EXACT RESULTS FOR A FLUID MODEL WITH STATE-DEPENDENT FLOW RATES

We consider a modulated fluid system with a finite state-space Markov chain Jt as modulating process and general state-dependent net input rates. We derive differential equations for the transient and the stationary distribution of (Wt, Jt), where Wt is the content process, and the corresponding Laplace transforms with respect to time. Moreover, we study the level hitting times of Wt. Our results lead to explicit formulas in the case of two modulating states.

[1]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[2]  David Perry,et al.  A mountain process with state dependent input and output and a correlated dam , 2002, Oper. Res. Lett..

[3]  F. Oberhettinger,et al.  Tables of Laplace Transforms , 1973 .

[4]  Onno Boxma,et al.  AN INTERMITTENT FLUID SYSTEM WITH EXPONENTIAL ON-TIMES AND SEMI-MARKOV INPUT RATES , 2001, Probability in the Engineering and Informational Sciences.

[5]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[6]  Hong Chen,et al.  A Fluid Model for Systems with Random Disruptions , 1992, Oper. Res..

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

[8]  Onno Boxma,et al.  Fluid queues and mountain processes , 1998 .

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

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

[11]  Offer Kella,et al.  RATE MODULATION IN DAMS AND RUIN PROBLEMS , 1996 .

[12]  Anwar Elwalid,et al.  Fluid models for the analysis and design of statistical multiplexing with loss priorities on multiple classes of bursty traffic , 1992, [Proceedings] IEEE INFOCOM '92: The Conference on Computer Communications.

[13]  R. Tweedie,et al.  Storage processes with general release rule and additive inputs , 1982, Advances in Applied Probability.

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

[15]  David Perry,et al.  A correlated M/G/1-type queue with randomized server repair and maintenance modes , 2000, Oper. Res. Lett..