Final answer:
Customers in a process without variability only experience waiting times when demand exceeds capacity. The exponential distribution is often used to model the time between events, such as customer arrivals, and can be analyzed for probabilities of different arrival intervals. The queuing system's efficiency can be statistically tested to determine if it leads to lower waiting times.
Step-by-step explanation:
In a process without variability, customers experience waiting time only when demand is greater than capacity. This situation can be imagined like a checkout line in a store where the service rate is constant. If customers arrive on average every two minutes, and they are being served at a rate that matches this arrival rate, they will not wait as long as there is an open service point when they arrive. However, if more customers arrive, causing the demand to exceed the store's capacity to serve them, the customers will start to queue and experience waiting times.
For example, if an average of 30 customers per hour arrive at a store, we expect on average one customer every two minutes. If the store first opens, it would take six minutes on average for three customers to arrive, as per Solution 5.11. However, if customers arrive less frequently, such as less than one minute apart, the probability will be determined by the exponential distribution's memoryless property. On the other hand, if customers arrive more than five minutes apart, determining this probability also involves understanding the specific distribution being used.
Real-world scenarios may require more complex models to account for variations in customer arrivals, as a single customer arrival assumption may not always hold. The effectiveness of queuing systems, such as whether a single line results in lower variation among waiting times, can be tested using statistical methods and a certain level of significance, for example, 5 percent.