Skorohod-loynes characterizations of queueing, fluid, and inventory processes

William L. Cooper, Volker Schmidt, Richard F. Serfozo

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We consider queueing, fluid and inventory processes whose dynamics are determined by general point processes or random measures that represent inputs and outputs. The state of such a process (the queue length or inventory level) is regulated to stay in a finite or infinite interval - inputs or outputs are disregarded when they would lead to a state outside the interval. The sample paths of the process satisfy an integral equation; the paths have finite local variation and may have discontinuities. We establish the existence and uniqueness of the process based on a Skorohod equation. This leads to an explicit expression for the process on the doubly-infinite time axis. The expression is especially tractable when the process is stationary with stationary input-output measures. This representation is an extension of the classical Loynes representation of stationary waiting times in single-server queues with stationary inputs and services. We also describe several properties of stationary processes: Palm probabilities of the processes at jump times, Little laws for waiting times in the system, finiteness of moments and extensions to tandem and treelike networks.

Original languageEnglish (US)
Pages (from-to)233-257
Number of pages25
JournalQueueing Systems
Issue number1-3
StatePublished - 2001


  • Fluid models
  • Inventory
  • Little's law
  • Loynes' representation
  • Palm probability
  • Queues
  • Skorohod equation


Dive into the research topics of 'Skorohod-loynes characterizations of queueing, fluid, and inventory processes'. Together they form a unique fingerprint.

Cite this