Quantitative Methods for Business

Queuing Theory

1. At a large Naval Ship Repair Facility mechanics have to make frequent trips to the tool crib for parts and specialized equipment. Records indicate that the tool crib serves an average of 18 mechanics each hour, and currently one attendant is available who can serve 20 per hour.

• a-Find the operating characteristics of the system.
• b-Find the probability of having 2 customers in the system at any time.

2. At a large Naval Ship Repair Facility mechanics have to make frequent trips to the tool crib for parts and specialized equipment. Records indicate that the tool crib serves an average of 18 mechanics each hour, and currently two attendants are available each can serve 20 per hour.

• a-Find the operating characteristics of the system.
• b-Find the probability of having 1 customer in the system at any time.
• c-Find the probability of having 3 customers in the system at any time.
• d-Find the probability an arriving unit will have to wait.

3-At a post office, customers arrive at an average rate of 18 customers per hour following a Poisson distribution. The store currently has one clerk who can service an average rate of 20 customers per hour (assume Exponential distribution).

If the manger is considering adding an extra attendant to improve the system performance. If a clerk is paid $30 per hour while customer waiting is estimated at $20, would it be more cost effective to have one or two clerks at the office?

4-A hotel is considering changing its waiting line system. In the current system, hotel guests divide themselves equally between the lines that form in front of 3 hotel clerks. The manager is considering having hotel guests wait in one line and then proceed to the next available clerk. If average service time is 6 minutes and the average number of arrivals per hour is 24 guests.

Which system do you propose?