Final answer:
The average waiting time increases exponentially as utilization levels rise due to compounding delays as resources become increasingly strained.
Step-by-step explanation:
The average waiting time grows at an exponential rate as utilization grows.
An organization's average waiting time is directly affected by its level of utilization, mirroring patterns seen in population dynamics. In scenarios where resources such as time or space are being consumed by incoming entities like customers or data packets, the waiting time between events can be well-characterized by the exponential distribution. This pattern correlates with how population sizes increase when conditions are ideal. Initially, the growth is slow, but as more entities arrive or are being served, the cumulative demand for resources grows. This increase leads to longer waiting times and can follow an exponential trend, as every increase in utilization further strains the availability of resources, compounding the delays.
Similarly, in the context of population dynamics, exponential growth signifies a situation where the growth rate is proportionate to the current population, resulting in the population doubling at regular intervals. The phenomenon continues unless a limiting factor, akin to reaching maximum capacity in a service environment, causes a shift to logistic growth where the rate of growth will eventually slow and level off.