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Queuing Theory

Description: This quiz covers the fundamental concepts and applications of queuing theory, a branch of mathematics that deals with the study of waiting lines and queues.
Number of Questions: 15
Created by:
Tags: queuing theory probability operations research
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In a queuing system, what is the average number of customers waiting in the queue?

  1. Arrival rate / (Arrival rate - Service rate)

  2. Service rate / (Service rate - Arrival rate)

  3. Arrival rate / (Arrival rate + Service rate)

  4. Service rate / (Service rate + Arrival rate)

Show answer
Correct Option: A
Explanation:

This is known as the average queue length and is calculated as the ratio of the arrival rate to the difference between the arrival rate and the service rate.

Which queuing model assumes that customers arrive at the system according to a Poisson distribution and are served according to an exponential distribution?

  1. M/M/1

  2. M/M/2

  3. M/M/C

  4. M/M/∞

Show answer
Correct Option: A
Explanation:

The M/M/1 model is the most basic queuing model and is widely used in practice due to its simplicity and tractability.

In a queuing system, what is the probability that a customer has to wait before being served?

  1. Arrival rate / Service rate

  2. Service rate / Arrival rate

  3. Arrival rate / (Arrival rate + Service rate)

  4. Service rate / (Service rate + Arrival rate)

Show answer
Correct Option: C
Explanation:

This is known as the probability of delay and is calculated as the ratio of the arrival rate to the sum of the arrival rate and the service rate.

Which queuing model assumes that customers arrive at the system according to a Poisson distribution and are served according to a general distribution?

  1. M/G/1

  2. M/G/2

  3. M/G/C

  4. M/G/∞

Show answer
Correct Option: A
Explanation:

The M/G/1 model is a more general queuing model that allows for a general service time distribution.

In a queuing system, what is the average time a customer spends in the system?

  1. 1 / (Arrival rate - Service rate)

  2. 1 / (Service rate - Arrival rate)

  3. 1 / (Arrival rate + Service rate)

  4. 1 / (Service rate + Arrival rate)

Show answer
Correct Option: B
Explanation:

This is known as the average sojourn time and is calculated as the reciprocal of the difference between the service rate and the arrival rate.

Which queuing model assumes that customers arrive at the system according to a general distribution and are served according to an exponential distribution?

  1. G/M/1

  2. G/M/2

  3. G/M/C

  4. G/M/∞

Show answer
Correct Option: A
Explanation:

The G/M/1 model is a queuing model that allows for a general arrival time distribution and an exponential service time distribution.

In a queuing system, what is the probability that a customer will be served immediately upon arrival?

  1. Service rate / (Arrival rate + Service rate)

  2. Arrival rate / (Arrival rate + Service rate)

  3. Service rate / Arrival rate

  4. Arrival rate / Service rate

Show answer
Correct Option: A
Explanation:

This is known as the probability of immediate service and is calculated as the ratio of the service rate to the sum of the arrival rate and the service rate.

Which queuing model assumes that customers arrive at the system according to a general distribution and are served according to a general distribution?

  1. G/G/1

  2. G/G/2

  3. G/G/C

  4. G/G/∞

Show answer
Correct Option: A
Explanation:

The G/G/1 model is the most general queuing model and allows for both a general arrival time distribution and a general service time distribution.

In a queuing system, what is the average number of customers in the system?

  1. Arrival rate / (Arrival rate - Service rate)

  2. Service rate / (Service rate - Arrival rate)

  3. Arrival rate / (Arrival rate + Service rate)

  4. Service rate / (Service rate + Arrival rate)

Show answer
Correct Option:
Explanation:

This is known as the average system size and is calculated as the ratio of the arrival rate to the difference between the service rate and the arrival rate.

Which queuing model assumes that customers arrive at the system according to a Poisson distribution and are served according to a deterministic distribution?

  1. M/D/1

  2. M/D/2

  3. M/D/C

  4. M/D/∞

Show answer
Correct Option: A
Explanation:

The M/D/1 model is a queuing model that assumes a Poisson arrival process and a deterministic service time distribution.

In a queuing system, what is the probability that a customer will have to wait more than a certain amount of time before being served?

  1. 1 - (Service rate / Arrival rate)

  2. 1 - (Arrival rate / Service rate)

  3. 1 - (Arrival rate / (Arrival rate + Service rate))

  4. 1 - (Service rate / (Service rate + Arrival rate))

Show answer
Correct Option: D
Explanation:

This is known as the probability of delay and is calculated as 1 minus the ratio of the service rate to the sum of the service rate and the arrival rate.

Which queuing model assumes that customers arrive at the system according to a Poisson distribution and are served according to a hyperexponential distribution?

  1. M/H/1

  2. M/H/2

  3. M/H/C

  4. M/H/∞

Show answer
Correct Option: A
Explanation:

The M/H/1 model is a queuing model that assumes a Poisson arrival process and a hyperexponential service time distribution.

In a queuing system, what is the average time a customer spends waiting in the queue?

  1. Arrival rate / (Arrival rate - Service rate)

  2. Service rate / (Service rate - Arrival rate)

  3. Arrival rate / (Arrival rate + Service rate)

  4. Service rate / (Service rate + Arrival rate)

Show answer
Correct Option: A
Explanation:

This is known as the average waiting time and is calculated as the ratio of the arrival rate to the difference between the arrival rate and the service rate.

Which queuing model assumes that customers arrive at the system according to a Poisson distribution and are served according to a Pareto distribution?

  1. M/Pa/1

  2. M/Pa/2

  3. M/Pa/C

  4. M/Pa/∞

Show answer
Correct Option: A
Explanation:

The M/Pa/1 model is a queuing model that assumes a Poisson arrival process and a Pareto service time distribution.

In a queuing system, what is the probability that a customer will be served within a certain amount of time?

  1. 1 - (Arrival rate / Service rate)

  2. 1 - (Service rate / Arrival rate)

  3. 1 - (Arrival rate / (Arrival rate + Service rate))

  4. 1 - (Service rate / (Service rate + Arrival rate))

Show answer
Correct Option: C
Explanation:

This is known as the probability of being served within a certain time and is calculated as 1 minus the ratio of the arrival rate to the sum of the arrival rate and the service rate.

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