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

Concept: The economic optimization of a service facility using queuing models relies on minimizing the Total Expected Cost ($E(TC)$) of the operation. This economic trade-off model balances two competing financial components: 1. The operational cost of providing service (paying for active service capacity/channels). 2. The cost of customer dissatisfaction and congestion caused by waiting in line. The governing cost optimization objective equation per unit time is: \[ E(TC) = C_s \cdot c + C_w \cdot L_s \] Where: * $c$ = Number of active parallel servers. * $C_s$ = Service cost per individual server per unit of time. * $C_w$ = Waiting cost per unit time per customer waiting in the system. * $L_s$ = Expected total number of customers present within the system.

Step 1: Identifying components utilized in the total cost model.
Let us look at the variables required to calculate the economic balance: * $C_s$ maps directly to Option (1): Cost per server per unit of time. * $C_w$ maps directly to Option (3): Cost per unit time for a customer waiting in the system. * $L_s$ maps directly to Option (4): The average number of customers in the system. These three criteria are essential parameters used to compute the overall hourly operating cost of a queue.

Step 2: Isolating the unused metric.
While the average waiting time of a customer in the system ($W_s$) is a valid performance measure for a queue, it is a time duration metric ($W_s = \frac{L_s}{\lambda}$ via Little's Law) rather than a direct cost or customer volume metric used in the $E(TC)$ objective formula. Since the equation multiplies financial rates by customer volume ($L_s$), $W_s$ itself is not directly plugged into the cost formula. This makes Option (2) the correct selection.