Monte Carlo simulation of queues is used when

Monte Carlo simulation of queues is used when Correct Answer mathematical analysis cannot be adopted

Explanation:

Monte Carlo Simulation for Queueing

• The Monte Carlo technique is quite useful for analyzing waiting line problems which are difficult or impossible to be analyzed mathematically.
• Simulated Sampling Method (SSM), helpful when first come, first served assumption is not valid for a particular queue.
• In many cases, the observed distribution of arrival times and service time can not be fitted to a certain mathematical distribution (Poisson and exponential distribution) and the Monte Carlo SSM is the only hope. 
• Multiple queues condition of arrival in one queue and departure from different queues is also well handled by the Monte Carlo SSM.
• SSM consist of replacing the actual universe of the item with its theoretical counterpart, which is the universe described by some assumed probability distribution.
• A random number table is then used for sampling from this theoretical population. Such SSM is called the Monte Carlo Method.

​Monte Carlo Method Advantages

• Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making.
• Computerization use makes easy storage and retrieval of a large amount of data for months and years.
• Manipulation of those factors which can be controlled. (i.e. simulating)
• Monte Carlo simulation performs risk analysis by building models of possible results by uncertainty. 
• It then calculates results over and over, each time using a different set of random values from the probability functions.
• Monte Carlo simulation helps the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action.

Queuing theory

• Queuing theory is the mathematical study of waiting for a queue.
• A queueing model is constructed so that queue lengths and waiting times can be predicted.
• Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.