Glossary

• Round-robin is a scheduling discipline that allows several data flows to fairly share the link capacity.
• Effective arrival rate is throughput.
• Model is an abstraction of the system. It should capture the essential characteristics of the system.
• Attribute is the property of an entity.
• Birth-Death process is a special case of Markov process.
• Ultilization is the percentage of time the server is busy, Σ s_i / total time or U = XS
• Service time = service requirement / server capacity.
• Little's Law is applicable to any types of queueing models, given the system is stable. Q = XR
• Z is think time; S is service time; R is response time = total response time / n; X is throughput = number of completion / time; U is utilization; μ is service rate; λ is arrival rate = n/L; Q is mean number of jobs in system; N* is the saturation point S+Z/S;
• Response variable is outcome of an experiment, typically a performance metric.
• Factor is a parameter that will be varied during the evaluation, may have several alternatives (levels).
• Level is a value that a factor may assume.
• Traffic intensity is ρ = λ / μ

Queueing Disciplines

• FCFS
• LCFS
• Shortest time first serve

Analysis of Variance

• Overall mean μ = 1/ar ( Σ&Sigma y_ij ).
• Effect α_j = y_.j - μ.
• SSY is the sum of all y squares over a levels and r repetitions.
• SSO is the square of mean times a levels and r repetitions.
• SSA is sum of effects.
• SST is the total variance = SSY - SSO
• SSE is the total error = SST - SSA

Performance Model Development

• Obtain a good understanding of the system
• Determine system components the model should include
• Use models done on similar systems
• Identify key entities and attributes
• Select queueing model
• Specify resource management schemes
• Specify system and workload parameters and performance metrics

Simulation Program Overview

• Initialization: resets clock, queues, event set.
• Main loop: advance clock and invoke events until termination condition is met.
• Event routine: a specialized routine for each event type, update statistical counter, insert future events to event queue.
• Report generator: invoked when simulation ends, compute and output results.

Random Number Generator

• Random numbers need to be uniformally distributed, independent from previous results, computationally inexpensive, large period.
• To test random number, create groups of 2 random numbers, (0th,1th)(2th,3th) ... draw them on a plane as (x,y). Partition the plane into k squares, and examine the result with chi square test.

Systematic Approach to Performance Evaluation

• State goal and define the system
• List services and out comes
• Select Metrics
• List parameters
  • System parameters: hardware and software resources, system design strategies
  • Workload parameters: user behavior
• Select factors
• Select evaluation technique
  • Measurement: involves event driven or time driven measurement done by software or hardware.
  • Simulation
  • Analytic Modelling
• Select workload
• Design experiments
• Analysis and interpretation of results
• Present results

Inverse Transformation Method

• Inverse transformation method is used to generate variates that follow arbitrary probability distribution.
• Generate a random number uniformally distributed across 0-1.
• Obtain the cumulative density function of the probability distribution.
• Equate the CDF with the random number generated and solve for x. x is the random variate of interest.

Birth-Death Process

• Works for exponential distributions
• Obtain a simplified form of P_n = P₀(λ₀λ₁λ₂...λ_n-1 / μ₁μ₂μ₃...μ_n)
• Determine p₀ = [ 1 + Σ^∞_n=0 (λ₀λ₁λ₂...λ_n-1 / μ₁μ₂μ₃...μ_n) ]^-1
• Determine E(n) = Σ^∞_n=0 (n p_n)
• Determine effective arrival rate: λ' = Σ^∞_n=0 (&lambda_np_n)
• Little's law E(r) = E(n) / λ'
• m servers: μ_j=jμ if j < m; μ_j=mμ if j >= m
• N population λ_j=(N-j)λ
• B buffer: λ_j = λ if j < B; λ_j = 0 if j=B

Markov Process

• Works for exponential distributions
• Draw the state transition diagram
• Obtain the balance equations
• Solve balance equation with normalizing equation given by Σ_{feasible states} p_s = 1
• Determine performance metrics from p_s

Product Form Networks

• Works for exponential distributions
• Draw the state transition diagram
• Obtain the balance equations
• Assume product form solution
• Verify that product form solution satisfies the balance equations
• Determine the normalizing constant
• Determine performance metrics from state probability