Question 1

Analytical queuing models are classified mainly on the basis of the calling population characteristics and the queue discipline.

Accepted Answer

False

Question 2

The graph depicting the economic trade-off in capacity planning has cost on the x-axis and the capacity to serve on the y-axis.

Accepted Answer

Typically, in capacity planning graphs, the capacity to serve is plotted on the x-axis, and the cost is plotted on the y-axis, showing how costs change as capacity increases or decreases.

Question 3

Excess capacity is required in a service system because variability in customer arrivals and service times creates idle capacity.

Accepted Answer

Excess capacity is necessary to handle variations in customer demand and service times. Without excess capacity, the system would easily become overwhelmed and customers would face long wait times or poor service quality.

Question 4

The main advantage of analytical models is that they can be used almost anywhere regardless of the underlying assumptions. They still will provide good results.

Accepted Answer

Analytical models rely on certain assumptions about the system being modeled, and if those assumptions are not met, the results could be incorrect. Therefore, analytical models are only applicable in specific situations where the assumptions hold.

Question 5

In the M/M/1 model the calling population is finite.

Accepted Answer

In the M/M/1 model, the calling population is assumed to be infinite.

Question 6

A queue is said to be finite if there is an upper limit on the number of consumers who are allowed to be in it. Consumers who come after the queue is full, either balk or are refused entrance.

Accepted Answer

This statement defines the concept of a finite queue and describes what happens when it becomes full. Therefore, the statement is true.

Question 7

A system is said to be in statistical equilibrium when the number in queue assumes a distribution that is independent of the starting condition.

Accepted Answer

In statistical equilibrium, the system reaches a steady-state where the distribution of the queue length becomes independent of the starting condition. Therefore, the statement is true.

Question 8

Capacity planning decisions deal implicitly with decisions on the cost of making consumers wait and the extent to which these costs can be borne.

Accepted Answer

Capacity planning involves determining the optimal level of resources (such as labor, equipment, space) needed to meet customer demand. This decision impacts wait times for customers, and businesses must consider the costs associated with making customers wait (such as lost sales or customer satisfaction) when making capacity planning decisions. Therefore, the statement is true.

Question 9

A system is said to be in a transient state when the values of its governing parameters in this state are expected to change uncontrollably with time.

Accepted Answer

This is the definition of a transient state.

Question 10

Pooling of services is an approach toward achieving economies of scale in services through better utilization of services.

Accepted Answer

Pooling of services involves combining resources and activities to achieve greater efficiency and cost savings through better utilization. This approach can help organizations reduce duplication of effort, optimize resources, and deliver more effective and efficient services to their customers.

Question 11

For a standard service system to operate over the long run, the servers must be idle part of the time.

Accepted Answer

If the servers are constantly busy, it means that the system is operating at its maximum capacity, leaving no room for new arrivals or unexpected increases in demand. This can lead to long waiting times, queueing, or even system breakdowns. Therefore, having idle time built into the system allows for better efficiency, flexibility, and resilience to fluctuations in demand. Additionally, idle servers can be used for maintenance, upgrades, or other tasks that improve the overall performance and quality of the system.

Question 12

The average time a customer should expect to wait can be calculated using just the mean arrival rate and the mean service rate.

Accepted Answer

The average time a customer should expect to wait in systems like queues can be calculated using the mean arrival rate ($\lambda$) and the mean service rate ($\mu$) through formulas derived from Queueing Theory, such as those found in the M/M/1 queue model.

Question 13

Capacity usually is measured in terms of outputs (e.g., guest nights) rather than inputs (e.g., number of hotel rooms) in service firms.

Accepted Answer

The answer of Capacity usually is measured in terms of...

Question 14

Reducing the variability either in service time or arrival time can reduce most of the waiting involved for the consumers.

Accepted Answer

The answer of Reducing the variability either in service time...

Question 15

When Xerox Corporation introduced the Model 9200 Duplicating System, the level of service dipped because technical representatives were assigned to territories.

Accepted Answer

The statement implies that the introduction of the Model 9200 Duplicating System had a negative impact on the level of service, indicating that there was a dip in service quality. Therefore, the statement is true.

Question 16

In the A/B/C classification of analytical queuing models, the term G refers to a general distribution with mean and variance.

Accepted Answer

In the A/B/C classification of analytical queuing models, the term G refers to a general distribution, which means that the service time distribution can be any probability distribution with known mean and variance.

Question 17

Planning for service capacity involves prediction of consumer waiting associated with different levels of capacity.

Accepted Answer

Planning for service capacity involves prediction of consumer waiting times, which are directly linked to the level of capacity available. Therefore, the statement is true.

Question 18

A Poisson process describing the distribution of departures from a busy server with an average rate of 15 per hour is equivalent to the negative exponential distribution of service times with a mean of 5 minutes.

Accepted Answer

A Poisson process with an average rate of 15 per hour corresponds to an exponential distribution of inter-arrival times with a mean of 4 minutes (60 minutes/15 arrivals), not 5 minutes.

Question 19

In analytical terms, the modern self-serve supermarket would be approximated best by the M /M /c model, where c is the number of servers.

Accepted Answer

The answer of In analytical terms, the modern self-serve supermarket...

Question 20

For a system to reach steady state, the arrival rate must always be greater than the service rate, i.e., the traffic intensity ρ must always be greater than unity.

Accepted Answer

For a system to reach steady state, the arrival rate must be equal to or less than the service rate, i.e., the traffic intensity ρ must be less than or equal to unity. If ρ is greater than unity, the system becomes unstable and queues will continue to grow.

Quiz 13: Capacity Planning and Queuing Models