Queuing Theory

Section A: Elements of Queuing Theory

What is the primary purpose of queuing theory?
a) To analyze waiting lines and determine suitable service capacity
b) To calculate inventory depreciation
c) To assign workers to jobs
d) To schedule project activities only
Answer: a) To analyze waiting lines and determine suitable service capacity
A queuing system is created when:
a) Service is always completed before arrival
b) Customers arrive for service and may have to wait
c) No service facility exists
d) Every customer is served simultaneously
Answer: b) Customers arrive for service and may have to wait
In queuing theory, a person, machine or item requiring service is called a:
a) Channel
b) Phase
c) Customer
d) Queue discipline
Answer: c) Customer
The facility that provides service to arriving customers is called the:
a) Calling population
b) Arrival process
c) Waiting line
d) Service mechanism
Answer: d) Service mechanism
The source from which customers arrive is known as the:
a) Calling population
b) Service channel
c) Queue capacity
d) Service discipline
Answer: a) Calling population
A calling population containing a very large number of potential customers is treated as:
a) Deterministic
b) Infinite
c) Single phase
d) Preemptive
Answer: b) Infinite
A repair facility serving a fixed number of machines is an example of a:
a) Multiple-channel system
b) Infinite-source model
c) Finite calling-population model
d) Zero-capacity system
Answer: c) Finite calling-population model
The maximum number of customers permitted in a queuing system is called:
a) Arrival intensity
b) Service level
c) Queue discipline
d) System capacity
Answer: d) System capacity
If any number of customers can wait, the queue is assumed to have:
a) Infinite capacity
b) No service mechanism
c) A finite population
d) Priority discipline
Answer: a) Infinite capacity
A service channel refers to:
a) One stage in service
b) One parallel service facility
c) The order of customer service
d) The source of arrivals
Answer: b) One parallel service facility
A bank with four tellers working in parallel has:
a) One phase only
b) A finite calling population
c) Multiple service channels
d) No waiting line
Answer: c) Multiple service channels
A service phase refers to:
a) One customer in the line
b) One unit of arrival rate
c) One service channel
d) One stage in a sequence of service activities
Answer: d) One stage in a sequence of service activities
A vehicle that is washed and then dried at separate stations experiences:
a) A multiphase service system
b) A single-phase queue
c) A finite-source model only
d) Random service order
Answer: a) A multiphase service system
A single cashier serving one customer at a time is a:
a) Multichannel system
b) Single-channel system
c) Multiphase system
d) Priority system
Answer: b) Single-channel system
The number of customers waiting but not receiving service is called:
a) The calling population
b) The service capacity
c) The queue length
d) The utilization rate
Answer: c) The queue length
The number of customers waiting plus those currently being served is:
a) The queue discipline
b) The arrival rate
c) The service rate
d) The number in the system
Answer: d) The number in the system
When a customer sees a long queue and decides not to join, this is called:
a) Balking
b) Reneging
c) Jockeying
d) Blocking
Answer: a) Balking
When a customer joins a queue but leaves before service, it is called:
a) Blocking
b) Reneging
c) Balking
d) Prioritizing
Answer: b) Reneging
Moving from one waiting line to another is known as:
a) Preemption
b) Balking
c) Jockeying
d) Blocking
Answer: c) Jockeying
When a customer cannot enter because the system is full, the customer is:
a) Reneging
b) Jockeying
c) Balking voluntarily
d) Blocked
Answer: d) Blocked
Which component determines the order in which customers are served?
a) Queue discipline
b) Calling population
c) Service-time distribution
d) Queue capacity
Answer: a) Queue discipline
Which component describes how customers enter the system?
a) Service mechanism
b) Arrival process
c) Departure process
d) Queue discipline
Answer: b) Arrival process
Which component specifies how quickly customers are served?
a) Queue capacity
b) Calling population
c) Service process
d) Arrival discipline
Answer: c) Service process
Which of the following is a common queuing application?
a) Product blending
b) Capital budgeting
c) Transportation allocation
d) Customer-service staffing
Answer: d) Customer-service staffing
Which is an example of a customer in queuing theory?
a) A data packet waiting for network transmission
b) A constraint in linear programming
c) A project activity
d) A warehouse location
Answer: a) A data packet waiting for network transmission

Section B: Arrival and Service-Time Distributions

The average number of arrivals per unit of time is represented by:
a) (\mu)
b) (\lambda)
c) (\rho)
d) (L_q)
Answer: b) (\lambda)
The average number of customers a server can process per unit of time is represented by:
a) (\lambda)
b) (W_q)
c) (\mu)
d) (P_0)
Answer: c) (\mu)
Which distribution commonly models the number of arrivals during a fixed period?
a) Normal distribution
b) Uniform distribution
c) Exponential distribution
d) Poisson distribution
Answer: d) Poisson distribution
If arrivals follow a Poisson process, interarrival times generally follow the:
a) Exponential distribution
b) Poisson distribution
c) Binomial distribution
d) Uniform distribution
Answer: a) Exponential distribution
A Poisson-arrival process assumes arrivals occur:
a) In equal-sized batches only
b) Independently at a constant average rate
c) At fixed time intervals
d) Only when the server is idle
Answer: b) Independently at a constant average rate
If the arrival rate is 10 customers per hour, then:
a) (\mu=10)
b) (\rho=10)
c) (\lambda=10) customers per hour
d) (W=10) hours
Answer: c) (\lambda=10) customers per hour
If a server completes 15 services per hour, then:
a) (\lambda=15)
b) (W_q=15)
c) (L=15)
d) (\mu=15) customers per hour
Answer: d) (\mu=15) customers per hour
The average interarrival time is:
a) (1/\lambda)
b) (\lambda/\mu)
c) (1/\mu)
d) (\mu-\lambda)
Answer: a) (1/\lambda)
The average service time is:
a) (1/\lambda)
b) (1/\mu)
c) (\lambda/\mu)
d) (\lambda+\mu)
Answer: b) (1/\mu)
If (\lambda=12) customers per hour, the average interarrival time is:
a) 12 minutes
b) 10 minutes
c) 5 minutes
d) 1 minute
Answer: c) 5 minutes
If (\mu=6) customers per hour, the average service time is:
a) 6 minutes
b) 5 minutes
c) 12 minutes
d) 10 minutes
Answer: d) 10 minutes
The exponential distribution is known for its:
a) Memoryless property
b) Symmetry
c) Fixed-value property
d) Integer-only outcomes
Answer: a) Memoryless property
The memoryless property means the remaining service time:
a) Always equals zero
b) Does not depend on how long service has already lasted
c) Increases with elapsed time
d) Must be constant
Answer: b) Does not depend on how long service has already lasted
In the M/M/1 model, service times are assumed to follow the:
a) Poisson distribution
b) Normal distribution
c) Exponential distribution
d) Uniform distribution
Answer: c) Exponential distribution
The first “M” in M/M/1 indicates:
a) Multiple servers
b) Mean service time
c) Maximum capacity
d) Markovian or Poisson arrivals
Answer: d) Markovian or Poisson arrivals
The second “M” in M/M/1 indicates:
a) Markovian or exponential service times
b) Multiple waiting lines
c) Maximum queue size
d) Mean number in the system
Answer: a) Markovian or exponential service times
The “1” in M/M/1 represents:
a) One customer in the queue
b) One service channel
c) One arrival per hour
d) One service phase only
Answer: b) One service channel
An M/D/1 model has:
a) Deterministic arrivals and exponential service
b) Multiple channels
c) Poisson arrivals and constant service times
d) General arrivals and deterministic service
Answer: c) Poisson arrivals and constant service times
A D/M/1 model has:
a) Poisson arrivals and deterministic service
b) General arrivals and one server
c) Multiple servers
d) Deterministic arrivals and exponential service times
Answer: d) Deterministic arrivals and exponential service times
In Kendall’s notation, G represents:
a) A general probability distribution
b) A guaranteed service rate
c) A geometric queue discipline
d) Group arrivals only
Answer: a) A general probability distribution
If arrivals occur at fixed intervals, the arrival process is:
a) Exponential
b) Deterministic
c) Poisson
d) General only
Answer: b) Deterministic
Which assumption is required for a standard Poisson arrival process?
a) Arrivals occur only in groups
b) Arrival probability depends on queue length
c) Arrivals are independent
d) Service times are constant
Answer: c) Arrivals are independent
For a very short interval, a Poisson process assumes the probability of more than one arrival is:
a) Equal to one
b) Very high
c) Equal to the service rate
d) Negligibly small
Answer: d) Negligibly small
If the service rate is 20 customers per hour, the mean service time is:
a) 3 minutes
b) 5 minutes
c) 20 minutes
d) 1 minute
Answer: a) 3 minutes
If the mean interarrival time is 4 minutes, the arrival rate is:
a) 4 customers per hour
b) 15 customers per hour
c) 20 customers per hour
d) 60 customers per hour
Answer: b) 15 customers per hour

Section C: Queue Disciplines

FIFO stands for:
a) Final in, first out
b) Fastest in, first out
c) First in, first out
d) First in, fixed order
Answer: c) First in, first out
Under FIFO, the next customer served is usually the customer who:
a) Requires the shortest service
b) Has the highest priority
c) Arrived last
d) Arrived first
Answer: d) Arrived first
Which setting commonly uses FIFO?
a) A supermarket checkout line
b) A stack of materials
c) Random lottery selection
d) Emergency-room triage
Answer: a) A supermarket checkout line
LIFO stands for:
a) Least important, first out
b) Last in, first out
c) Longest in, first out
d) Lowest input, final output
Answer: b) Last in, first out
Which situation commonly illustrates LIFO?
a) Bank teller service
b) Airport check-in
c) Items removed from the top of a stack
d) Hospital triage
Answer: c) Items removed from the top of a stack
SIRO means:
a) Service in regular order
b) Shortest item removed first
c) System input, random output
d) Service in random order
Answer: d) Service in random order
Under a priority discipline, customers are served according to:
a) Their assigned priority levels
b) Arrival time only
c) Longest service time
d) Random order
Answer: a) Their assigned priority levels
A hospital emergency department usually applies:
a) LIFO
b) Priority service
c) SIRO
d) Pure FIFO in all cases
Answer: b) Priority service
In a preemptive-priority system, a high-priority customer may:
a) Be denied service
b) Join the end of the queue only
c) Interrupt a lower-priority service
d) Be served randomly
Answer: c) Interrupt a lower-priority service
In a nonpreemptive-priority system, a high-priority customer must:
a) Interrupt current service
b) Leave the system
c) Join a separate system
d) Wait until current service is completed
Answer: d) Wait until current service is completed
Which queue discipline is often viewed as fair in ordinary service systems?
a) FIFO
b) LIFO
c) SIRO
d) Preemptive priority
Answer: a) FIFO
The queue discipline determines:
a) The service rate
b) The order in which waiting customers are served
c) The size of the calling population
d) The arrival distribution
Answer: b) The order in which waiting customers are served
A shortest-processing-time rule gives preference to customers with:
a) The highest cost
b) The earliest arrival
c) The shortest expected service time
d) The longest waiting time
Answer: c) The shortest expected service time
Under random service, the next customer is:
a) Always the first arrival
b) Always the last arrival
c) Selected by service time
d) Chosen randomly from the queue
Answer: d) Chosen randomly from the queue
Which discipline may reduce average waiting time but may appear unfair?
a) Shortest-processing-time discipline
b) FIFO
c) Random service
d) LIFO only
Answer: a) Shortest-processing-time discipline
A queue discipline based on customer urgency is a:
a) Random discipline
b) Priority discipline
c) LIFO discipline
d) Batch-service discipline
Answer: b) Priority discipline
Priority queues may be classified as:
a) Finite and infinite only
b) Single and multiple channel
c) Preemptive and nonpreemptive
d) Poisson and exponential
Answer: c) Preemptive and nonpreemptive
A lower-priority customer may experience long delays under:
a) Pure FIFO only
b) Random service only
c) Deterministic service
d) Strict priority service
Answer: d) Strict priority service
Which behavior changes the customer’s position by moving to another line?
a) Jockeying
b) Reneging
c) Balking
d) Blocking
Answer: a) Jockeying
Which behavior occurs before joining a queue?
a) Reneging
b) Balking
c) Jockeying
d) Preemption
Answer: b) Balking
Which behavior occurs after a customer has already joined the queue?
a) Balking
b) Blocking
c) Reneging
d) Preemption
Answer: c) Reneging
Which discipline serves the most recently arrived customer first?
a) FIFO
b) SIRO
c) Priority only
d) LIFO
Answer: d) LIFO
Which queue discipline is often used in computer-processing systems with urgent tasks?
a) Priority discipline
b) FIFO only
c) LIFO only
d) No discipline
Answer: a) Priority discipline
A single common line feeding several servers is often preferred because it:
a) Eliminates service time
b) Reduces imbalance among separate lines
c) Makes arrivals deterministic
d) Prevents all waiting
Answer: b) Reduces imbalance among separate lines
Which queue discipline serves customers in the order they arrive?
a) SIRO
b) LIFO
c) FIFO
d) Priority
Answer: c) FIFO

Section D: Operating Characteristics

The utilization factor in an M/M/1 model is:
a) (\mu/\lambda)
b) (\lambda+\mu)
c) (\mu-\lambda)
d) (\rho=\lambda/\mu)
Answer: d) (\rho=\lambda/\mu)
If (\lambda=8) and (\mu=10), utilization is:
a) 0.80
b) 0.20
c) 1.25
d) 18
Answer: a) 0.80
A utilization of 0.65 means the server is busy approximately:
a) 35% of the time
b) 65% of the time
c) 100% of the time
d) 6.5% of the time
Answer: b) 65% of the time
In an M/M/1 system, the probability that the server is idle is:
a) (\rho)
b) (\rho^2)
c) (1-\rho)
d) (1+\rho)
Answer: c) (1-\rho)
If utilization is 0.70, the idle probability is:
a) 0.70
b) 1.70
c) 0.07
d) 0.30
Answer: d) 0.30
The average number of customers in the system is denoted by:
a) (L)
b) (L_q)
c) (W)
d) (W_q)
Answer: a) (L)
The average number of customers waiting in line is denoted by:
a) (W)
b) (L_q)
c) (P_0)
d) (\rho)
Answer: b) (L_q)
The average time spent in the system is denoted by:
a) (L)
b) (L_q)
c) (W)
d) (W_q)
Answer: c) (W)
The average waiting time before service is denoted by:
a) (L)
b) (P_0)
c) (\rho)
d) (W_q)
Answer: d) (W_q)
Little’s Law for the entire system is:
a) (L=\lambda W)
b) (L=\mu W)
c) (W=\lambda L)
d) (L_q=\mu W)
Answer: a) (L=\lambda W)
Little’s Law for the queue is:
a) (L_q=\mu W_q)
b) (L_q=\lambda W_q)
c) (W_q=\mu L_q)
d) (L=\lambda W_q)
Answer: b) (L_q=\lambda W_q)
In an M/M/1 model, the average number in the system is:
a) (\lambda/\mu)
b) (\mu/(\mu-\lambda))
c) (\lambda/(\mu-\lambda))
d) (\lambda\mu)
Answer: c) (\lambda/(\mu-\lambda))
In an M/M/1 model, the average time in the system is:
a) (1/\lambda)
b) (\lambda/\mu)
c) (1/\mu)
d) (1/(\mu-\lambda))
Answer: d) (1/(\mu-\lambda))
The average waiting time in queue for M/M/1 is:
a) (\lambda/[\mu(\mu-\lambda)])
b) (1/(\mu-\lambda))
c) (\mu/(\mu-\lambda))
d) ((\mu-\lambda)/\lambda)
Answer: a) (\lambda/[\mu(\mu-\lambda)])
The average number waiting in queue for M/M/1 is:
a) (\lambda/(\mu-\lambda))
b) (\lambda^2/[\mu(\mu-\lambda)])
c) (1-\lambda/\mu)
d) (\mu/(\mu-\lambda))
Answer: b) (\lambda^2/[\mu(\mu-\lambda)])
Which equation relates total time in system to waiting time?
a) (W=W_q-1/\mu)
b) (W_q=W+1/\mu)
c) (W=W_q+1/\mu)
d) (W=W_q+\mu)
Answer: c) (W=W_q+1/\mu)
Which equation relates (L) and (L_q)?
a) (L=L_q-\rho)
b) (L_q=L+\rho)
c) (L=L_q+\mu)
d) (L=L_q+\rho)
Answer: d) (L=L_q+\rho)
If (\lambda=4) and (\mu=6), then (L) equals:
a) 2 customers
b) 1 customer
c) 4 customers
d) 6 customers
Answer: a) 2 customers
If (\lambda=4) and (\mu=6), then (W) equals:
a) 0.25 hour
b) 0.5 hour
c) 1 hour
d) 2 hours
Answer: b) 0.5 hour
If (\lambda=3) and (W=0.4) hour, Little’s Law gives:
a) 0.4 customer
b) 3 customers
c) 1.2 customers
d) 7.5 customers
Answer: c) 1.2 customers
If (L_q=2) and (\lambda=4) per hour, (W_q) equals:
a) 2 hours
b) 4 hours
c) 8 hours
d) 0.5 hour
Answer: d) 0.5 hour
If (\rho=0.75), the average number in system is:
a) 3 customers
b) 0.75 customer
c) 4 customers
d) 1 customer
Answer: a) 3 customers
In M/M/1, (L) can also be written as:
a) (1-\rho)
b) (\rho/(1-\rho))
c) (\rho^2)
d) (1/\rho)
Answer: b) (\rho/(1-\rho))
In M/M/1, (L_q) can be written as:
a) (\rho/(1-\rho))
b) (1-\rho)
c) (\rho^2/(1-\rho))
d) (\rho+1)
Answer: c) (\rho^2/(1-\rho))
As utilization approaches 1, waiting time generally:
a) Approaches zero
b) Becomes negative
c) Remains constant
d) Increases sharply
Answer: d) Increases sharply

Section E: Steady and Transient States

A queuing system is in steady state when:
a) Long-run probabilities become stable over time
b) No customers arrive
c) Queue length never changes
d) Service time equals zero
Answer: a) Long-run probabilities become stable over time
For an M/M/1 system to reach steady state, the usual condition is:
a) (\lambda>\mu)
b) (\lambda<\mu)
c) (\lambda=\mu)
d) (\lambda=0)
Answer: b) (\lambda<\mu)
If the arrival rate exceeds the service rate, the queue tends to:
a) Remain empty
b) Stabilize at one customer
c) Grow without bound
d) Have zero utilization
Answer: c) Grow without bound
The transient state refers to:
a) Long-run equilibrium
b) A system with no service
c) A constant queue length
d) The period before probabilities stabilize
Answer: d) The period before probabilities stabilize
Transient analysis is especially relevant:
a) During startup or after a major system change
b) Only after infinite operating time
c) Only when utilization is zero
d) Only for deterministic systems
Answer: a) During startup or after a major system change
A steady-state probability (P_n) represents:
a) The service rate of customer (n)
b) The long-run probability of (n) customers in the system
c) The average waiting time
d) The probability of exactly (n) arrivals only
Answer: b) The long-run probability of (n) customers in the system
For M/M/1, the probability of zero customers is:
a) (\rho)
b) (\rho^2)
c) (P_0=1-\rho)
d) (1+\rho)
Answer: c) (P_0=1-\rho)
For M/M/1, the probability of (n) customers in the system is:
a) (1-\rho^n)
b) (\rho/(1-\rho))
c) (\rho+n)
d) ((1-\rho)\rho^n)
Answer: d) ((1-\rho)\rho^n)
If (\rho=0.6), the probability of no customers is:
a) 0.4
b) 0.6
c) 1.6
d) 0.36
Answer: a) 0.4
If (\rho=0.5), the probability of exactly one customer is:
a) 0.50
b) 0.25
c) 0.75
d) 0.125
Answer: b) 0.25
If (\rho=0.5), the probability of exactly two customers is:
a) 0.50
b) 0.25
c) 0.125
d) 0.0625
Answer: c) 0.125
If (\lambda=\mu), an M/M/1 system is generally:
a) Empty
b) Stable with no waiting
c) Stable only under FIFO
d) Not steady-state stable
Answer: d) Not steady-state stable
A stable system requires average service capacity to be:
a) Greater than the average arrival rate
b) Equal to the arrival rate
c) Less than the arrival rate
d) Independent of the arrival rate
Answer: a) Greater than the average arrival rate
A system with (\lambda=5) and (\mu=7) is:
a) Unstable
b) Potentially steady-state stable
c) Always empty
d) Deterministic
Answer: b) Potentially steady-state stable
A system with (\lambda=9) and (\mu=8) is:
a) Stable
b) Idle most of the time
c) Unstable in the long run
d) Guaranteed to have no queue
Answer: c) Unstable in the long run
Steady-state formulas describe:
a) Exact conditions at system startup
b) One specific customer only
c) The first arrival
d) Long-run average system performance
Answer: d) Long-run average system performance
Which quantity becomes time-independent in steady state?
a) State probabilities
b) Individual service times
c) Customer identities
d) Arrival order
Answer: a) State probabilities
During the transient period, state probabilities:
a) Are always zero
b) Change with time
c) Equal steady-state values immediately
d) Are independent of initial conditions
Answer: b) Change with time
Initial conditions are especially important in:
a) Steady-state analysis only
b) Long-run equilibrium only
c) Transient analysis
d) Little’s Law only
Answer: c) Transient analysis
Which statement best describes steady-state analysis?
a) It applies only when no arrivals occur
b) It describes the first few seconds only
c) It assumes queue length is fixed
d) It studies long-run average behavior after initial effects diminish
Answer: d) It studies long-run average behavior after initial effects diminish
If utilization is close to one, the system may be stable but:
a) Average waiting can still be very high
b) The server is mostly idle
c) No customers wait
d) Transient analysis becomes unnecessary
Answer: a) Average waiting can still be very high
In a stable M/M/1 system, the sum of all (P_n) values equals:
a) Zero
b) One
c) (\rho)
d) (\lambda)
Answer: b) One
The steady-state probability distribution for M/M/1 is:
a) Normal
b) Uniform
c) Geometric
d) Binomial
Answer: c) Geometric
The probability of at least one customer in an M/M/1 system equals:
a) (1+\rho)
b) (1-\rho)
c) (\rho^2)
d) (\rho)
Answer: d) (\rho)
The probability that the server is busy in M/M/1 equals:
a) (\rho)
b) (1-\rho)
c) (\rho^2)
d) (1/\rho)
Answer: a) (\rho)

Section F: Single-Channel M/M/1 Model and Applications

The standard M/M/1 model assumes:
a) Deterministic arrivals and service
b) Poisson arrivals, exponential service times and one server
c) Multiple servers and finite capacity
d) General arrivals and no queue
Answer: b) Poisson arrivals, exponential service times and one server
Which queue discipline is usually assumed in the basic M/M/1 model?
a) LIFO
b) SIRO
c) FIFO
d) Preemptive priority
Answer: c) FIFO
The basic M/M/1 model generally assumes:
a) A finite calling population only
b) Deterministic service
c) Multiple channels
d) Infinite calling population and queue capacity
Answer: d) Infinite calling population and queue capacity
The arrival and service processes in the basic M/M/1 model are assumed to be:
a) Independent
b) Identical
c) Deterministic
d) Dependent on queue length
Answer: a) Independent
If (\lambda=5) and (\mu=8), utilization is:
a) 0.375
b) 0.625
c) 1.60
d) 13
Answer: b) 0.625
If (\lambda=5) and (\mu=8), average time in the system is:
a) (1/8) hour
b) (1/5) hour
c) (1/3) hour
d) (3/8) hour
Answer: c) (1/3) hour
If (\lambda=5) and (\mu=8), the average number in the system is:
a) (3/5)
b) (8/3)
c) 13
d) (5/3)
Answer: d) (5/3)
If (\lambda=4) and (\mu=5), (L) equals:
a) 4 customers
b) 0.8 customer
c) 5 customers
d) 1 customer
Answer: a) 4 customers
If (\lambda=4) and (\mu=5), (W) equals:
a) 0.25 hour
b) 1 hour
c) 4 hours
d) 5 hours
Answer: b) 1 hour
If (\lambda=2) and (\mu=4), (L_q) equals:
a) 1 customer
b) 2 customers
c) 0.5 customer
d) 0.25 customer
Answer: c) 0.5 customer
If (\lambda=2) and (\mu=4), (W_q) equals:
a) 0.5 hour
b) 1 hour
c) 2 hours
d) 0.25 hour
Answer: d) 0.25 hour
If (\lambda=6) and (\mu=9), utilization is:
a) (2/3)
b) (1/3)
c) 1.5
d) 15
Answer: a) (2/3)
If (\lambda=6) and (\mu=9), (W) equals:
a) (1/9) hour
b) (1/3) hour
c) (1/6) hour
d) 3 hours
Answer: b) (1/3) hour
If (\lambda=6) and (\mu=9), (L) equals:
a) 1 customer
b) 3 customers
c) 2 customers
d) 6 customers
Answer: c) 2 customers
If (\lambda=6) and (\mu=9), (L_q) equals:
a) 2 customers
b) 1 customer
c) (2/3) customer
d) (4/3) customers
Answer: d) (4/3) customers
Increasing the service rate while holding arrivals constant will usually:
a) Reduce waiting time
b) Increase utilization
c) Increase queue length
d) Make the system unstable
Answer: a) Reduce waiting time
Increasing the arrival rate while holding service capacity constant will usually:
a) Reduce utilization
b) Increase congestion
c) Reduce the average number in system
d) Increase idle probability
Answer: b) Increase congestion
Which cost generally increases when service capacity is expanded?
a) Waiting cost
b) Customer-delay cost
c) Service-facility cost
d) Reneging cost only
Answer: c) Service-facility cost
Which cost generally decreases when service capacity is expanded?
a) Server salary
b) Equipment cost
c) Facility operating cost
d) Customer waiting cost
Answer: d) Customer waiting cost
Queuing decisions often seek to minimize:
a) Total service cost plus waiting cost
b) Arrival rate only
c) Service time only
d) Queue capacity only
Answer: a) Total service cost plus waiting cost
Extremely high server utilization may be undesirable because it:
a) Guarantees no waiting
b) Can produce long queues and delays
c) Eliminates congestion
d) Increases idle time
Answer: b) Can produce long queues and delays
Which is a suitable application of an M/M/1 model?
a) A bank with ten parallel tellers
b) A fixed-interval production line
c) One repair technician serving random machine failures
d) A deterministic two-stage service process
Answer: c) One repair technician serving random machine failures
Which condition would violate the basic M/M/1 assumptions?
a) One server
b) FIFO service
c) Poisson arrivals
d) Constant rather than exponential service times
Answer: d) Constant rather than exponential service times
A manager should add service capacity when:
a) The reduction in waiting-related cost justifies the added service cost
b) Utilization is always below one
c) No customer has complained
d) The service rate is already zero
Answer: a) The reduction in waiting-related cost justifies the added service cost
Which statement best summarizes single-channel queuing analysis?
a) Maximum utilization always gives minimum total cost
b) It evaluates the trade-off between service capacity and customer waiting
c) Waiting can always be eliminated at no cost
d) Arrival and service rates have no effect on congestion
Answer: b) It evaluates the trade-off between service capacity and customer waiting

Category

Queuing Theory