goes from there on in the steady state quickly to infinity, because the waiting lines get endless long. If the arrival rate is increased step-wise from 100 to 450, Figure 2 indicates that there is some qualitative moment of change where the waiting time increases dras- tically and leads to infinite waiting times. In accordance with the amount of five servers and the given service time distribution with a mean value of 41,6 seconds and an arrival rate with a mean value of 250 arrivals per hour, a utilization rate of around 80 % in steady state can be measured under the boundary condition that the amount of waiting people has not an effect on the service time. On the right hand side of the figure, the amount of waiting customers are depicted in the upper diagram and the utilization rate of the servers are shown over time. The arrival process and the service rate are Poisson distributed. The set-up consists of five servers and a single queue in front of the servers.
In Figure 1, a snapshot of a M/M/5 -queuing-system-simulation is shown.
#RELATIONSHIP BETWEEN WIP AND WIPQ QUEUING THEORY SOFTWARE#
The Java-based software Anylogic is used here for the simulation of pedestrian queuing. And thirdly, simulation enables to endogenize key factors and therefore to push the model boundary forward. Secondly, in case of pedestrian queuing situations, the physical layout of the queuing environment – the servicescape – can be taken into account, leading to minor delays, if a walking distance from the end of the queue to the server is necessary. First of all, different from the analytic approach, simulation enables the generation of benchmarks for more complex queuing situations (e.g. Finally, in respect of the research topic, Kendall’s notation may have contributed to the erroneous assumption that the amount of waiting people and the service time distribution are in each case two independent variables. Simulation enables to take into account more dynamic arrival patterns or variations of the service time or to endogenize these key factors. Therefore, the formulas are helpful to get some quick benchmarks on how the queuing system would perform under the given narrow model boundary constrains, but taking into account more realistic sce- narios with variations of the arrival pattern, the analytic approach is of limited help, if an overall evaluation is necessary and thus there is need for simulation. Firstly, Kendall’s notation includes the steady state assumption, as the arrival process and the service time distribution remain constant.
Although it is of scientific value to solve queuing systems mathematically, some managerial implications remain especially in the domain of pedestrian queuing situations. approach as their hammer saw every waiting time prob- lem as a nail, nevertheless which limitations this approach embrace.