Random walks in a queueing network environment

We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The tool is the detailed balance equations.

[1]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[2]  Antonis Economou,et al.  Generalized product-form stationary distributions for Markov chains in random environments with queueing applications , 2005, Advances in Applied Probability.

[3]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[4]  T. Liggett Continuous Time Markov Processes: An Introduction , 2010 .

[5]  M. Evans,et al.  Nonequilibrium statistical mechanics of the zero-range process and related models , 2005, cond-mat/0501338.

[6]  G. Mil’shtein,et al.  Interaction of Markov Processes , 1972 .

[7]  J. Černý,et al.  Randomly trapped random walks on Zd , 2015 .

[8]  R. Serfozo Introduction to Stochastic Networks , 1999 .

[9]  J. R. Jackson Networks of Waiting Lines , 1957 .

[10]  Condensation in the Zero Range Process: Stationary and Dynamical Properties , 2003, cond-mat/0302079.

[11]  U. Narayan Bhat,et al.  Queueing and related models , 1992 .

[12]  K. Banasiewicz Economic and organizational effects of different legal and organizational forms of enterprises , 2006 .

[13]  T. Liggett,et al.  Stochastic Interacting Systems: Contact, Voter and Exclusion Processes , 1999 .

[14]  G. B. Arous,et al.  Randomly trapped random walks , 2013, 1302.7227.

[15]  Adam Bowditch Central limit theorems for biased randomly trapped random walks on Z , 2016, Stochastic Processes and their Applications.

[16]  Erwin Bolthausen,et al.  Ten Lectures on Random Media , 2002 .

[17]  Yixin Zhu,et al.  Markovian queueing networks in a random environment , 1994, Oper. Res. Lett..

[18]  Randolph D. Nelson,et al.  The mathematics of product form queuing networks , 1993, CSUR.

[19]  Vadim Malyshev,et al.  Condensation in large closed Jackson networks , 1996 .

[20]  W. J. Gordon,et al.  Closed Queuing Systems with Exponential Servers , 1967, Oper. Res..

[21]  James R. Jackson,et al.  Jobshop-Like Queueing Systems , 2004, Manag. Sci..

[22]  Stefan Grosskinsky Warwick,et al.  Interacting Particle Systems , 2016 .

[23]  V. A. Malyshev,et al.  On mathematical models of the service networks , 2009 .

[24]  D. Tibi,et al.  Explicit Lyapunov functions and estimates of the essential spectral radius for Jackson networks , 2012, 1206.3066.