Queueing Systems

, Volume 71, Issue 1, pp 79-95

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Strong stationary duality for Möbius monotone Markov chains

  • Paweł LorekAffiliated withMathematical Institute, University of Wrocław
  • , Ryszard SzekliAffiliated withMathematical Institute, University of Wrocław Email author 


For Markov chains with a finite, partially ordered state space, we show strong stationary duality under the condition of Möbius monotonicity of the chain. We give examples of dual chains in this context which have no downwards transitions. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an interpretation for unreliable networks of queues.


Strong stationary times Strong stationary duals Speed of convergence Random walk on cube Möbius function Möbius monotonicity

Mathematics Subject Classification (2000)

60G40 60J10 60K25