An exhaustive lĕvy storage process with intermittent output

We consider a Lĕvy storage model in which the output is shut off every time the system reaches zero, for a length of time which is determined by an arbitrary stopping time with respect to a filtration which may be richer than the one generated by the Lĕvy process. The main contribution is in showing that under suitable conditions, the steady state distribution associated with such a model exhibits a new decomposition property. Namely it can be written as an independent sum of two random variables. One has the distribution associated with a standard reflected Lĕvy process and the other has the steady state distribution of some clearing process (in contrast to excess lifetime or excess number of customers arriving during a vacation). A special case of such a model is the workload process in an M/G/l queue, in particular with the well known T, N and D-policies

[1]  Ward Whitt,et al.  Queues with Server Vacations and Levy Processes with Secondary Jump Input , 1991 .

[2]  Matthew J. Sobel,et al.  Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs , 1969, Oper. Res..

[3]  Eugene A. Feinberg,et al.  Optimal Switching Policies for M/G/1 Queues with Two Performance Criteria , 1995 .

[4]  O. J. Boxma,et al.  Note---Note on a Control Problem of Balachandran and Tijms , 1976 .

[5]  Kashi R. Balachandran,et al.  Control Policies for a Single Server System , 1973 .

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

[7]  Onno Boxma,et al.  Useful Martingales for Stochastic Storage Processes with Lévy-Type Input , 2013, Journal of Applied Probability.

[8]  Offer Kella.  Optimal Control of the Vacation Scheme in an M/G/1 Queue , 1990, Oper. Res..

[9]  Offer Kella.  The threshold policy in the M/G/1 queue with server vacations , 1989 .

[10]  Micha Hofri.  Queueing systems with a procrastinating server , 1986, SIGMETRICS '86/PERFORMANCE '86.

[11]  M. Yadin,et al.  Queueing Systems with a Removable Service Station , 1963 .

[12]  W. Whitt,et al.  Diffusion approximations for queues with server vacations , 1990, Advances in Applied Probability.

[13]  Mandyam M. Srinivasan,et al.  Control policies for the M X /g/ 1 queueing system , 1989 .

[14]  H. C. Tijms,et al.  Optimal control of the workload in an m/g/1 queueing system with removable server , 1975 .

[15]  Jacques Teghem,et al.  Control of the service process in a queueing system , 1986 .

[16]  Daniel P. Heyman,et al.  Optimal Operating Policies for M/G/1 Queuing Systems , 1968, Oper. Res..

[17]  V. Balachandran,et al.  Comment on “Solving the 'Marketing Mix' Problem using Geometric Programming” , 1975 .

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

[19]  Colin E. Bell,et al.  Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server , 1971, Oper. Res..

[20]  Ushio Sumita,et al.  Modified Lindley process with replacement: dynamic behavior, asymptotic decomposition and applications , 1989 .

[21]  K. C. So,et al.  Optimality of threshold policies in single-server queueing systems with server vacations , 1991, Advances in Applied Probability.

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

[23]  Optimal control of the M/G/1 queue with repeated vacations of the server , 1993, IEEE Trans. Autom. Control..

[24]  Henk C. Tijms,et al.  On a switch-over policy for controlling the workload in a queueing system with two constant service rates and fixed switch-over costs , 1977, Math. Methods Oper. Res..

[25]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[26]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..

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

[28]  Michael I. Taksar,et al.  A Heavy-Traffic Limit for the Cycle Counting Process in G/G/1, Optional Interruptions and Elastic Screen Brownian Motion , 1994, Math. Oper. Res..