Mastering Waiting Line Models in Service Management | MCQs

mastering-waiting-line-models-mba-mcqs

MBA Guide to Waiting Line Analysis: Multiple Choice Questions

1. Introduction to Waiting Line Models

What does the “M” in M/M/1 model represent?

  • A) Memory
  • B) Markovian (Poisson distribution)
  • C) Multiple Queues
  • D) Mean service time
    Answer: B

In the M/M/1 model, what does the single '1' represent?

  • A) One waiting line
  • B) One service channel
  • C) One minute of service time
  • D) One queue type
    Answer: B

Which of the following is NOT an assumption of the M/M/1 model?

  • A) Arrival follows a Poisson distribution
  • B) Service time is exponentially distributed
  • C) Queue discipline is FIFO
  • D) Infinite number of servers
    Answer: D

In a typical M/M/S queue, 'S' represents the number of:

  • A) Servers
  • B) Stages in service
  • C) Simultaneous arrivals
  • D) Service priorities
    Answer: A

Which of the following is a key trade-off in waiting line management?

  • A) Minimizing both waiting time and service costs
  • B) Maximizing waiting time to reduce costs
  • C) Reducing customer arrival rate
  • D) Increasing service capacity regardless of cost
    Answer: A

2. Formulas and Calculations

What is the formula for the utilization factor in the M/M/1 model?

  • A) λ×μ\lambda \times \mu
  • B) λμ \frac{\lambda}{\mu}
  • C) μ−λ\mu - \lambda
  • D) μλ \frac{\mu}{\lambda}
    Answer: B

If the arrival rate (λ) is 6 customers/hour and service rate (μ) is 10 customers/hour in an M/M/1 system, what is the utilization rate?

  • A) 0.4
  • B) 0.6
  • C) 1.5
  • D) 4
    Answer: B

The expected number of customers in the system (L) in an M/M/1 model is given by:

  • A) λμ−λ \frac{\lambda}{\mu - \lambda}
  • B) μλ \frac{\mu}{\lambda}
  • C) λ+μ\lambda + \mu
  • D) μμ−λ \frac{\mu}{\mu - \lambda}
    Answer: A

For an M/M/S system, the probability that all servers are busy is calculated using:

  • A) Poisson distribution
  • B) Exponential distribution
  • C) Erlang C formula
  • D) Binomial distribution
    Answer: C

If λ = 5, μ = 8, and S = 2 in an M/M/S system, what is the traffic intensity (ρ)?

  • A) 0.5
  • B) 1.25
  • C) 0.625
  • D) 0.8
    Answer: C

3. Trade-Offs in Waiting Line Management

What happens when the service capacity is increased in a queueing system?

  • A) Waiting time increases
  • B) Service cost increases
  • C) Customer satisfaction decreases
  • D) Arrival rate decreases
    Answer: B

Which factor is critical in balancing the cost of service and the cost of waiting?

  • A) Arrival rate
  • B) Utilization rate
  • C) Service rate
  • D) Traffic intensity
    Answer: C

In a waiting line analysis, which of the following trade-offs is considered optimal?

  • A) Long waiting times with minimal costs
  • B) High service costs with no waiting time
  • C) Moderate waiting times and service costs
  • D) No waiting lines at any cost
    Answer: C

What is the primary goal of waiting line management in service industries?

  • A) To reduce the number of arrivals
  • B) To ensure no one waits
  • C) To optimize the trade-off between customer satisfaction and cost
  • D) To increase server idle time
    Answer: C

Which of the following is a key decision in waiting line management?

  • A) Hiring more employees than required
  • B) Determining the optimal number of servers
  • C) Reducing the quality of service
  • D) Extending customer wait times deliberately
    Answer: B

4. Application Scenarios

A bank has two tellers working at the counter. If customers arrive at an average of 10 per hour and each teller can handle 7 customers per hour, what queue model should be used?

  • A) M/M/1
  • B) M/M/2
  • C) M/G/1
  • D) M/D/1
    Answer: B

If an airline has 5 check-in counters and the arrival rate is 50 passengers per hour with each counter serving 15 passengers per hour, what is the system’s traffic intensity?

  • A) 0.6
  • B) 0.67
  • C) 0.8
  • D) 1.0
    Answer: B

A fast-food restaurant uses an M/M/1 system for its drive-through. If waiting times become excessive, what is the best solution?

  • A) Increase arrival rate
  • B) Add a second server
  • C) Close the queue during peak hours
  • D) Decrease service rate
    Answer: B

A supermarket queue with multiple cashiers operating under FIFO discipline is an example of which model?

  • A) M/M/1
  • B) M/M/S
  • C) M/G/1
  • D) M/D/S
    Answer: B

Which metric indicates how busy the servers are in a queueing system?

  • A) Queue length (Lq)
  • B) Utilization factor (ρ)
  • C) Waiting time (Wq)
  • D) Service rate (μ)
    Answer: B

1. Basics of Waiting Line Analysis

What is a waiting line also called in operations management?

  • A) Queue
  • B) Bottleneck
  • C) Delay system
  • D) Service chain
    Answer: A

Which term describes the number of customers in a queueing system?

  • A) Utilization rate
  • B) System population
  • C) Queue length
  • D) Throughput
    Answer: C

What is the primary objective of waiting line analysis?

  • A) Minimize service costs
  • B) Reduce waiting time
  • C) Balance costs and customer satisfaction
  • D) Increase the number of servers
    Answer: C

What is the most common queue discipline in real-world systems?

  • A) LIFO
  • B) FIFO
  • C) Random
  • D) Priority-based
    Answer: B

In waiting line analysis, what does the term "utilization" measure?

  • A) The efficiency of the servers
  • B) The proportion of time servers are busy
  • C) The number of arrivals per unit time
  • D) The service cost per customer
    Answer: B

2. Assumptions and Characteristics of M/M/1 Models

The first "M" in M/M/1 signifies:

  • A) Markovian arrivals
  • B) Multi-server system
  • C) Mean waiting time
  • D) Multiple queues
    Answer: A

Which of the following is NOT an assumption of the M/M/1 model?

  • A) Infinite queue capacity
  • B) FIFO queue discipline
  • C) Constant service time
  • D) Poisson arrival process
    Answer: C

The M/M/1 queue model is best suited for:

  • A) A supermarket with multiple cashiers
  • B) A single ATM machine
  • C) A call center with multiple agents
  • D) A manufacturing assembly line
    Answer: B

In an M/M/1 system, which distribution is used for service time?

  • A) Normal distribution
  • B) Exponential distribution
  • C) Uniform distribution
  • D) Binomial distribution
    Answer: B

Which metric in an M/M/1 system represents the average number of customers in the system?

  • A) L
  • B) W
  • C) Lq
  • D) Wq
    Answer: A

3. Calculations in M/M/1 Models

If λ = 5 and μ = 8 in an M/M/1 system, what is the utilization rate (ρ)?

  • A) 0.625
  • B) 1.6
  • C) 0.4
  • D) 0.8
    Answer: A

What is the formula to calculate the probability of zero customers in the system in an M/M/1 model?

  • A) P0=1−ρ P_0 = 1 - \rho
  • B) P0=λμ P_0 = \frac{\lambda}{\mu}
  • C) P0=μλ P_0 = \frac{\mu}{\lambda}
  • D) P0=1+ρ P_0 = 1 + \rho
    Answer: A

If the arrival rate is 6 customers per hour and the service rate is 10 customers per hour, what is the average number of customers in the system (L)?

  • A) 0.6
  • B) 1.5
  • C) 2.4
  • D) 3.0
    Answer: B

What is the expected waiting time in the queue (Wq) for an M/M/1 system where λ = 4 and μ = 7?

  • A) 0.25 hours
  • B) 0.5 hours
  • C) 0.6 hours
  • D) 1 hour
    Answer: C

How is the average time a customer spends in the system (W) calculated in an M/M/1 model?

  • A) W=1μ W = \frac{1}{\mu}
  • B) W= 1μ−λ W = \frac{1}{\mu - \lambda}
  • C) W=λμ W = \frac{\lambda}{\mu}
  • D) W=μ−λW = \mu - \lambda
    Answer: B

4. Assumptions and Characteristics of M/M/S Models

The M/M/S model is applicable for systems with:

  • A) A single server
  • B) Multiple servers
  • C) Constant arrival rate
  • D) Deterministic service time
    Answer: B

Which formula is used to calculate the probability of all servers being busy in an M/M/S system?

  • A) Poisson formula
  • B) Erlang B formula
  • C) Exponential formula
  • D) Priority formula
    Answer: B

If there are three servers and the arrival rate is 12 customers per hour, what is the traffic intensity (ρ)?

  • A) 4
  • B) 1.33
  • C) 0.67
  • D) 3
    Answer: C

In an M/M/S model, what happens as the number of servers increases?

  • A) Waiting time decreases
  • B) Utilization increases
  • C) Arrival rate increases
  • D) Service cost decreases
    Answer: A

What is the key trade-off in M/M/S systems?

  • A) Cost of waiting vs service cost
  • B) Queue length vs arrival rate
  • C) Service time vs arrival time
  • D) Traffic intensity vs idle time
    Answer: A

5. Applications of Waiting Line Models

Which waiting line model is best for a call center with 10 agents?

  • A) M/M/1
  • B) M/M/S
  • C) M/G/1
  • D) D/D/1
    Answer: B

Which system uses the priority discipline for serving customers?

  • A) Emergency rooms
  • B) Retail checkout lines
  • C) Fast food drive-throughs
  • D) Supermarket queues
    Answer: A

A hospital with multiple doctors serving patients can be modeled as:

  • A) M/M/1
  • B) M/M/S
  • C) G/M/1
  • D) M/D/1
    Answer: B

What is a common real-world example of an M/M/1 queue?

  • A) Bank teller counters
  • B) Self-checkout lanes
  • C) Toll booths
  • D) Automated car washes
    Answer: D

If a queue has limited capacity, which model is appropriate?

  • A) M/M/1
  • B) M/M/S/K
  • C) M/G/1
  • D) M/D/1
    Answer: B

6. Trade-offs in Waiting Line Systems

What is the primary trade-off in managing waiting lines?

  • A) Customer satisfaction vs service rate
  • B) Cost of service vs cost of waiting
  • C) Arrival rate vs service time
  • D) Utilization vs server idleness
    Answer: B

Which of the following increases when more servers are added to a system?

  • A) Cost of waiting
  • B) Cost of service
  • C) Average queue length
  • D) Arrival rate
    Answer: B

In an M/M/1 system, increasing the service rate (μ) will:

  • A) Increase waiting time
  • B) Reduce queue length
  • C) Increase utilization
  • D) Reduce arrival rate
    Answer: B

When customer waiting times decrease significantly, what typically happens to service costs?

  • A) Service costs remain unchanged
  • B) Service costs increase
  • C) Service costs decrease
  • D) Service costs fluctuate unpredictably
    Answer: B

A system with underutilized servers leads to:

  • A) Higher customer satisfaction
  • B) Lower total cost
  • C) Wasted service resources
  • D) Long waiting times
    Answer: C

7. Advanced Metrics in Waiting Line Analysis

What does "Lq" represent in queueing theory?

  • A) Average time in the system
  • B) Average number of customers in the queue
  • C) Average utilization rate
  • D) Average service time
    Answer: B

Which metric is calculated as W=Wq+1μ W = Wq + \frac{1}{\mu} ?

  • A) Time in queue
  • B) Time in system
  • C) Number in queue
  • D) Number in system
    Answer: B

If the arrival rate ( λ\lambda ) doubles in an M/M/1 system, the waiting time will:

  • A) Stay the same
  • B) Double
  • C) Decrease by half
  • D) Increase exponentially
    Answer: D

Which formula determines the probability that a customer has to wait in an M/M/S system?

  • A) Poisson probability
  • B) Erlang C formula
  • C) Little’s Law
  • D) Service rate formula
    Answer: B

The relationship L=λ×WL = \lambda \times W is known as:

  • A) Queue length equation
  • B) Service efficiency law
  • C) Little’s Law
  • D) Utilization theorem
    Answer: C

8. Variations and Extensions

Which model accommodates varying service times?

  • A) M/M/1
  • B) M/G/1
  • C) M/D/1
  • D) G/M/1
    Answer: B

A system with a finite queue length is denoted as:

  • A) M/M/1
  • B) M/M/S/K
  • C) M/G/1
  • D) G/M/1
    Answer: B

What happens in an M/G/1 system if service times are highly variable?

  • A) Average queue length increases
  • B) Queue length decreases
  • C) Arrival rate doubles
  • D) Service rate decreases
    Answer: A

What does the "G" in M/G/1 represent?

  • A) Gaussian distribution
  • B) General distribution
  • C) Global distribution
  • D) Generalized arrival rate
    Answer: B

A system with deterministic service times is represented by:

  • A) M/M/1
  • B) M/G/1
  • C) M/D/1
  • D) G/M/1
    Answer: C

9. Little’s Law and Applications

Little’s Law is applicable for:

  • A) Single-server systems only
  • B) Multi-server systems only
  • C) Any stable queueing system
  • D) Systems with deterministic arrivals
    Answer: C

If L = 10 and λ=2\lambda = 2 , what is W according to Little’s Law?

  • A) 2 hours
  • B) 5 hours
  • C) 10 hours
  • D) 20 hours
    Answer: B

Little’s Law helps managers understand the relationship between:

  • A) Queue length, arrival rate, and service time
  • B) Utilization, service cost, and queue length
  • C) Queue length, arrival rate, and time in system
  • D) Service rate, arrival rate, and waiting time
    Answer: C

What does Lq=λWqLq = \lambda Wq represent?

  • A) Little’s Law applied to waiting time
  • B) Service time calculation
  • C) Probability of waiting
  • D) Total cost of service
    Answer: A

Little’s Law assumes which of the following?

  • A) Deterministic service rate
  • B) System is in a steady state
  • C) Infinite population
  • D) FIFO queue discipline
    Answer: B

10. Real-World Scenarios

Which waiting line model is best suited for airport security checkpoints?

  • A) M/M/1
  • B) M/M/S
  • C) M/G/1
  • D) G/M/1
    Answer: B

What is a key metric for evaluating performance in call centers?

  • A) Traffic intensity
  • B) Average handle time
  • C) Probability of waiting
  • D) Queue length
    Answer: C

Drive-through restaurants are often modeled as:

  • A) M/M/1
  • B) M/M/S
  • C) M/G/1
  • D) M/D/1
    Answer: A

A hospital emergency room with triage prioritization follows which queue discipline?

  • A) FIFO
  • B) Priority
  • C) LIFO
  • D) Random
    Answer: B

A bank with multiple tellers can be best modeled as:

  • A) M/M/1
  • B) M/M/S
  • C) G/M/1
  • D) M/D/1
    Answer: B

11. Queue Disciplines and Policies

Which queue discipline is most common in real-life systems like grocery store checkouts?

  • A) FIFO (First In, First Out)
  • B) LIFO (Last In, First Out)
  • C) Priority
  • D) Random
    Answer: A

In LIFO queueing, which customer is served first?

  • A) The customer with the highest priority
  • B) The customer who arrived first
  • C) The customer who arrived last
  • D) The customer with the shortest service time
    Answer: C

Which queue discipline is used in emergency services like ambulances or hospitals?

  • A) FIFO
  • B) Priority
  • C) LIFO
  • D) Random
    Answer: B

Random queue discipline is often used in:

  • A) Inventory management systems
  • B) Customer support services
  • C) Computer memory allocation
  • D) Crowded events without organized queues
    Answer: D

In a priority queue system, low-priority customers may face:

  • A) Shorter wait times
  • B) Starvation (indefinite delay)
  • C) Random service order
  • D) Immediate service
    Answer: B

12. Optimization in Queueing Systems

What is the primary goal of optimizing a queueing system?

  • A) To minimize the number of servers
  • B) To maximize customer satisfaction and minimize cost
  • C) To ensure equal waiting times for all customers
  • D) To eliminate all waiting times
    Answer: B

Increasing service rates (μ) without increasing servers will:

  • A) Reduce utilization
  • B) Reduce waiting times
  • C) Increase arrival rates
  • D) Increase queue length
    Answer: B

What is a bottleneck in a queueing system?

  • A) A server that is idle
  • B) The point with the longest service time
  • C) The server with the highest efficiency
  • D) A random point in the system
    Answer: B

Which of the following helps in optimizing queue performance?

  • A) Reducing service times
  • B) Increasing arrival rates
  • C) Reducing server availability
  • D) Increasing waiting area size
    Answer: A

Balancing the number of servers and customer arrival rates is critical to:

  • A) Achieving zero queues
  • B) Maximizing traffic intensity
  • C) Maintaining an optimal cost-service balance
  • D) Avoiding server utilization
    Answer: C

13. Multi-Server Models

In an M/M/S queue, “S” represents:

  • A) Service rate
  • B) Number of servers
  • C) System arrival rate
  • D) Total cost
    Answer: B

The probability of all servers being busy in an M/M/S system is called:

  • A) Traffic intensity
  • B) Idle probability
  • C) Blocking probability
  • D) Queue probability
    Answer: C

As the number of servers increases in an M/M/S model, what happens to customer wait times?

  • A) They remain constant
  • B) They increase
  • C) They decrease
  • D) They fluctuate
    Answer: C

What happens when servers in an M/M/S system are underutilized?

  • A) Waiting times increase
  • B) Service costs increase
  • C) System becomes unstable
  • D) Arrival rates decrease
    Answer: B

Which type of queueing system is best for bank teller counters with multiple staff?

  • A) M/M/1
  • B) M/M/S
  • C) M/D/1
  • D) M/G/1
    Answer: B

14. Real-World Applications

Supermarkets often use which type of queueing model?

  • A) Single-server, single-queue (M/M/1)
  • B) Multi-server, single-queue (M/M/S)
  • C) Single-server, multiple-queue
  • D) Multi-server, multiple-queue
    Answer: D

In fast-food restaurants, drive-thru systems are modeled as:

  • A) Multi-server, single queue
  • B) Single-server, single queue
  • C) Multi-server, multiple queues
  • D) Single-server, multiple queues
    Answer: B

For large-scale call centers, the ideal queueing model is:

  • A) M/M/1
  • B) M/M/S
  • C) M/D/1
  • D) G/M/1
    Answer: B

Public transportation systems often use:

  • A) FIFO queue discipline
  • B) Priority queue discipline
  • C) Random queue discipline
  • D) LIFO queue discipline
    Answer: A

Which queue type is seen in online ticketing platforms with limited availability?

  • A) Priority queues
  • B) FIFO queues
  • C) LIFO queues
  • D) Blocking queues
    Answer: D

15. Advanced Queueing Topics

The Erlang B formula is used to calculate:

  • A) Blocking probability in finite queues
  • B) Utilization in infinite queues
  • C) Arrival rates for multi-server systems
  • D) Average queue length
    Answer: A

Which queueing model considers balking and reneging behaviors?

  • A) M/M/1
  • B) M/M/1/K
  • C) M/G/1
  • D) M/M/S/K
    Answer: D

Reneging refers to:

  • A) Customers leaving without entering the queue
  • B) Customers leaving after joining the queue
  • C) Customers joining a priority queue
  • D) Servers leaving the system
    Answer: B

Balking refers to:

  • A) Customers skipping the queue
  • B) Customers refusing to join the queue
  • C) Servers refusing service
  • D) Customers leaving mid-service
    Answer: B

In real-world scenarios, queues with high variability often require:

  • A) M/D/1 models
  • B) M/G/1 models
  • C) M/M/S models
  • D) G/G/1 models
    Answer: B

16. Queueing Systems with Finite Capacity

A queue with finite capacity is represented as:

  • A) M/M/1
  • B) M/M/1/K
  • C) M/G/1
  • D) M/M/S
    Answer: B

In a finite capacity queue, if the system is full, new arrivals:

  • A) Wait outside the system
  • B) Are blocked or lost
  • C) Are given priority
  • D) Increase the service rate
    Answer: B

Finite capacity queues are ideal for modeling:

  • A) Public parks with limited parking spaces
  • B) Online shopping platforms
  • C) Hospitals with unlimited patient capacity
  • D) Call centers with unlimited lines
    Answer: A

The arrival rate in a finite capacity queue decreases due to:

  • A) Server breakdowns
  • B) Blocking of customers
  • C) Increased service times
  • D) Decreased queue length
    Answer: B

What is the primary difference between finite and infinite queueing models?

  • A) Service discipline
  • B) Arrival rate
  • C) Queue length limitation
  • D) Number of servers
    Answer: C

17. Impact of Variability in Queues

High variability in arrival and service rates leads to:

  • A) Longer queues and waiting times
  • B) Shorter queues and increased efficiency
  • C) No change in system performance
  • D) Increased system stability
    Answer: A

The coefficient of variation (CV) is used to measure:

  • A) System utilization
  • B) Variability in service or arrival rates
  • C) Queue length
  • D) Server efficiency
    Answer: B

Which model handles variability better?

  • A) M/M/1
  • B) M/G/1
  • C) G/G/1
  • D) M/D/1
    Answer: C

If service times have zero variability, the model becomes:

  • A) M/M/1
  • B) M/G/1
  • C) M/D/1
  • D) G/G/1
    Answer: C

Reducing variability in queues leads to:

  • A) Increased wait times
  • B) Smoother flow and reduced delays
  • C) Higher blocking probabilities
  • D) Decreased server efficiency
    Answer: B

Call centers with a mix of high-priority and regular customers use:

  • A) FIFO queue discipline
  • B) Multi-priority queueing
  • C) LIFO queue discipline
  • D) Random queue discipline
    Answer: B

A queue with servers that operate at different speeds is called a:

  • A) Homogeneous server model
  • B) Heterogeneous server model
  • C) FIFO model
  • D) Multi-channel model
    Answer: B

Cloud computing systems use queueing models to:

  • A) Maximize hardware costs
  • B) Balance server loads and optimize response times
  • C) Eliminate all waiting times
  • D) Ensure zero utilization of servers
    Answer: B

Healthcare systems often prioritize queues based on:

  • A) Random service order
  • B) Customer arrival time
  • C) Severity of the case
  • D) Customer’s age
    Answer: C

Which queueing model applies best to data packet routing in networks?

  • A) M/M/1
  • B) Priority queueing
  • C) Multi-server model
  • D) Blocking queue
    Answer: B

Queueing simulations are used to:

  • A) Replace mathematical models
  • B) Approximate real-world queue performance
  • C) Reduce server efficiency
  • D) Eliminate arrival rate variability
    Answer: B

Monte Carlo simulations in queueing focus on:

  • A) Deterministic outcomes
  • B) Predicting service rate variances
  • C) Randomized processes to model complex systems
  • D) Simplifying finite queue models
    Answer: C

Discrete-event simulation is commonly used in:

  • A) Queueing theory
  • B) Statistical modeling
  • C) Physical sciences
  • D) Random number generation
    Answer: A

The first step in queue simulation is to:

  • A) Analyze output data
  • B) Develop a conceptual model
  • C) Optimize queue lengths
  • D) Increase server utilization
    Answer: B

Which software is widely used for queueing simulations?

  • A) MATLAB
  • B) Microsoft Excel
  • C) Arena Simulation Software
  • D) Tableau
    Answer: C

AI-powered queueing systems are primarily used to:

  • A) Reduce costs by eliminating servers
  • B) Predict and manage demand more efficiently
  • C) Increase manual intervention in queues
  • D) Avoid customer interaction
    Answer: B

Which technology helps monitor real-time queue performance?

  • A) Blockchain
  • B) IoT (Internet of Things)
  • C) Virtual Reality
  • D) 3D Printing
    Answer: B

Dynamic queue management systems adjust based on:

  • A) Pre-determined schedules
  • B) Real-time data and demand forecasting
  • C) Fixed queue lengths
  • D) Customer feedback only
    Answer: B

Self-service kiosks in fast-food restaurants are an example of:

  • A) Eliminating queues
  • B) Reducing service variability
  • C) Replacing servers with automation
  • D) Using dynamic queue management
    Answer: C

Predictive analytics in queueing systems can help with:
- A) Increasing customer complaints
- B) Proactive scheduling of resources
- C) Slowing down service rates
- D) Randomizing queue disciplines

Answer: B

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