ON/OFF STORAGE SYSTEMS WITH STATE-DEPENDENT INPUT, OUTPUT, AND SWITCHING RATES

We consider a storage model that can be on or off. When on, the content increases at some state-dependent rate and the system can switch to the off state at a state-dependent rate as well. When off, the content decreases at some state-dependent rate (unless it is at zero) and the system can switch to the on position at a state-dependent rate. This process is a special case of a piecewise deterministic Markov process. We identify the stationary distribution and conditions for its existence and uniqueness.

[1]  Michel Mandjes,et al.  Models of Network Access Using Feedback Fluid Queues , 2003, Queueing Syst. Theory Appl..

[2]  J. Michael Harrison,et al.  The Stationary Distribution and First Exit Probabilities of a Storage Process with General Release Rule , 1976, Math. Oper. Res..

[3]  Ivo J. B. F. Adan,et al.  Analysis of a single-server queue interacting with a fluid reservoir , 1998, Queueing Syst. Theory Appl..

[4]  J. Azema,et al.  Mesure invariante sur les classes récurrentes des processus de Markov , 1967 .

[5]  Offer Kella,et al.  Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates , 1997, Queueing Syst. Theory Appl..

[6]  L. Schmetterer.  Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete. , 1963 .

[7]  Michel Mandjes,et al.  Continuous feedback fluid queues , 1998 .

[8]  Ward Whitt,et al.  A Storage Model with a Two-State Random Environment , 1992, Oper. Res..

[9]  D. Mitra,et al.  Stochastic theory of a data-handling system with multiple sources , 1982, The Bell System Technical Journal.

[10]  S. Meyn,et al.  Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes , 1993, Advances in Applied Probability.

[11]  Mark H. A. Davis.  Piecewise‐Deterministic Markov Processes: A General Class of Non‐Diffusion Stochastic Models , 1984 .

[12]  Sem C. Borst,et al.  Queues with Workload-Dependent Arrival and Service Rates , 2004, Queueing Syst. Theory Appl..

[13]  Michel Mandjes,et al.  Simple models of network access, with applications to the design of joint rate and admission control , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[14]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.