Stochastic inventory models with bulk demand and state-dependent leadtimes

1971 ◽  
Vol 8 (3) ◽  
pp. 521-534 ◽  
Author(s):  
Donald Gross ◽  
Carl M. Harris ◽  
James A. Lechner
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Inventory Models ◽  
Inventory Cost ◽  
Stochastic Inventory ◽  
State Dependent ◽  
Optimal Value ◽  
Server Queue ◽  
Time Required ◽  
Stochastic Inventory Models

This paper describes two one-for-one ordering (S − 1, S) inventory models in which the time required for order replenishment is state-dependent. The demand is assumed to follow a compound Poisson distribution, and that portion of the leadtime corresponding to the actual filling of orders is assumed to depend on the number of outstanding orders. Since the orders placed are assumed to go into a single-server queue, queuing results are used to obtain the expected inventory cost as a function of S in order to obtain an optimal value of S.

Stochastic inventory models with bulk demand and state-dependent leadtimes

1971 ◽  
Vol 8 (03) ◽  
pp. 521-534
Author(s):  
Donald Gross ◽  
Carl M. Harris ◽  
James A. Lechner
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Inventory Models ◽  
Inventory Cost ◽  
Stochastic Inventory ◽  
State Dependent ◽  
Optimal Value ◽  
Server Queue ◽  
Time Required ◽  
Stochastic Inventory Models

This paper describes two one-for-one ordering (S − 1, S) inventory models in which the time required for order replenishment is state-dependent. The demand is assumed to follow a compound Poisson distribution, and that portion of the leadtime corresponding to the actual filling of orders is assumed to depend on the number of outstanding orders. Since the orders placed are assumed to go into a single-server queue, queuing results are used to obtain the expected inventory cost as a function of S in order to obtain an optimal value of S.

OPTIMALITY OF STATE DEPENDENT SINGLE SERVER QUEUE WITH MMPP INPUT

2020 ◽  
Vol 9 (3) ◽  
pp. 1197-1204
Author(s):  
R. Sakthi ◽  
R. Raghavendran ◽  
V. Vidhya
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
State Dependent ◽  
Server Queue

ON AN EQUIVALENCE BETWEEN LOSS RATES AND CYCLE MAXIMA IN QUEUES AND DAMS

2005 ◽  
Vol 19 (2) ◽  
pp. 241-255 ◽  
Author(s):  
René Bekker ◽  
Bert Zwart
Keyword(s):  
Loss Probability ◽  
Single Server ◽  
Finite Buffer ◽  
Single Server Queue ◽  
Release Rates ◽  
Asymptotic Results ◽  
State Dependent ◽  
Tail Distribution ◽  
Server Queue ◽  
Cycle Maximum

We consider the loss probability of a customer in a single-server queue with finite buffer and partial rejection and show that it can be identified with the tail distribution of the cycle maximum of the associated infinite-buffer queue. This equivalence is shown to hold for the GI/G/1 queue and for dams with state-dependent release rates. To prove this equivalence, we use a duality for stochastically monotone recursions, developed by Asmussen and Sigman (1996). As an application, we obtain several exact and asymptotic results for the loss probability and extend Takács' formula for the cycle maximum in the M/G/1 queue to dams with variable release rate.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

Sign in / Sign up

Export Citation Format

Share Document