Operational Laws: Little’s Law, response-time law, asymptotic bounds, modification analysis, performance metrics; Markov Chain Theory: discrete-time Markov chains, continuous-time Markov chains, renewal theory, time- reversibility; Poisson Process: memorylessness, Bernoulli splitting, uniformity, PASTA; Queueing Theroy: open networks, closed networks , time-reversibility, RenewalReward, M/M/l, M/M/k, M/M/k/k, burke’s theorem, Jackson networks, classed networks, load-dependent servers, BCMP result and proof, M/G/l full analysis, M/G/k, G/G/l, transform analysis (Laplace and z-transforms);
Simulation: time averages versus ensemble averages, generating random variables for simulation, Inspection Paradox; Modeling empirical Workloads: heavy-tailed property, Pareto distributions, heavy-tailed distributions, understanding variability and tail behavior, Matrix analytic methods; Management of Server Farms: capacity provisioning, dynamic power management, routing policies;
Analysis of Scheduling: FCFS, non-preemtive priorities, preemtive priorities, PS, LCFS, FB, SJF, PSJF, SRPT, etc.