Final answer:
The primary characteristic of an M/G/I queue with bulk arrivals is b. Poisson arrivals, where arrivals are modeled by a Poisson process and inter-arrival times are exponentially distributed.
Step-by-step explanation:
The primary characteristic of an M/G/I queue with bulk arrivals at a rate λ is b. Poisson arrivals. The 'M' indicates that the arrival of entities into the system follows a Poisson process, meaning that the time between arrivals is exponentially distributed.
Given the assumption that an average of 30 customers per hour arrive at a store, and if the time between arrivals is exponentially distributed, we can determine probabilities related to customer arrivals using properties of the exponential distribution. For example, we can calculate the probability of the next customer arriving within a certain time frame after the previous customer.
The exponential distribution is characterized by its memorylessness, meaning that the probability of an event occurring in the future is not affected by how much time has already elapsed. As such, the exponential distribution is closely related to the Poisson distribution, where the rate of events per unit of time (λ) is the reciprocal of the mean time between events in the exponential distribution (μ).