1. What does the M/M/1 notation represent in waiting line models?
a) Multiple servers with exponential service times
b) Single server with exponential service times
c) Multiple servers with constant service times
d) Single server with constant service times
Answer: b) Single server with exponential service times
Explanation: In waiting line models, M/M/1 signifies a single-server system where arrivals and service times follow exponential distributions.
2. Which factor is crucial for determining the average length of customers in an M/M/1 queue?
a) Arrival rate
b) Service rate
c) Number of servers
d) Queue discipline
Answer: a) Arrival rate
Explanation: The average length of customers in an M/M/1 queue heavily depends on the rate at which customers arrive.
3. What is the optimum service rate in an M/M/1 queue system?
a) Equal to the arrival rate
b) Equal to half of the arrival rate
c) Greater than the arrival rate
d) Independent of the arrival rate
Answer: c) Greater than the arrival rate
Explanation: The optimum service rate in an M/M/1 queue system is greater than the arrival rate to prevent infinite queue growth.
4. In a multiple-server model (M/M/s), what does ‘s’ represent?
a) Number of servers
b) Arrival rate
c) Service rate
d) Queue size
Answer: a) Number of servers
Explanation: ‘s’ in the M/M/s model denotes the number of servers available to serve customers concurrently.
5. What is a competitive strategy in game theory?
a) A strategy aimed at cooperation
b) A strategy to dominate opponents
c) A strategy focused on minimizing losses
d) A strategy aimed at outperforming others
Answer: d) A strategy aimed at outperforming others
Explanation: A competitive strategy in game theory involves making decisions to achieve an advantage over other participants.
6. Which method can be used to solve two-person zero-sum games graphically?
a) Simplex method
b) Linear programming
c) Dominance
d) Payoff matrix
Answer: d) Payoff matrix
Explanation: Two-person zero-sum games can be solved graphically using a payoff matrix, where each player’s strategies and payoffs are outlined.
7. What is a pure strategy in game theory?
a) A strategy involving random choices
b) A strategy based on mixed actions
c) A deterministic strategy
d) A strategy aimed at cooperation
Answer: c) A deterministic strategy
Explanation: A pure strategy in game theory involves selecting a specific action with certainty, without incorporating random elements.
8. In game theory, what does dominance refer to?
a) Strategy that always yields the highest payoff
b) Strategy that eliminates all opponents
c) Strategy that guarantees a win
d) Strategy that is always better regardless of opponents’ choices
Answer: d) Strategy that is always better regardless of opponents’ choices
Explanation: Dominance in game theory refers to a strategy that is superior to others regardless of opponents’ choices.
9. What does LP stand for in solving game theory problems?
a) Linear Probability
b) Linear Performance
c) Linear Programming
d) Limited Play
Answer: c) Linear Programming
Explanation: LP stands for Linear Programming, a method used to solve various optimization problems, including those in game theory.
10. In a two-person zero-sum game, what is a saddle point?
a) A point of equilibrium
b) A point of maximum payoff
c) A point of minimum payoff
d) A point of dominance
Answer: a) A point of equilibrium
Explanation: In a two-person zero-sum game, a saddle point is a point of equilibrium where neither player has an incentive to change their strategy.
11. What assumption is commonly made in waiting line models regarding service times?
a) Exponential distribution
b) Constant distribution
c) Normal distribution
d) Poisson distribution
Answer: a) Exponential distribution
Explanation: Waiting line models often assume that service times follow an exponential distribution, allowing for mathematical tractability.
12. In game theory, what does a mixed strategy involve?
a) Using a combination of deterministic actions
b) Randomly selecting strategies
c) Collaborating with opponents
d) Eliminating opponents
Answer: a) Using a combination of deterministic actions
Explanation: A mixed strategy in game theory involves using a combination of deterministic actions to create uncertainty for opponents.
13. What factor is crucial for determining the average time a customer spends in a waiting line?
a) Service rate
b) Arrival rate
c) Queue discipline
d) Number of servers
Answer: c) Queue discipline
Explanation: The average time a customer spends in a waiting line is influenced by the discipline followed in managing the queue, such as first-come-first-served or priority-based.
14. Which method is used to solve game theory problems algebraically?
a) Dominance
b) Payoff matrix
c) Linear programming
d) Graphical method
Answer: c) Linear programming
Explanation: Game theory problems can be solved algebraically using techniques like linear programming to optimize strategies and outcomes.
15. What does the ‘M’ represent in M/M/s waiting line models?
a) Maximum queue size
b) Minimum service time
c) Markovian property
d) Maximum arrival rate
Answer: c) Markovian property
Explanation: In M/M/s waiting line models, the ‘M’ signifies the Markovian property, where the next state of the system depends only on its current state, not its history.