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.

- 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*= minutes_{q}

*W*= minutes

*P*=_{w} - 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. - 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*= minutes_{q}

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} = λ^{2} / {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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