Customers enter the spare-parts department of an automobile dealership at the si

Question

Customers enter the spare-parts department of an automobile dealership at the six 3. (8 points) rate of six per hour. The department is staffed by one employee, who takes an average of minutes to serve each customer. Assume Poisson arrivals and exponentially distributed service times. State which model(s) you are using! How long would a customer expect to spend in the department? a. b. What is the utilization of the clerk? c. What is the probability that an entering customer finds no one waiting in line? If another clerk is hired (with identical service rate), how long would a customer expect to spend in the department now? d.

Explanation / Answer

Here = 10 customers per hour

= 6 customers per hour

we are using M/M/1 queuing model

(a) Average waiting time for a customer = 1/ ( - ) =1/(10 -6) = 1/ (10-6) = 0.25 hour = 15 minutes

(b) Utilization of clerk = 1 - Probability of clerk being idle = / = 6/10 = 0.6

(c) Pr(No queue) = 1 - / = 1 - (6/10) = 0.4

(d) Here one more clerk has been hired that means there are two service station with service time of 6 minutes.

Average waiting time in line = 1/ + Lq/ = 0.10989 Hours

where Lq is the average number of customers in line.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.