Question

A document clerk earns 15/hour, processes an average of 5 documents per hour throughout the workday, and receives documents at the rate of 4 per hour. There is a cost of waiting for the documents (by an office paralegal) of 25.00 per hour. For this problem, the mean or average service rate is mu = 5 documents per hour, and the mean or average arrival rate is lambda = 4 documents per hour. The law firm is interested in knowing the operating characteristics of this waiting line system, such as the average time a document spends in the waiting line, the number of documents in the waiting line, the utilization rate of the document clerk, the probability of 3 documents in the system, and the cost of the system. What are the operating characteristics of this waiting line system?

Answer 1

The operating characteristics of this waiting line system can be calculated using queuing theory. Key characteristics include the average time a document spends in the waiting line, the number of documents in the waiting line, the utilization rate of the document clerk, the probability of 3 documents in the system, and the cost of the system.

Step-by-step explanation:

The operating characteristics of this waiting line system can be calculated using queuing theory. Here are the key operating characteristics:

1. Average time a document spends in the waiting line: This can be calculated using the Little's Law, which states that the average waiting time (W) equals the average number of documents in the system (L) divided by the average arrival rate (λ). In this case, L = λW, so W = L / λ.
2. Number of documents in the waiting line: This can be calculated using the queuing theory formulas. In this case, the number of documents in the system (L) equals the average arrival rate (λ) multiplied by the average waiting time (W). So, L = λW.
3. Utilization rate of the document clerk: This can be calculated by dividing the average service rate (μ) by the arrival rate (λ). So, utilization rate = μ / λ.
4. Probability of 3 documents in the system: This can be calculated using the queuing theory formulas. In this case, the probability of having 3 documents in the system (P3) equals (1 - utilization rate) multiplied by the utilization rate to the power of 3. So, P3 = (1 - utilization rate) * utilization rate^3.
5. Cost of the system: The cost of the system includes the cost of waiting for the documents by the office paralegal and the cost of the document clerk. The cost of waiting can be calculated by multiplying the cost per hour of waiting by the average waiting time. The cost of the document clerk can be calculated by multiplying the hourly rate by the utilization rate.