Stochastic Decomposition in Retrial Queueing Inventory System

2016 ◽  
Author(s):  
A. Krishnamoorthy ◽  
Dhanya Shajin
Keyword(s):  
Inventory System ◽  
Stochastic Decomposition ◽  
Retrial Queueing

Stochastic decomposition in retrial queueing-inventory system

2020 ◽  
Vol 54 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Dhanya Shajin ◽  
A. Krishnamoorthy
Keyword(s):  
Joint Distribution ◽  
Storage System ◽  
Retrial Queue ◽  
Form Solution ◽  
Inventory System ◽  
Product Form ◽  
Stochastic Decomposition ◽  
Retrial Queueing ◽  
Long Run ◽  
Number Of Customers

The purpose of this paper is to obtain product form solution for retrial – queueing – inventory system. We study an M/M/1 retrial queue with a storage system driven by an (s,S) policy. When server is idle, external arrivals enter directly to an orbit. Inventory replenishment lead time is exponentially distributed. The interval between two successive retrials is exponentially distributed and only the customer at the head of the orbit is permitted to access the server. No customer is allowed to join the orbit when the storage system is empty and also when the serer is busy. We first derive the stationary joint distribution of the queue length and the on-hand inventory in explicit product form. Using the joint distribution, we investigate long-run performance measures such as distribution of number of customers served, number of arrivals, number of customers lost during an interval of random duration and a cost function. The optimal pair (s,S) is numerically investigated.

scholarly journals A retrial queueing-inventory system with J-additional options for service and finite source

ORiON ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 105 ◽  
Author(s):  
VSS Yadavalli ◽  
K Jeganathan ◽  
T Venkadesan ◽  
S Padmasekaran ◽  
S Jehoashan Kingsly
Keyword(s):  
Inventory System ◽  
Finite Source ◽  
Retrial Queueing

Analysis of M/G/1 retrial queues with second optional service and customer balking under two types of Bernoulli vacation schedule

2019 ◽  
Vol 53 (2) ◽  
pp. 415-443 ◽  
Author(s):  
S. Pavai Madheswari ◽  
B. Krishna Kumar ◽  
P. Suganthi
Keyword(s):  
Performance Measures ◽  
System Size ◽  
Retrial Queues ◽  
Stochastic Decomposition ◽  
Second Phase ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Special Cases ◽  
Orbit Size ◽  
Bernoulli Vacation

An M/G/1 retrial queueing system with two phases of service of which the second phase is optional and the server operating under Bernoulli vacation schedule is investigated. Further, the customer is allowed to balk upon arrival if he finds the server unavailable to serve his request immediately. The joint generating functions of orbit size and server status are derived using supplementary variable technique. Some important performance measures like the orbit size, the system size, the server utilisation and the probability that the system is empty are found. Stochastic decomposition law is established when there is no balking permitted. Some existing results are derived as special cases of our model under study. Interestingly, these performance measures are compared for various vacation schedules namely exhaustive service, 1-limited service, Bernoulli vacation and modified Bernoulli vacation schedules. Extensive numerical analysis is carried out to exhibit the effect of the system parameters on the performance measures.

A retrial queueing-inventory system with service option on arrival and Multiple vacations

2019 ◽  
Vol 14 (1) ◽  
pp. 1917-1936
Author(s):  
Jothivel kathiresan ◽  
Kathirvel Jeganathan ◽  
Neelamegam Anbazhagan
Keyword(s):  
Inventory System ◽  
Multiple Vacations ◽  
Retrial Queueing ◽  
Service Option

scholarly journals A Discrete-Time UnreliableGeo/G/1Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Feng Zhang ◽  
Zhifeng Zhu
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
System Size ◽  
Stochastic Decomposition ◽  
State Behavior ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Optional Service ◽  
Second Optional Service

This paper deals with the steady-state behavior of a discrete-time unreliableGeo/G/1retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system.

scholarly journals Analysis of an M/PH/1 Retrial Queueing-Inventory System with Level Dependent Retrial Rate

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zaiming Liu ◽  
Xuxiang Luo ◽  
Jinbiao Wu
Keyword(s):  
Life Time ◽  
Maximum Size ◽  
Inventory System ◽  
Phase Type Distribution ◽  
Steady State Probability ◽  
Numerical Illustration ◽  
Retrial Queueing ◽  
Common Life Time ◽  
The Stability ◽  
Number Of Customers

We analyze a queueing-inventory system which can model airline and railway reservation systems. An arriving customer to an idle server joins for service immediately with exactly one item from inventory at the moment of service completion if there are some on-hand inventory, or else he accesses to a buffer of varying size (the buffer capacity varies and equals to the number of the items in the inventory with maximum size S). When the buffer overflows, the customer joins an orbit of infinite capacity with probability p or is lost forever with probability 1−p. Arrivals form a Poisson process, and service time has phase type distribution. The time between any two successive retrials of the orbiting customer is exponentially distributed with parameter depending on the number of customers in the orbit. In addition, the items have a common life time with exponentially distributed. Cancellation of orders is possible before their expiry and intercancellation times are assumed to be exponentially distributed. The stability condition and steady-state probability vector have been studied by Neuts–Rao truncation method using the theory of Level Dependent Quasi-Birth-Death (LDQBD) processes. Several stationary performance measures are also computed. Furthermore, we provide numerical illustration of the system performance with variation in values of underlying parameters and analyze an optimization problem.

scholarly journals A Discrete-TimeGeo/G/1Retrial Queue withJVacations and Two Types of Breakdowns

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Feng Zhang ◽  
Zhifeng Zhu
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Queueing System ◽  
System Size ◽  
Stochastic Decomposition ◽  
Size Distributions ◽  
System State ◽  
State Distribution ◽  
Retrial Queueing ◽  
Orbit Size

This paper is concerned with a discrete-timeGeo/G/1retrial queueing model withJvacations and two types of breakdowns. If the orbit is empty, the server takes at mostJvacations repeatedly until at least one customer appears in the orbit upon returning from a vacation. It is assumed that the server is subject to two types of different breakdowns and is sent immediately for repair. We analyze the Markov chain underlying the considered queueing system and derive the system state distribution as well as the orbit size and the system size distributions in terms of their generating functions. Then, we obtain some performance measures through the generating functions. Moreover, the stochastic decomposition property and the corresponding continuous-time queueing system are investigated. Finally, some numerical examples are provided to illustrate the effect of vacations and breakdowns on several performance measures of the system.

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