Quadratic Programming optimizes a quadratic objective function subject to linear constraints. Standard form: minimize (1/2)xᵀQx + cᵀx subject to Ax ≤ b, x ≥ 0. If Q is positive semidefinite, the problem is convex and efficiently solvable. Solution methods: interior point algorithms, active set methods, and specialized quadratic solvers. For convex QP, KKT conditions are necessary and sufficient. Applications include: portfolio optimization (minimize risk subject to return constraints), support vector machines in machine learning, and least-squares problems with constraints. Mixed-integer quadratic programming (MIQP) combines quadratic objectives with integer variables, important for portfolio optimization with transaction constraints and feature selection.

Queueing Theory analyzes waiting lines and service systems using mathematical models. A queueing system consists of: arrival process (often Poisson with rate λ), service process (often exponential with rate μ), number of servers c, queue capacity, and queue discipline (FIFO, LIFO, priority). Kendall notation A/B/c/K/N/D describes systems where A is arrival distribution, B is service distribution, c is servers, K is capacity, N is population size, D is discipline. Key measures: average number in system (L), average waiting time (W), utilization (ρ = λ/cμ). Little's Law: L = λW. Models include M/M/1, M/M/c, M/G/1, and queueing networks. Applications: call centers, healthcare, telecommunications, and manufacturing.