Modeling and Simulation Examination Review

Vocabulary practice flashcards covering fundamental concepts in computer simulation and modeling, including discrete-event architectures, random number generation techniques, queueing system metrics, and model verification/validation methodologies.

System Detailing (Specification)

The formal identification and mutual agreement of system factors, states, and parameters based on the study's research goals, established between the system manager and the model project authors.

Simulation Model Classification Dimensions

The three primary classification aspects of simulation models: static versus dynamic, deterministic versus stochastic, and continuous versus discrete.

Synchronization Routine (Clock Routine)

A simulation subprogram that searches the event list for the next scheduled event and advances the simulation clock to the occurrence time of that event.

Event Handler Routine

A simulation subprogram responsible for updating the state variables of the system and modifying system and statistical counters when a specific event occurs.

Initialization Routine

A simulation subprogram that resets and prepares the simulation model by placing state variables and clocks into their initial, zero baseline state at time zero.

Library Routine

A collection of utility subprograms used to generate pseudo-random numbers and random variates from specific probability distributions for use in the simulation model.

Report Generator

A subprogram that computes estimates of performance measures from statistical counters and formats the final output summary report upon model termination.

Statistical Counters

Simulation variables designated to collect, accumulate, and store numerical data regarding performance characteristics throughout the execution of a model run.

Event List

A scheduled data structure that maintains the impending event notices, specifically recording the future execution time for each scheduled type of event.

Simulation Clock (MDS)

A system variable tracking current model time that advances instantaneously from the current moment to the execution epoch of the next imminent event.

Next-Event Time Progression

A time advancement approach in simulation where the clock jumps directly from one event time to the next nearest event time, bypassing inactive periods.

Fixed-Increment Time Progression

A simulation timing approach where the model time advances in uniform, discrete time intervals of constant duration $\Delta t$.

Linear Congruential Generator (LCG)

A pseudo-random number generator defined by the recurrence $z_i = (a \cdot z_{i-1} + c) \pmod m$, subject to parameter constraints $m > 0$, $0 \le a < m$, $0 \le c < m$, and seed $0 \le z_0 < m$.

Multiplicative Congruential Generator

A special class of linear congruential generator in which the additive constant $c = 0$, restricting the maximum possible period to at most $m - 1$.

Mixed (Shifted) Congruential Generator

A linear congruential generator where the additive constant $c \neq 0$, enabling the generation of a full sequence period equal to the modulus $m$.

Full Period in an LCG

The condition achieved when a linear congruential generator cycles through all $m$ possible states before repeating any value.

Tausworthe Generator

A linear feedback shift-register random bit generator defined by the recurrence $b_i = (b_{i-r} + b_{i-q}) \pmod 2$, frequently utilized in cryptographic applications.

L'Ecuyer Combined Generator

A random number generation algorithm that combines independent congruential generators to achieve vastly increased period length, formulated as $z_i = (z_{1,i} + z_{2,i}) \pmod m$.

Marsa and Roberts Multiplicative Generator

A multiplicative generator utilizing a modulus of the form $m = 2^b - q$ (such as $m = 2^{31} - 1$ with multiplier $a = 16807$), enabling fast division via bit shifts.

Blum-Blum-Shub Generator

A cryptographically secure pseudorandom bit generator widely deployed in cryptographic security protocols.

Inverse Transform Method

An algorithm that converts a standard uniform variate $g \sim U(0,1)$ into a variate of an arbitrary continuous distribution using the inverse cumulative distribution function, such as $X = -\frac{1}{\lambda} \ln(1 - g)$ for exponential distributions.

Convolution Method

A variate generation technique where a target random variable is generated by taking the sum of $m$ independent random variables: $X = Y_1 + Y_2 + \dots + Y_m$.

Composition Method

A random variate generation algorithm applied when a target cumulative distribution function is represented as a weighted convex combination of sub-distributions: $F(x) = \sum_{j=1}^N p_j \cdot F_j(x)$.

Box-Muller Polar Method

An exact algorithm for producing two independent standard normal random variates via $X_1 = h_1 Y$ and $X_2 = h_2 Y$, where $Y = \sqrt{\frac{-2 \ln(s)}{s}}$, $s = h_1^2 + h_2^2$, and $h_i = 2g_i - 1$.

Central Limit Theorem Normal Approximation

An approximate method for generating standard normal random variables using the summation of 12 uniform variates: $x = \sum_{i=1}^{12} g_i - 6$, where $g_i \sim U(0,1)$.

Poisson Variate Generation Formula

The algorithm for generating a discrete Poisson random variate with parameter $\lambda$: $X = \min\left\{ i : \prod_{j=1}^i g_j < e^{-\lambda} \right\}$, where $g_j \sim U(0,1)$.

Poisson Process Interarrival Time Formula

The recursive expression generating event arrival times in a stationary Poisson process: $t_i = t_{i-1} - \frac{1}{\lambda} \ln(1 - g)$, leveraging exponentially distributed interarrival gaps.

Serial Test for Uniformity

A statistical test verifying the multidimensional uniformity of generated random sequences by computing $\chi^2(d) = \frac{k^d}{n} \sum_{j_1=1}^k \dots \sum_{j_d=1}^k f^2_{j_1 \dots j_d} - n$.

Runs Up Test

A statistical test for independence of pseudorandom numbers based on the frequency of increasing sequences, evaluated via the statistic $R = \frac{1}{n} \sum_{i=1}^6 \sum_{j=1}^6 a_{ij} (r_i - n \cdot b_i)(r_j - n \cdot b_j)$.

Discrete-Event Simulation (DES)

A simulation modeling paradigm where the system state changes instantaneously at separated, discrete points in time upon the occurrence of individual events.

Single-Server Queueing System (M/M/1)

A standard discrete-event queueing model consisting of one service node where both customer interarrival intervals and service durations follow exponential distributions.

Queue Waiting Time Dependence

The property that sequential customer queue delays ($D_1, D_2, \dots, D_n$) in an M/M/1 system constitute dependent, autocorrelated random variables rather than independent observations.

Expected Average Delay in Queue ($\hat{d}(n)$)

An M/M/1 queue performance measure estimating average waiting time before service: $\hat{d}(n) = \frac{1}{n} \sum_{i=1}^n D_i$.

Time-Average Number in Queue ($\hat{q}(n)$)

An M/M/1 system metric tracking the time-integrated queue length, estimated as $\hat{q}(n) = \frac{1}{T(n)} \int_0^{T(n)} Q(t)\,dt$ or discretely as $\hat{q}(n) = \frac{1}{T(n)} \sum_{i=0}^\infty i \cdot T_i(n)$.

Server Utilization Factor ($\hat{u}(n)$)

The estimated proportion of total simulation time that a server remains occupied, given by $\hat{u}(n) = \frac{1}{T(n)} \int_0^{T(n)} B(t)\,dt$, where $B(t) \in \{0, 1\}$.

Model Verification

The rigorous process of determining whether the conceptual simulation model has been correctly and accurately transformed into an executable computer program.

Model Validation

The evaluative process of establishing whether the simulation model represents an adequately accurate depiction of the actual real-world system under study.

Model Credibility

The formal trust and acceptance of model accuracy and correctness by system managers and decision-makers, leading to the actual practical utilization of the model's outputs.

VV&A (Verification, Validation, and Accreditation)

A formal three-tier assurance standard, adopted by institutions such as the U.S. Department of Defense, used to certify simulation models for mission-critical operations.

Universal vs. Domain-Oriented Simulation Packages

The two primary classifications of simulation software packages: general-purpose languages/libraries suitable across disciplines versus application-specific environments tailored to particular domains.