Final answer:
The assertion in the question is false because it doesn't consider the non-uniform arrival of customers and variations in demand throughout the day. Moreover, self-scan aisles affect the cashier-to-lane ratio. The lanes should be modeled taking into account actual arrival patterns and the system's potential saturation points.
Step-by-step explanation:
The question relates to the modeling of checkout lanes in a grocery store. The assertion that multiple checkout lanes with one cashier each should be modeled using the overall arrival rate to all lanes, equating the number of lanes to the number of workers, is false. It does not account for the fact that customers may not arrive evenly across all lanes or at a constant rate throughout the day. Moreover, the presence of self-scan aisles, where one cashier can oversee multiple aisles, also affects how the lanes should be modeled, as this changes the cashier-to-lane ratio.
When collecting data to model such systems, one must consider both the average time between arrivals and any variations in the arrival patterns. For instance, while it might take on average six minutes for three customers to arrive, if customers arrive in groups or there are peak and off-peak periods, the arrival rate can fluctuate significantly. Moreover, to test the efficacy of different checkout systems, one could collect data on wait times and use statistical methods to analyze whether a single line leads to lower variation among waiting times for customers.
An analogy using taxis illustrates the concept of arrival rate saturation, which might be similar in a grocery store's checkout lanes. The analogy helps to understand how the system's throughput is determined both by the number of service points (lanes or cashiers) and the arrival rate of customers. Beyond a certain point, adding more cashiers won't decrease waiting times if the arrival rate doesn't match.