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What is the probability that no customers are in the system (Po)? b. What is the average number of customers waiting for service ( Lq)? c. What is the average number of customers in the system (L)? d. What is the average time a customer waits for service(Wq)? e. What is the average time in the system (W)? f. What is the probability that a customer will have to wait for service (Pw)? g What is the probability that there is exactly 2 customers in the system h) What is the probability that there are more than 3 customers in the system

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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Question

A petrol station in the capital Kingstown has a single pump manned by one attendant.
Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on an
average. Assume the arrival rate is Poisson probability distribution and service rate is
exponentially distributed. Arrivals tend to follow a Poisson distribution, and service times
tend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill and
sales, station loses about $15 per hour of customer time spent waiting for the attendant to
service and order.

a. What is the probability that no customers are in the system (Po)?
b. What is the average number of customers waiting for service ( Lq)?
c. What is the average number of customers in the system (L)?
d. What is the average time a customer waits for service(Wq)?
e. What is the average time in the system (W)?
f. What is the probability that a customer will have to wait for service (Pw)?
g What is the probability that there is exactly 2 customers in the system
h) What is the probability that there are more than 3 customers in the system

Part B
The Petrol station is considering adding a second pump with an attendant to service
customers. The station would pay that person the same $10 per hour.
Using appropriate formula for the multiple channel model, answer the following questions:

a. What is the probability that no customers are in the system (Po)?
b. What is the average number of customers waiting for service (Lq)?
c. What is the average number of customers in the system (L)?
d. What is the average time a customer waits for service (Wq)?
e. What is the average time in the system (W)?
f. What is the probability that a customer will have to wait for service (Pw)?
g. What is the probability that there is exactly 2 customers in the system
h. Should it hire another clerk? Explain by showing the cost savings

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