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Lindley equation
Summary
The Lindley equation (or Lindley recursion) is a discrete-time stochastic process used in probability and queueing theory to model dynamic systems over time, most notably the waiting time of customers in a single-server queue with a First-In, First-Out (FIFO) service discipline. Formally expressed as $W_{n+1} = \max(0, W_n + U_n)$, where $W_n$ represents the waiting time of the $n$-th customer and $U_n$ is the difference between service time and inter-arrival time, it captures how a customer's wait depends on whether the previous customer finished serving before the next arrived.
First introduced by Dennis Lindley in 1952, the concept extends to tracking queue lengths and yields Lindley's integral equation, which helps determine stationary waiting time distributions in $G/G/1$ queues using mathematical techniques like the Wiener–Hopf method.
ARTICLE
Summary
The Lindley equation (or Lindley recursion) is a discrete-time stochastic process used in probability and queueing theory to model dynamic systems over time, most notably the waiting time of customers in a single-server queue with a First-In, First-Out (FIFO) service discipline. Formally expressed as $W_{n+1} = \max(0, W_n + U_n)$, where $W_n$ represents the waiting time of the $n$-th customer and $U_n$ is the difference between service time and inter-arrival time, it captures how a customer's wait depends on whether the previous customer finished serving before the next arrived.
First introduced by Dennis Lindley in 1952, the concept extends to tracking queue lengths and yields Lindley's integral equation, which helps determine stationary waiting time distributions in $G/G/1$ queues using mathematical techniques like the Wiener–Hopf method.
ARTICLE
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