scholarly journals A QUEUEING MODEL WITH RANDOMIZED DEPLETION OF INVENTORY

2016 ◽  
Vol 31 (1) ◽  
pp. 43-59 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Onno Boxma ◽  
Rim Essifi ◽  
Richard Kuijstermans
Keyword(s):  
Differential Equations ◽  
Poisson Process ◽  
Current Level ◽  
Inventory Level ◽  
Queueing Model ◽  
Homogeneous Poisson Process ◽  
Stationary Density ◽  
Non Homogeneous Poisson Process

In this paper, we study an M/M/1 queue, where the server continues to work during idle periods and builds up inventory. This inventory is used for new arriving service requirements, but it is completely emptied at random epochs of a non-homogeneous Poisson process, whose rate depends on the current level of the acquired inventory. For several shapes of depletion rates, we derive differential equations for the stationary density of the workload and the inventory level and solve them explicitly. Finally, numerical illustrations are given for some particular examples, and the effects of this depletion mechanism are discussed.

Some results for infinite server poisson queues

1969 ◽  
Vol 6 (03) ◽  
pp. 604-611 ◽  
Author(s):  
Mark Brown ◽  
Sheldon M. Ross
Keyword(s):  
Poisson Process ◽  
Infinite Number ◽  
Queueing Model ◽  
Homogeneous Poisson Process ◽  
Infinite Server ◽  
Non Homogeneous Poisson Process

We consider a queueing model in which arrivals occur according to a non-homogeneous Poisson process in batches of varying size, and in which a customer is served immediately upon arrival by one of an infinite number of servers.

Some results for infinite server poisson queues

1969 ◽  
Vol 6 (3) ◽  
pp. 604-611 ◽  
Author(s):  
Mark Brown ◽  
Sheldon M. Ross
Keyword(s):  
Poisson Process ◽  
Infinite Number ◽  
Queueing Model ◽  
Homogeneous Poisson Process ◽  
Infinite Server ◽  
Non Homogeneous Poisson Process

We consider a queueing model in which arrivals occur according to a non-homogeneous Poisson process in batches of varying size, and in which a customer is served immediately upon arrival by one of an infinite number of servers.

Weak limit results for the extremes of a class of shot noise processes

1995 ◽  
Vol 32 (03) ◽  
pp. 707-726 ◽  
Author(s):  
Patrick Homble ◽  
William P. McCormick
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Impulse Response Function ◽  
Weak Limit ◽  
Intensity Function ◽  
Important Class ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Non Homogeneous Poisson Process ◽  
Over Time

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

An optimal parking problem

1982 ◽  
Vol 19 (4) ◽  
pp. 803-814 ◽  
Author(s):  
Mitsushi Tamari
Keyword(s):  
Poisson Process ◽  
Decision Maker ◽  
Optimal Stopping ◽  
Renewal Process ◽  
A Priori ◽  
Expected Loss ◽  
Homogeneous Poisson Process ◽  
Optimal Stopping Rule ◽  
Non Homogeneous Poisson Process ◽  
Parking Place

The decision-maker drives a car along a straight highway towards his destination and looks for a parking place. When he finds a parking place, he can either park there and walk the distance to his destination or continue driving. Parking places are assumed to occur in accordance with a Poisson process along the highway. The decision-maker does not know the distance Y to his destination exactly in advance. Only an a priori distribution is assumed for Y and cases of typically important distribution are examined. When we take as loss the distance the decision-maker must walk and wish to minimize the expected loss, the optimal stopping rule and the minimum expected loss are obtained. In Section 3 a generalization to the cases of a non-homogeneous Poisson process and a renewal process is considered.

Sign in / Sign up

Export Citation Format

Share Document