A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT

We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.

[1]  Shaler Stidham,et al.  Cost Models for Stochastic Clearing Systems , 1977, Oper. Res..

[2]  W. Stadje,et al.  Risk analysis for a stochastic cash management model with two types of customers , 2000 .

[3]  Søren Asmussen,et al.  An Operational Calculus for Matrix-Exponential Distributions, with Applications to a Brownian (q, Q) Inventory Model , 1998, Math. Oper. Res..

[4]  Onno Boxma,et al.  The workload in the M/G/1 queue with work removal , 1995 .

[5]  Xiuli Chao,et al.  A queueing network model with catastrophes and product form solution , 1995, Oper. Res. Lett..

[6]  J. Harrison,et al.  Brownian motion and stochastic flow systems , 1986 .

[7]  Shaler Stidham,et al.  Stochastic clearing systems , 1974 .

[8]  Kisu Kim,et al.  A generalized cost model for stochastic clearing systems , 1993, Comput. Oper. Res..

[9]  Offer Kella,et al.  A multi-dimensional martingale for Markov additive processes and its applications , 2000, Advances in Applied Probability.

[10]  Erol Gelenbe,et al.  Queues with negative arrivals , 1991, Journal of Applied Probability.

[11]  Jesús R. Artalejo,et al.  Analysis of a stochastic clearing system with repeated attempts , 1998 .

[12]  Offer Kella,et al.  An exhaustive lĕvy storage process with intermittent output , 1998 .

[14]  Agnès Sulem,et al.  Explicit Solution of Inventory Problems with Delivery Lags , 1995, Math. Oper. Res..

[15]  Onno Boxma,et al.  A Note on Negative Customers, GI/G/1 Workload and Risk Processes , 1996 .

[16]  Peter G. Harrison,et al.  The M/G/1 queue with negative customers , 1996, Advances in Applied Probability.

[17]  Gordon F. Newell,et al.  Applications of queueing theory , 1971 .

[18]  Shaler Stidham,et al.  Clearing Systems and (s, S) Inventory Systems with Nonlinear Costs and Positive Lead Times , 1986, Oper. Res..

[19]  David Perry,et al.  Clearing Models for M/G/1 Queues , 2001, Queueing Syst. Theory Appl..

[20]  Ward Whitt.  The Stationary Distribution of a Stochastic Clearing Process , 1981, Oper. Res..

[21]  Paul H. Zipkin,et al.  Inventory Models with Continuous, Stochastic Demands , 1991 .

[22]  Shaler Stidham,et al.  Semi-Stationary Clearing Processes. , 1978 .

[23]  A. W. Kemp,et al.  Applied Probability and Queues , 1989 .

[24]  Peter G. Harrison,et al.  SOJOURN TIMES IN SINGLE-SERVER QUEUES WITH NEGATIVE CUSTOMERS , 1993 .