Question 1

The Erlang distribution with k = 4 has higher variability than the Erlang distribution with k = 2.&#10;Multiple Choice Questions

Accepted Answer

The Erlang distribution's variability decreases as the shape parameter k increases, meaning k = 4 has lower variability than k = 2.

Question 2

The utilization factor for the finite queue variation must be less than 1 in order for the system to reach a steady state.

Accepted Answer

False

Question 3

The Erlang distribution has less variability than the exponential distribution for the same mean.

Accepted Answer

The Erlang distribution is a gamma distribution with an integer shape parameter, which causes it to have less variability than the exponential distribution for the same mean.

Question 4

When designing a queueing system with a finite queue,one important decision is how much waiting room to provide.

Accepted Answer

The amount of waiting room provided in a finite queueing system is an important decision that needs to be made by the designer. This is because if the queue is too small, customers may not be able to wait if the servers are busy, leading to lost business. On the other hand, if the queue is too large, it may result in unnecessary waiting and dissatisfaction among customers. Therefore, the decision of how much waiting room to provide is significant and needs to be carefully considered.

Question 5

Rank the exponential,degenerate,Erlang (k = 2),and Erlang (k = 4)distributions from highest to lowest variability,given the same mean.&#10;A)degenerate,Erlang (k = 2),Erlang (k = 4),exponential.&#10;B)degenerate,Erlang (k = 4),Erlang (k = 2),exponential.&#10;C)exponential,Erlang (k = 2),Erlang (k = 4),degenerate.&#10;D)exponential,Erlang (k = 4),Erlang (k = 2),degenerate.&#10;E)none of the above.

Accepted Answer

The exponential distribution has the highest variability, followed by Erlang (k = 2), Erlang (k = 4), and the degenerate distribution, which has zero variability.

Question 6

The finite calling population queueing model is appropriate when the potential calling population is relatively small.

Accepted Answer

The finite calling population queueing model assumes that the potential calling population is fixed and relatively small, unlike the infinite calling population model which assumes an unlimited potential calling population.

Question 7

Given the same utilization factor,waiting time in the queue will be less for a finite queue than the corresponding value for the M/M/s model.

Accepted Answer

In a finite queue, arrivals are blocked once the queue reaches its maximum capacity, which means customers cannot enter the system when the queue is full. This results in a decrease in waiting time in the queue as compared to the M/M/s model, where customers can enter the system regardless of the queue length. Thus, the statement is true.

Question 8

A basic difference between infinite calling population and finite calling population queueing models is:&#10;A)the number of servers.&#10;B)the average waiting time.&#10;C)the arrival distribution.&#10;D)the size of the potential customer base.&#10;E)the processing rate.

Accepted Answer

The basic difference between infinite calling population and finite calling population queueing models is the size of the potential customer base. In an infinite calling population model, the potential customer base is assumed to be large enough that the arrival rate does not change as customers enter or exit the system. In a finite calling population model, the potential customer base is smaller and the arrival rate can change as customers enter or exit the system. Therefore, the size of the potential customer base is the best choice to differentiate between the two queueing models.

Deck 13: CD Supplement - Additional Queueing Models