Probability

• The Quiet Calculus of Probabilistic Commutativity · 2025-09-27

  A practical calculus for quantifying when non-commutative operations in distributed systems can be safely executed without heavyweight coordination.

• Queueing Theory for Systems Engineers: From M/M/1 to Heavy-Tail Distributions and Tail-at-Scale · 2025-07-18

  Master queueing theory as a practical tool for systems design: the M/M/1 model, Little's Law, Jackson networks, the dramatic impact of heavy-tailed service times on tail latency, and how to apply these insights to load balancers, microservices, and capacity planning.

• Large Deviations Theory: Cramér's Theorem, Importance Sampling, and Rare Event Simulation · 2022-02-13

  A rigorous exploration of large deviations—the theory of exponentially rare events—from Cramér's theorem to Sanov's theorem, and their application to importance sampling for reliable networks.

• Renewal Theory for Computer Science: The Renewal Equation, Key Renewal Theorem, and Applications in Cache Analysis and Failure Recovery · 2022-02-12

  A rigorous journey through renewal theory—the mathematics of recurring events—from the renewal equation and key renewal theorem to applications in garbage collection, cache replacement, and fault-tolerant system analysis.

• Stochastic Processes for Computer Science: Poisson, Brownian Motion, Queueing and Reliability · 2022-02-12

  A rigorous treatment of continuous-time stochastic processes—Poisson processes, CTMCs, Brownian motion with the reflection principle—and their applications in queueing theory, reliability engineering, and network performance.

• Markov Chains for Computer Science: MCMC, Mixing Times, and Randomized Algorithms · 2022-01-31

  A rigorous treatment of Markov chains from a computer science perspective—Metropolis-Hastings, coupling bounds, spectral gaps, and the role of rapid mixing in modern randomized algorithms.

• Probabilistic Reasoning in Intelligent Systems