Question

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 3.2 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 12 minutes with each customer.

1. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. Round your answers to four decimal places. Do not round intermediate calculations.
   
   L_q =  
   
   L =  
   
   W_q =  minutes
   
   W =  minutes
   
   P_w =  
   
2. Service goals dictate that an arriving customer should not wait for service more than an average of 8 minutes. Is this goal being met? If not, what action do you recommend?
   
   No. Firm should increase the mean service rate u for the consultant or hire a second consultant.  
   
3. If the consultant can reduce the average time spent per customer to 9 minutes, what is the mean service rate? Round your answer to four decimal places. Do not round intermediate calculations.
   
   µ =  customers per hour
   
   W_q =  minutes
   
   Will the service goal be met?
   
   No

Answer 1

ANSWER:

a).

Average arrival rate, λ = 3.2 per hr.
Average service rate, μ = 1 in 12 minutes = 5 per hr.
No. of servers, s = 1

L_q = λ² / {μ.(μ - λ)} = (3.2^2)/(5*(5 - 3.2)) = 1.1378

L = L_q + (λ/μ) = 1.1378+3.2/5 = 1.7778

W_q = L_q / λ = 1.1378/3.2 hrs. = 60*1.1378/3.2 minutes = 21.3333 minutes

W = W_q + 12 minutes = 33.3333 minutes

P_w = λ/μ = 3.2/5 = 0.64

b).

No. because the Wq value is 21.333 which is more than 8 minutes. So, increase the number of servers.

c).

μ = 1 in 9 minutes = 6.6667 per hr.

W_q = λ / {μ.(μ - λ)} = (3.2)/(6.6667*(6.6667 - 3.2)) = 0.1385 hrs. = 8.3077 minutes.

No. the goal is still not met.

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