CMA Intermediate · Operations Management and Strategic Management · Scheduling and Queuing Models
A bank branch has 3 tellers working as an M/M/3 system. Customers arrive at an average of 20 per hour and each teller serves an average of 10 customers per hour. What is the utilisation factor of the system (ρ = λ/sμ)?
The utilisation factor is arrivals divided by total service capacity: 20 ÷ (3 × 10) = 0.67. The system is stable because this is below 1. Using λ/μ = 2 ignores that three tellers serve in parallel, which gives the wrong figure.
- A2.00
- B0.67Correct
- C0.33
- D0.50
Explanation
ρ = λ/(sμ) = 20/(3 × 10) = 20/30 = 0.67. The value 2.00 is λ/μ, which ignores the number of channels. The value 0.33 would result from dividing by 60 (3 × 20) wrongly using λ as the service rate base.
Did you get it right without looking?
One question tells you little. A timed set on Scheduling and Queuing Models shows your real accuracy, how long you take and where you lose marks.
More Scheduling and Queuing Models questions
- Four jobs are waiting at one machine with processing times (days) and due dates (days from today): A (4, 6), B (2, 9), C (6, 8), D (3, 5). J…
- Mehta Fabricators receives an order that must be delivered on 30 June. The planner starts from 30 June and works back through each operation…
- In Johnson's rule for sequencing n jobs through two machines (M1 then M2), which step correctly describes how the optimal sequence is built?
- In production scheduling, a Gantt load chart is primarily used to show which of the following?
- In the standard M/M/1 queuing model, the first M, the second M and the 1 respectively describe:
- Johnson's rule gives an optimal sequence for which of the following situations?