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Explore Semi‑Markov Process Example: Taxi Routing & Traveling Problem (Step‑by‑Step Solution) with 222 views, 1 likes, and 0 comments. Experience the impact of this video content that has captured audience attention.

In this video, we solve a classic Semi‑Markov Process problem involving a taxi that moves between three locations with given transition probabilities and travel times. We answer three key questions: Limiting probability that the taxi’s most recent stop was at each location Limiting probability that the taxi is heading toward location 2 Fraction of time the taxi spends traveling from location 2 to location 3 What you’ll learn: How to set up global balance equations for an embedded Markov chain How to compute stationary probabilities of the embedded chain How to calculate mean holding times (τᵢ) for each state How to find the expected cycle time Σ πⱼ τⱼ How to apply the semi‑Markov limiting probability formula for transitions Problem setup (for reference): Locations: 1, 2, 3 Travel times: t₁₂=20, t₁₃=30, t₂₃=30 (symmetric) Transition rules: From 1 → equally likely to 2 or 3 From 2 → 1 with prob 1/3, to 3 with prob 2/3 From 3 → always to 1 Upon arrival, taxi departs immediately Final results: π₁ = 3/7 ≈ 42.86% π₂ = 3/14 ≈ 21.43% π₃ = 5/14 ≈ 35.71% P(heading to 2) = 3/19 ≈ 15.79% P(traveling 2→3) = 3/19 ≈ 15.79% Perfect for students of stochastic processes, operations research, Markov chains, and queueing theory. 📌 Like & subscribe for more probability and stochastic process examples.

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