Question

A local fast-food restaurant wants to analyze its drive-thru window. At this time, the only information known is the average number of customers in the system (4.00) and the average time a customer spends at the restaurant (1.176 minutes). What are the arrival rate and the service rate?

Short answer

A client is a person as well as a company who buys products as well as service providers from some other firm.

Step-by-step solution

Average number of clients

W = the average time a client spends within the framework. 1/h = the average benefit time per client. The proportion of client entry rate to client benefit rate, x = a/h, moreover reflects the average number of entries amid a standard benefit time.

An average number of clients or units holding up in line for benefit.

$\mathrm{L}={\mathrm{L}}_{\mathrm{q}}+\raisebox{1ex}{$\mathrm{\lambda }$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\mu }$}\right.$

The average number of customers or units-

${\mathrm{W}}_{\mathrm{q}}=\frac{{\mathrm{L}}_{\mathrm{q}}}{\mathrm{\lambda }}$

The average time a client or department spends holding up in line for benefit.

$\mathrm{W}={\mathrm{W}}_{\mathrm{q}}+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{\mu }$}\right.$

Time a customer or unit pays within the system.

A local fast-food restaurant wants to analyze its drive-thru window. At this time, the only information known is the average number of customers in the system (4.00) and the average time a customer spends at the restaurant (1.176 minutes). The arrival rate and the service rate are-

Calculate the value of the service rate as follows:

$$\begin{gathered} \frac{1}{\mu -\lambda }=1.176 \\ \frac{1}{\mu -(3.401)}=1.176 \\ \mu =4.2517\mathrm{per}\min \mathrm{or}255\mathrm{per}\sec \end{gathered}$$

Hence, the arrival rate and the customer rate of the system are 3.401 per min and 4.2517 per min, respectively.