Final answer:
To determine the maximum customer arrival rate for a balanced line in a queuing situation, we must consider the service rate, the average processing time at the bottleneck, and the variability of processing times. An arrival rate of 30 customers per hour requires using the exponential distribution for calculation of wait times and probabilities in this M/G/1 queuing model.
Step-by-step explanation:
To find the maximum customer arrival rate that the balanced line with five workers can accommodate while keeping the average customer waiting time below five minutes using the M/G/1 queuing model, we analyze several pieces of information:
- The service rate of the balanced line which determines how quickly each of the five workers can process a customer.
- The average processing time of the bottleneck station is vital as it will determine the maximum throughput of the system.
- The coefficient of variation provides a measure of the relative variability of the processing times at Station 1 and can influence the queue dynamics.
Based on the given scenario that one customer arrives on average every two minutes, this translates to an arrival rate of 30 customers per hour. Using an exponential distribution to model these arrival times, we can calculate the required statistics such as average wait times and probabilities.
For example, the probability that it takes more than five minutes for the next customer to arrive, if arrivals are evenly spaced, can be found using the exponential distribution and is equivalent to e-λt, with λ being the arrival rate and t being the time.