Queuing theory - single server and multi-server models, Erlang service distributions, cost models and optimization - One Line Questions

1. If λ = 5 customers/hour and μ = 10 customers/hour in an M/M/1 system, what is the average number of customers in the queue (Lq)? — 0.25
2. Erlang service distributions are characterized by: — Two parameters: the number of phases and the mean service time per phase
3. What does 'reneging' mean in queuing theory? — A customer leaving the queue before being served
4. What does 'balking' mean in queuing theory? — A customer deciding not to join the queue because it is too long
5. In queuing theory, what does 'server' refer to? — A facility or person providing service
6. Which scenario would typically NOT be modeled using basic M/M/1 or M/M/c models? — A system with non-exponential service times and batch arrivals
7. In multi-server systems, if the number of servers 'c' is very large, the system behavior approaches that of: — An infinite-server system
8. Which of the following is NOT a component of a queuing system definition? — Customer balking
9. The term 'traffic intensity' in a queuing system is often synonymous with: — Utilization factor (ρ)
10. What is the 'Erlang C formula' used for? — Calculating the probability of a customer having to wait in a multi-server system
11. In a multi-server system (M/M/c), what is the condition for stability? — cμ > λ
12. Which distribution assumes that the time between arrivals follows an exponential distribution? — Poisson distribution
13. What is the primary characteristic of an M/D/1 queue (constant service time)? — Exponential arrivals, constant service, 1 server
14. The Kendall notation 'M/M/1' describes a queuing system with: — Exponential arrivals, exponential service, and 1 server
15. What does 'FIFO' stand for in the context of queue discipline? — First In, First Out
16. What does the 'G' in Kendall notation (e.g., M/G/1) represent? — General distribution of service times
17. What is the impact of reducing the service time (increasing μ) in a stable M/M/1 system? — Decreases L, decreases Wq
18. Which of the following is a common assumption in basic queuing models? — No balking or reneging
19. If a queuing system has a finite queue capacity, what is a potential consequence? — Lost customers due to blockage
20. If the arrival rate (λ) increases while the service rate (μ) and number of servers (c) remain constant, what happens to the average waiting time? — It increases
21. If a system is unstable (e.g., λ > μ in M/M/1), what is the expected behavior of the queue? — It will grow indefinitely
22. The Little's Law states that: — L = λW and Lq = λWq
23. What does the 'M' in M/M/1 notation signify regarding arrival and service processes? — Markovian
24. The Erlang distribution is a special case of the Gamma distribution. What is its primary application in queuing theory? — Modeling service times when they are not exponential but have a specific variance
25. Which queuing model has only one service channel? — Single-server model
26. What is the key difference between the M/M/1 and M/M/c models? — Number of servers
27. Which of the following decisions can be informed by queuing theory analysis? — Number of service personnel to employ
28. In a cost model, if the cost of waiting is very high compared to the cost of service, what strategy would likely be chosen? — Increase the number of servers or service rate
29. What is the main challenge in applying queuing theory to real-world problems? — Obtaining accurate estimates for arrival and service rates, and ensuring model assumptions hold
30. What does the symbol 'μ' typically represent in a queuing system? — The service rate
31. In a multi-server model, what is 'c' usually denoted as? — The number of parallel servers
32. In the context of Erlang distributions, what does the parameter 'k' (number of phases) represent? — The number of sequential exponential stages the service time passes through
33. What does 'queue capacity' refer to? — The maximum number of customers allowed to wait in the queue
34. Which of the following is a characteristic of a Poisson arrival process? — The probability of an arrival in a small interval is proportional to the length of the interval
35. In an M/M/c system, what is 'c'? — The number of parallel servers
36. The Erlang-B formula is used to calculate: — The probability of all servers being busy (blocking) in a multi-server system with no queue
37. What does the symbol 'λ' typically represent in a queuing system? — The arrival rate
38. What is the steady-state condition in queuing theory? — The probability distributions of system state variables do not change over time
39. What is the primary goal of Queuing Theory? — To balance service cost and waiting cost
40. What is the average time a customer spends in the system (W) for an M/M/1 queue? — W = Wq + 1/μ
41. Which cost model in queuing theory considers the cost of providing service? — Service cost
42. The total cost in a queuing system is generally the sum of: — Waiting cost and service cost
43. Optimization in queuing theory aims to find the point where: — Total cost is minimized
44. For an M/M/1 queue, what is the average number of customers in the system (L)? — λ / (μ - λ)
45. In an M/M/1 queue, what is the average waiting time in the queue (Wq)? — λ / (μ * (μ - λ))
46. The condition for a stable queuing system (M/M/1) is: — μ > λ
47. What is the utilization factor (ρ) of a single-server system with arrival rate λ and service rate μ? — λ / μ
48. What is the probability of zero customers in an M/M/1 system where ρ = λ/μ? — 1 - ρ
49. Which of the following statements about the utilization factor (ρ) in an M/M/c system is true? — ρ = λ / (cμ)
All One Line Questions
E-Book Queuing theory - single server and multi-server models, Erlang service distributions, cost models and optimization Online Test Queuing theory - single server and multi-server models, Erlang service distributions, cost models and optimization Question Bank Queuing theory - single server and multi-server models, Erlang service distributions, cost models and optimization