MGMT430 Columbia College Exponential Probability Distribution Problems

Problem 1:The problem should be worked in the attached Queue Template. All formulas should be editable in each celled when clicked. Submit the ‘Queue Template’ spreadsheet used.Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a Poisson probability distribution, with an arrival rate of 1 car every 10 minutes and the service times follow an exponential probability distribution, with a service rate of 8 cars per hour. Answer the attached questions in DB_8.Problem 2:Is attached in the file titled DB_9. Given the following Operating Characteristics from a queuing model with time units specified in hours, answer the five questions:

Problem 1:
Assume that for a gas and car wash station one car can be serviced at a time. The arrivals follow a
Poisson probability distribution, with an arrival rate of 1 car every 10 minutes and the service times
follow an exponential probability distribution, with a service rate of 8 cars per hour.
1. What is the probability that the station will be idle?
2. What is the average number of cars that will be waiting for service?
3. What is the average time a car will be waiting for service?
4. What is the average time a car will be at the gas and wash station?
The problem should be worked in the attached Queue Template. All formulas should be editable in
each celled when clicked. Submit the ‘Queue Template’ spreadsheet used.
Given the following Operating Characteristics from a queuing
model with time units specified in hours, answer the five
questions:
Po
= 0.4000
Lq
= 0.9000
L
Wq
= 1.5000
= 0.2000
W
= 0.3000
Pw
= 0.6000
1. What is the average time, in minutes, a customer waits in line
before being served?
2. What is the average time, in minutes, a customer spends waiting
and being served?
3. What is the average number of customers in the system?
4. What is the probability that there are no customers in the
system?
5. If the system serves a customer every 4 minutes, what is the
service rate?
Multiple-Channel Waiting Line Model
Assumptions
Poisson Arrivals
Exponential Service Times
Number of Channels
Arrival Rate
Service Rate For Each Channel
0
0
0
Operating Characteristics
Probability that no customers are in the system, Po
Average number of customers in the waiting line, Lq
Average number of customers in the system, L
Average time a customer spends in the waiting line, Wq
Average time a customer spends in the system, W
Probability an arriving customer has to wait, Pw
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