CHAPTER 11 WAITING LINE MODELS A waiting line with only one service facility.
Arrival rate Steady-state operation
The mean number of customers or units The normal operation of the waiting line
arriving in a given period of time. after it has gone through a startup or transient
period. The operating characteristics of waiting
Blocked
lines are computed for steady-state conditions.
When arriving units cannot enter the waiting
Transient period
line because the system is full. Blocked
The startup period for a waiting line,
units can occur when waiting lines are not
occurring before the waiting line reaches a
allowed or when waiting lines have a finite
normal or steady-state operation.
capacity.
Exponential probability distribution
CHAPTER 12 SIMULATION
A probability distribution used to describe
the service time for some waiting line models. Base-case scenario
Finite calling population Determining the output assuming the most
likely values for the random variables of a
The population of customers or units that may
model.
seek service has a fixed and finite value.
Best-case scenario
First-come, first-served (FCFS)
Determining the output assuming the best
The queue discipline that serves waiting units
values that can be expected for the random
on a first-come, first-served basis.
variables of a model.
Infinite calling population
Continuous probability distribution
The population of customers or units that
A probability distribution where the
may seek service has no specified upper limit.
possible values for a random variable can take
Multiple-server waiting line any value between two specified values. The
specified values can include negative and
A waiting line with two or more parallel positive infinity.
service facilities.
Controllable input
Operating characteristics
Input to a simulation model that is selected
The performance measures for a waiting by the decision maker.
line, including the probability that no units are
in the system, the average number of units in Discrete-event simulation model
the waiting line, the average waiting time, and
A simulation model that describes how a
so on.
system evolves over time by managing a
Poisson probability distribution discrete sequence of events (i.e., customer
arrival or departure, over time).
A probability distribution used to describe the
arrival pattern for some waiting line models. Discrete probability distribution
Queue A probability distribution where the possible
values for a random variable can take on only
A waiting line. specified discrete values.
Queueing theory Dynamic simulation model
The body of knowledge dealing with waiting A simulation model used in situations where
lines. the state of the system affects how the system
Service rate changes or evolves over time.
, A description of the range and relative
likelihood of possible values of an uncertain
variable.
Chance event
Random variable or uncertain variable
An uncertain future event affecting the
Input to a simulation model whose value is
consequence, or payoff, associated with a
un-certain and described by a probability
decision.
distribution.
Chance nodes
Risk analysis
Nodes indicating points where an uncertain
The process of evaluating a decision in the
event will occur.
face of uncertainty by quantifying the likelihood
and magnitude of an undesirable outcome. Conditional probabilities
Simulation The probability of one event given the known
outcome of a (possibly) related event.
A method that uses repeated random
sampling of values to represent uncertainty in a Consequence
model representing a real system and computes
the values of model outputs. The result obtained when a decision
alternative is chosen and a chance event occurs.
Static simulation model A measure of the consequence is often called a
payoff.
A simulation model in which each trial used
in situations where the state of the system at Consequence nodes
one point in time does not affect the state of
the system at future points in time. Each trial of Nodes of an influence diagram indicating
the simulation is independent. points where a payoff will occur.
Validation Conservative approach
The process of determining that a simulation An approach to choosing a decision
model provides an accurate representation of a alternative without using probabilities. For a
real system. maximization problem, it leads to choosing the
decision alternative that maximizes the
Verification minimum payoff; for a minimization problem, it
leads to choosing the decision alternative that
The process of determining that a computer
minimizes the maximum payoff.
program implements a simulation model as it is
intended. Decision alternatives
What-if analysis Options available to the decision maker.
A trial-and-error approach to learning about Decision nodes
the range of possible out
puts for a model. Trial values are chosen for the Nodes indicating points where a decision is
model inputs (these are the what-ifs) and the made.
value of the output(s) is computed. Decision strategy
Worst-case scenario A strategy involving a sequence of decisions
Determining the output assuming the worst and chance outcomes to provide the optimal
values that can be expected for the random solution to a decision problem.
variables of a model. Decision tree
CHAPTER 13 DECISION ANALYSIS A graphical representation of the decision
Bayes’ theorem problem that shows the sequential nature of
the decision-making process.
Arrival rate Steady-state operation
The mean number of customers or units The normal operation of the waiting line
arriving in a given period of time. after it has gone through a startup or transient
period. The operating characteristics of waiting
Blocked
lines are computed for steady-state conditions.
When arriving units cannot enter the waiting
Transient period
line because the system is full. Blocked
The startup period for a waiting line,
units can occur when waiting lines are not
occurring before the waiting line reaches a
allowed or when waiting lines have a finite
normal or steady-state operation.
capacity.
Exponential probability distribution
CHAPTER 12 SIMULATION
A probability distribution used to describe
the service time for some waiting line models. Base-case scenario
Finite calling population Determining the output assuming the most
likely values for the random variables of a
The population of customers or units that may
model.
seek service has a fixed and finite value.
Best-case scenario
First-come, first-served (FCFS)
Determining the output assuming the best
The queue discipline that serves waiting units
values that can be expected for the random
on a first-come, first-served basis.
variables of a model.
Infinite calling population
Continuous probability distribution
The population of customers or units that
A probability distribution where the
may seek service has no specified upper limit.
possible values for a random variable can take
Multiple-server waiting line any value between two specified values. The
specified values can include negative and
A waiting line with two or more parallel positive infinity.
service facilities.
Controllable input
Operating characteristics
Input to a simulation model that is selected
The performance measures for a waiting by the decision maker.
line, including the probability that no units are
in the system, the average number of units in Discrete-event simulation model
the waiting line, the average waiting time, and
A simulation model that describes how a
so on.
system evolves over time by managing a
Poisson probability distribution discrete sequence of events (i.e., customer
arrival or departure, over time).
A probability distribution used to describe the
arrival pattern for some waiting line models. Discrete probability distribution
Queue A probability distribution where the possible
values for a random variable can take on only
A waiting line. specified discrete values.
Queueing theory Dynamic simulation model
The body of knowledge dealing with waiting A simulation model used in situations where
lines. the state of the system affects how the system
Service rate changes or evolves over time.
, A description of the range and relative
likelihood of possible values of an uncertain
variable.
Chance event
Random variable or uncertain variable
An uncertain future event affecting the
Input to a simulation model whose value is
consequence, or payoff, associated with a
un-certain and described by a probability
decision.
distribution.
Chance nodes
Risk analysis
Nodes indicating points where an uncertain
The process of evaluating a decision in the
event will occur.
face of uncertainty by quantifying the likelihood
and magnitude of an undesirable outcome. Conditional probabilities
Simulation The probability of one event given the known
outcome of a (possibly) related event.
A method that uses repeated random
sampling of values to represent uncertainty in a Consequence
model representing a real system and computes
the values of model outputs. The result obtained when a decision
alternative is chosen and a chance event occurs.
Static simulation model A measure of the consequence is often called a
payoff.
A simulation model in which each trial used
in situations where the state of the system at Consequence nodes
one point in time does not affect the state of
the system at future points in time. Each trial of Nodes of an influence diagram indicating
the simulation is independent. points where a payoff will occur.
Validation Conservative approach
The process of determining that a simulation An approach to choosing a decision
model provides an accurate representation of a alternative without using probabilities. For a
real system. maximization problem, it leads to choosing the
decision alternative that maximizes the
Verification minimum payoff; for a minimization problem, it
leads to choosing the decision alternative that
The process of determining that a computer
minimizes the maximum payoff.
program implements a simulation model as it is
intended. Decision alternatives
What-if analysis Options available to the decision maker.
A trial-and-error approach to learning about Decision nodes
the range of possible out
puts for a model. Trial values are chosen for the Nodes indicating points where a decision is
model inputs (these are the what-ifs) and the made.
value of the output(s) is computed. Decision strategy
Worst-case scenario A strategy involving a sequence of decisions
Determining the output assuming the worst and chance outcomes to provide the optimal
values that can be expected for the random solution to a decision problem.
variables of a model. Decision tree
CHAPTER 13 DECISION ANALYSIS A graphical representation of the decision
Bayes’ theorem problem that shows the sequential nature of
the decision-making process.
