Q.1 What does a queue in queuing theory represent?
A set of random variables
A waiting line of customers or items
A statistical distribution
A financial transaction record
Explanation - In queuing theory, a queue is simply the waiting line of customers, tasks, or entities waiting for service.
Correct answer is: A waiting line of customers or items
Q.2 What does the term 'arrival rate' usually represent in queuing models?
Average service time per customer
Average number of arrivals per unit time
Number of servers in the system
Total time spent by customers
Explanation - Arrival rate (λ) refers to how many customers or jobs arrive per unit of time.
Correct answer is: Average number of arrivals per unit time
Q.3 Which distribution most commonly models arrivals in queuing systems?
Normal distribution
Poisson distribution
Exponential distribution
Binomial distribution
Explanation - The Poisson distribution is widely used to model the probability of a given number of arrivals within a time period.
Correct answer is: Poisson distribution
Q.4 What is the symbol usually used for service rate?
λ
μ
ρ
σ
Explanation - In queuing theory, μ represents the service rate (average number of customers served per unit of time).
Correct answer is: μ
Q.5 What does Little’s Law state?
L = λW
W = λL
L = μW
μ = λL
Explanation - Little’s Law states that the average number in the system (L) equals the arrival rate (λ) multiplied by the average waiting time (W).
Correct answer is: L = λW
Q.6 In Kendall’s notation M/M/1, what does the first 'M' stand for?
Markov chain
Memoryless arrivals (Poisson)
Multiple servers
Maximum waiting time
Explanation - The first 'M' in M/M/1 indicates that arrivals follow a Poisson process (memoryless inter-arrival times).
Correct answer is: Memoryless arrivals (Poisson)
Q.7 In Kendall’s notation M/M/1, what does the second 'M' represent?
Poisson service time
Exponential service time
Multiple arrivals
Markov queue
Explanation - The second 'M' in M/M/1 indicates service times follow an exponential distribution.
Correct answer is: Exponential service time
Q.8 What does the single '1' in M/M/1 stand for?
One server
One customer
One queue length
One time unit
Explanation - The final number in M/M/1 refers to the number of servers, here being a single server system.
Correct answer is: One server
Q.9 If arrival rate λ = 3 per minute and service rate μ = 5 per minute, what is system utilization ρ?
0.6
1.2
0.3
2.0
Explanation - Utilization ρ = λ/μ = 3/5 = 0.6.
Correct answer is: 0.6
Q.10 Which of the following is NOT a common performance measure in queuing theory?
Average waiting time
Average queue length
Server utilization
Compound interest rate
Explanation - Compound interest rate belongs to finance, not queuing system performance.
Correct answer is: Compound interest rate
Q.11 In an M/M/1 queue, what is the formula for average number in system (L)?
λ/(μ-λ)
μ/(λ-μ)
λμ
1/(μλ)
Explanation - For an M/M/1 queue, L = λ/(μ−λ), assuming λ < μ.
Correct answer is: λ/(μ-λ)
Q.12 What condition ensures stability in a queuing system?
λ ≥ μ
λ < μ
μ < λ
λ = μ
Explanation - For a queue to be stable, the arrival rate must be less than the service rate.
Correct answer is: λ < μ
Q.13 What is the average waiting time in the system (W) in an M/M/1 queue?
1/(μ-λ)
μ/λ
λ/μ
1/λμ
Explanation - In an M/M/1 queue, W = 1 / (μ−λ).
Correct answer is: 1/(μ-λ)
Q.14 What does FIFO discipline mean in queuing theory?
Fastest in, first out
First in, first out
Fewest in, first out
Final in, first out
Explanation - FIFO means the first customer to enter the queue is the first to be served.
Correct answer is: First in, first out
Q.15 Which service discipline gives priority to the last arriving customer?
FIFO
LIFO
SIRO
Priority Queue
Explanation - LIFO stands for Last In, First Out, meaning the most recent arrival is served first.
Correct answer is: LIFO
Q.16 Which of these is a random service discipline?
FIFO
LIFO
SIRO
Priority Queue
Explanation - SIRO (Service In Random Order) selects the next customer randomly.
Correct answer is: SIRO
Q.17 If λ = 4 per hour and μ = 6 per hour, what is the average number in the system (L) for M/M/1?
1
2
3
4
Explanation - L = λ / (μ−λ) = 4 / (6−4) = 2.
Correct answer is: 2
Q.18 Which notation describes a system with exponential arrivals, exponential service, and 2 servers?
M/M/1
M/M/2
M/2/M
M/E/1
Explanation - M/M/2 represents Poisson arrivals, exponential service, and 2 servers.
Correct answer is: M/M/2
Q.19 Which of these is NOT an assumption of the basic M/M/1 queue?
Poisson arrivals
Exponential service times
Single server
Deterministic arrivals
Explanation - M/M/1 assumes random (Poisson) arrivals, not deterministic arrivals.
Correct answer is: Deterministic arrivals
Q.20 What is the probability that there are zero customers in an M/M/1 system?
1 − ρ
ρ
λ/μ
μ − λ
Explanation - The steady-state probability of zero customers is P0 = 1 − ρ, where ρ = λ/μ.
Correct answer is: 1 − ρ
Q.21 Which parameter defines the 'traffic intensity' of a system?
μ/λ
λ/μ
λμ
λ+μ
Explanation - Traffic intensity is ρ = λ/μ, indicating system load.
Correct answer is: λ/μ
Q.22 What happens if λ ≥ μ in an M/M/1 queue?
Queue stabilizes
Queue grows infinitely
Queue disappears
System becomes idle
Explanation - If arrivals exceed service capacity, the queue grows without bound.
Correct answer is: Queue grows infinitely
Q.23 Which of the following is a multi-server model?
M/M/1
M/M/c
M/D/1
M/G/1
Explanation - M/M/c is the notation for a queue with multiple servers (c servers).
Correct answer is: M/M/c
Q.24 What is the average number of customers in the queue (Lq) for M/M/1?
ρ^2 / (1−ρ)
ρ / (1−ρ)
λ / (μ−λ)
ρ(1−ρ)
Explanation - For M/M/1, the average queue length is Lq = ρ² / (1−ρ).
Correct answer is: ρ^2 / (1−ρ)
Q.25 What is the expected waiting time in queue (Wq) in M/M/1?
λ / μ²
ρ / (μ−λ)
1 / (μ−λ)
ρ / μ
Explanation - Wq = ρ / (μ−λ), where ρ = λ/μ.
Correct answer is: ρ / (μ−λ)