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Exam 18: Management of Waiting Lines

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Question 1

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A single channel queuing system has an average service time of 16 minutes per customer, which is exponentially distributed.The manager is thinking of converting to a system with a constant service time of 16 minutes.The arrival rate will remain the same.The effect will be to:

A) increase utilization
B) decrease utilization
C) increase the average waiting time
D) decrease the average waiting time
E) not have any effect since the service time is unchanged

F) C) and D)
G) None of the above

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D

Question 2

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If variation in arrival and service rates can be reduced, waiting lines will be shortened.

A) True
B) False

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Question 3

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How many spaces should be provided to have a 96% probability of accommodating all of the waiting cars?

On average, how many parties without player's cards are waiting to be seated?

Which of the following is not generally considered as a measure of system performance in a queuing analysis?

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each.Find: (A) the average number of customers waiting for service if 6 clerks are used (B) the minimum number of clerks needed to keep the average time in the system to under 5 minutes (C) If clerk cost is $30 per hour and customer waiting time represents a "cost" of $20 per hour, how many clerks can be justified on a cost basis?

The cost of customer waiting is easy to estimate, the number waiting multiplied by the wait cost per minute.

To reduce the average number waiting in line, it is important to increase utilization.

What is system utilization?

What is average time in the system for a low priority item?

The point that minimizes total queuing system costs is that point where waiting costs and capacity costs are equal.

On average, how much longer do parties without player's cards spend in the system, compared to parties with the player's cards?

In a _______ system, customers enter the waiting line, receive service and leave.

In an infinite source model, the system utilization is the ratio of the arrival rate to the service capacity.

An approach to reducing the variability in processing times might include greater standardization.

A Single Server, Variable Service Time is known as an M/D/1 system.

Balking is when customers grow impatient and leave a line.

A department has 5 machines that each run for an average of 8.4 hours (exponential) before service is required.Service time average is 1.6 hours (exponential). (A) While running, each machine can produce 120 pieces per hour.With one server, what is the average hourly output actually achieved? (B) With 2 servers, what is the probability that a machine would be served immediately when it requires service? (C) If machine downtime cost is $100 per hour per machine, and server time costs $30 per hour, how many servers would be optimal?

What is the average number of machines down with one operator?

Customers arrive at a video rental desk at the rate of one per minute (Poisson).Each server can handle 0.40 customers per minute (Poisson). (A) If there are four servers, determine: (1) The average time it takes to rent a video tape (2) The probability of three or fewer customers in the system (B) What is the minimum number of servers needed to achieve an average time in the system of less than three minutes?