Question

Which of the cost estimates and performance measures are not used for economic analysis of a queuing system?

• A. Cost per server per unit of time
• B. Average waiting time of customers in the system
• C. Cost per unit time for a customer waiting in the system
• D. The average number of customers in the system

Hint:

To optimize a queue's cost, remember the balancing scale formula: \[ \text{Total Cost} = (\text{Server Cost} \times \text{Servers}) + (\text{Waiting Cost Rate} \times \text{Number of Customers}) \] This makes it clear that the *number of customers* ($L_s$) is used to compute costs, rather than the *waiting time duration* ($W_s$).

Answer 1

The Correct Option is B

The total expected cost of running a queue is built from a service cost term and a waiting cost term, written as \( E(TC) = C_s c + C_w L_s \), where \( C_s \) is the cost per server, \( C_w \) is the waiting cost per customer per unit time, and \( L_s \) is the average number of customers in the system. Every quantity that goes directly into this formula, the cost per server, the cost per waiting customer, and the average number in the system, appears in the given options as 1, 3 and 4. The average waiting time \( W_s \) is certainly a useful performance measure and is linked to \( L_s \) through Little's law, but it is a time value, not a cost or a headcount, so it does not feed directly into the economic cost formula. That leaves option 2 as the one not used for the economic analysis.