A continuous review (s, S) inventory system in a random environment

1978 ◽  
Vol 15 (3) ◽  
pp. 654-659 ◽  
Author(s):  
Richard M. Feldman
Keyword(s):  
Poisson Process ◽  
External Environment ◽  
Compound Poisson Process ◽  
Inventory System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Compound Poisson ◽  
Continuous Review ◽  
Environmental Process ◽  
State Of The Environment

The steady-state distribution of the inventory position for a continuous review (s, S) inventory system is derived. The demand for items in inventory is dependent on an external environment. During an interval of time in which the environment is in a fixed state, the demand follows a discrete-valued compound Poisson process. The parameters of the compound Poisson process depend completely on the state of the environment. The environmental process is modeled as a continuous-time Markov process.

A continuous review (s, S) inventory system in a random environment

1978 ◽  
Vol 15 (03) ◽  
pp. 654-659 ◽  
Author(s):  
Richard M. Feldman
Keyword(s):  
Poisson Process ◽  
External Environment ◽  
Compound Poisson Process ◽  
Inventory System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Compound Poisson ◽  
Continuous Review ◽  
Environmental Process ◽  
State Of The Environment

The steady-state distribution of the inventory position for a continuous review (s, S) inventory system is derived. The demand for items in inventory is dependent on an external environment. During an interval of time in which the environment is in a fixed state, the demand follows a discrete-valued compound Poisson process. The parameters of the compound Poisson process depend completely on the state of the environment. The environmental process is modeled as a continuous-time Markov process.

Algorithms for a continuous-review (s, S) inventory system

1981 ◽  
Vol 18 (02) ◽  
pp. 461-472
Author(s):  
V. Ramaswami
Keyword(s):  
Steady State ◽  
Inventory System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Continuous Review ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Phase Type ◽  
Markov Modulated ◽  
Stimulation Of

The steady-state distribution of the inventory position for a continuous-review (s, S) inventory system is derived in a computationally tractable form. Demands for items in inventory are assumed to form an N-process which is the ‘versatile Markovian point process' introduced by Neuts (1979). The N-process includes the phase-type renewal process, Markov-modulated Poisson process etc., as special cases and is especially useful in modelling a wide variety of qualitative phenomena such as peaked arrivals, interruptions, inhibition or stimulation of arrivals by certain events etc.

scholarly journals Queues with Delays in Two-State Strategies and Lévy Input

2008 ◽  
Vol 45 (2) ◽  
pp. 314-332 ◽  
Author(s):  
R. Bekker ◽  
O. J. Boxma ◽  
O. Kella
Keyword(s):  
Brownian Motion ◽  
Steady State ◽  
Poisson Process ◽  
Lévy Process ◽  
Compound Poisson Process ◽  
Levy Process ◽  
Original Function ◽  
Steady State Distribution ◽  
State Distribution ◽  
Negative Drift

We consider a reflected Lévy process without negative jumps, starting at the origin. When the reflected process first upcrosses level K, a timer is activated. After D time units, the timer expires and the Lévy exponent of the Lévy process is changed. As soon as the process hits zero again, the Lévy exponent reverses to the original function. If the process has reached the origin before the timer expires then the Lévy exponent does not change. Using martingale techniques, we analyze the steady-state distribution of the resulting process, reflected at the origin. We pay special attention to the cases of deterministic and exponential timers, and to the following three special Lévy processes: (i) a compound Poisson process plus negative drift (corresponding to an M/G/1 queue), (ii) Brownian motion, and (iii) a Lévy process that is a subordinator until the timer expires.

scholarly journals Queues with Delays in Two-State Strategies and Lévy Input

2008 ◽  
Vol 45 (02) ◽  
pp. 314-332
Author(s):  
R. Bekker ◽  
O. J. Boxma ◽  
O. Kella
Keyword(s):  
Brownian Motion ◽  
Steady State ◽  
Poisson Process ◽  
Lévy Process ◽  
Compound Poisson Process ◽  
Levy Process ◽  
Original Function ◽  
Steady State Distribution ◽  
State Distribution ◽  
Negative Drift

We consider a reflected Lévy process without negative jumps, starting at the origin. When the reflected process first upcrosses level K, a timer is activated. After D time units, the timer expires and the Lévy exponent of the Lévy process is changed. As soon as the process hits zero again, the Lévy exponent reverses to the original function. If the process has reached the origin before the timer expires then the Lévy exponent does not change. Using martingale techniques, we analyze the steady-state distribution of the resulting process, reflected at the origin. We pay special attention to the cases of deterministic and exponential timers, and to the following three special Lévy processes: (i) a compound Poisson process plus negative drift (corresponding to an M/G/1 queue), (ii) Brownian motion, and (iii) a Lévy process that is a subordinator until the timer expires.

Algorithms for a continuous-review (s, S) inventory system

1981 ◽  
Vol 18 (2) ◽  
pp. 461-472 ◽  
Author(s):  
V. Ramaswami
Keyword(s):  
Steady State ◽  
Inventory System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Continuous Review ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Phase Type ◽  
Markov Modulated ◽  
Stimulation Of

The steady-state distribution of the inventory position for a continuous-review (s, S) inventory system is derived in a computationally tractable form. Demands for items in inventory are assumed to form an N-process which is the ‘versatile Markovian point process' introduced by Neuts (1979). The N-process includes the phase-type renewal process, Markov-modulated Poisson process etc., as special cases and is especially useful in modelling a wide variety of qualitative phenomena such as peaked arrivals, interruptions, inhibition or stimulation of arrivals by certain events etc.

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