Question 1

A bank office with five tellers, each with a separate line of customers, exhibits the characteristics of a multiphase queuing system.

Accepted Answer

A bank office with five tellers, each with a separate line of customers, exhibits the characteristics of a single-phase, multi-channel queuing system, not a multiphase system.

Question 2

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute; the average queue length of the M/M/1 will be twice that of the M/D/1.

Accepted Answer

The average queue length of an M/M/1 model can be calculated using the formula Lq = (ρ^2)/(1-ρ), where ρ is the traffic intensity, which is equal to λ/μ in this case (arrival rate/ service rate). Thus, ρ = 1/3, and Lq = (1/9)/(2/3) = 1/6. 
For the M/D/1 model, the queue length will be zero if the service time is less than the inter-arrival time, and will be equal to the arrival rate minus the service rate otherwise. Since the service rate (3) is greater than the arrival rate (1), the queue length for the M/D/1 model will be 2, which is twice as small as the queue length for the M/M/1 model. Therefore, the statement is true.

Question 3

Four of the most widely used waiting line models-M/M/1 or A, M/M/S or B, M/D/1 or C, and Limited population or D-all share three characteristics: Poisson arrivals, FIFO discipline, and exponential service times.

Accepted Answer

While M/M/1, M/M/S, and M/D/1 models assume Poisson arrivals and (for M/M/1 and M/M/S) exponential service times, the characteristic of exponential service times does not apply to the M/D/1 model, which assumes a constant (deterministic) service time. FIFO discipline is common but not exclusive, as other service disciplines can also be applied.

Question 4

The greater the margin by which the arrival rate exceeds the service rate, the better the performance of the waiting line.

Accepted Answer

The greater the margin by which the arrival rate exceeds the service rate, the longer the waiting time and the worse the performance of the waiting line. A smaller difference or a balanced arrival and service rate typically leads to a more efficient waiting line with shorter wait times.

Question 5

If the service time within a queuing system is constant, the service rate can be easily described by a negative exponential distribution.

Accepted Answer

When the service time is constant, the service rate is better described by a deterministic distribution, not a negative exponential distribution, which is used for random service times.

Question 6

The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.

Accepted Answer

The study of waiting lines, also known as queueing theory, does take into account the cost of customers' waiting time. One of the main goals of queueing theory is to minimize the total cost of providing service, which includes both the cost of providing service and the cost of customers' waiting time.

Question 7

The two characteristics of the waiting line itself are whether its length is limited or unlimited and the discipline of the people or items in it.

Accepted Answer

The statement is true. The two characteristics of a waiting line are its length, which can either be limited or unlimited, and the discipline of the people/items in it.

Question 8

As the average service rate μ grows larger, the slope of the distribution of service time probabilities grows larger and larger, eventually becoming positive.

Accepted Answer

As the average service rate μ grows larger, the distribution of service time probabilities becomes steeper, but the slope remains negative or decreases because the service times become shorter, leading to a higher concentration of probabilities towards shorter service times.

Question 9

The cost of waiting decreases as the service level increases.

Accepted Answer

As the service level increases, the wait time and waiting cost decreases. Therefore, the cost of waiting decreases as the service level increases.

Question 10

Balk and renege are elements of queue discipline.

Accepted Answer

Balk refers to the decision not to join a queue, and renege involves leaving a queue after joining it, but queue discipline specifically refers to the rules determining the order in which members of the queue are served, such as first-come, first-served.

Question 11

A waiting-line system has three parts: the size of the arrival population, the behaviour of arrivals, and the statistical distribution of arrivals.

Accepted Answer

The answer of A waiting-line system has three parts: the...

Question 12

In the M/M/1 waiting line model with an arrival rate of 2 per hour and a service rate of 6 per hour, the utilization factor for the system is approximately 0.333.

Accepted Answer

The utilization factor (ρ) is given by ρ = λ/μ, where λ is the arrival rate and μ is the service rate. Plugging in the given values, we get ρ = 2/6 = 0.333, which confirms that the answer is A.

Question 13

In the analysis of queuing models, the Poisson distribution often describes arrival rates and service times are often described by the negative exponential distribution.

Accepted Answer

This is true. The Poisson distribution is often used to model arrival rates in queuing systems, as it describes the occurrence of events in a given interval of time. The negative exponential distribution is often used to model service times in queuing systems, as it describes the time between consecutive events in a Poisson process.

Question 14

A copy centre has five machines that serve many customers throughout the day; the waiting-line system for copy service has an infinite population while the waiting-line system for copier maintenance has a finite population.

Accepted Answer

The statement indicates that the waiting-line system for copy service has an infinite population, meaning that there is no limit to the number of customers who could potentially need this service. In contrast, the waiting-line system for copier maintenance has a finite population, as there is a limit to the number of copiers that can require maintenance at any given time. Therefore, the statement is true.

Question 15

LIFS (last-in, first-served) is a common queue discipline, most often seen where people, not objects, form the waiting line.

Accepted Answer

LIFS (Last-In, First-Served) is not a common queue discipline for managing people or objects in waiting lines; instead, FIFO (First-In, First-Out) is more commonly used for orderly and fair service.

Question 16

Waiting-line models are useful to operations in such diverse settings as service systems, maintenance activities, and shop-floor control.

Accepted Answer

Waiting-line models can be applied in various operations such as service systems, maintenance activities, and shop-floor control.

Question 17

In queuing problems, arrival rates are generally described by the normal probability distribution.

Accepted Answer

Arrival rates in queuing problems are generally described by the Poisson probability distribution.

Question 18

In queuing problems, the term "renege" refers to the fact that some customers leave the queue before service is completed.

Accepted Answer

Renege is the term used to describe customers who leave the queue before receiving service.

Question 19

A waiting-line system with one waiting line and three sequential processing stages is a multichannel single-phase system.

Accepted Answer

A waiting-line system with one waiting line and three sequential processing stages is a multistage (or multiphase) system, not a multichannel single-phase system.

Question 20

A hospital emergency room always follows a first-in, first-served queue discipline in the interest of fairness.

Accepted Answer

Although many hospitals strive to follow a first-in, first-served queue discipline, emergency rooms often prioritize patients based on the severity of their condition. This is known as triage and ensures that those who require urgent medical attention are seen first, regardless of their arrival time.

Quiz 21: Waiting-Line Models