scholarly journals On the stochastic decomposition property of single server retrialqueuing systems

2017 ◽  
Vol 41 ◽  
pp. 918-932
Author(s):  
Nawel ARRAR ◽  
Natalia DJELLAB ◽  
Jean-Bernard BAILLON
Keyword(s):  
Stochastic Decomposition ◽  
Single Server ◽  
Decomposition Property

Decomposition property in a discrete-time queue with multiple input streams and service interruptions

2004 ◽  
Vol 41 (02) ◽  
pp. 524-534
Author(s):  
Fumio Ishizaki
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Single Server Queue ◽  
General Process ◽  
Decomposition Property ◽  
Service Interruptions ◽  
Virtual Waiting Time ◽  
Server Queue

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.

scholarly journals On the single-server retrial queue

2006 ◽  
Vol 16 (1) ◽  
pp. 45-53 ◽  
Author(s):  
Natalia Djellab
Keyword(s):  
Approximate Solution ◽  
Retrial Queue ◽  
Retrial Queues ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Queue Size ◽  
Decomposition Property ◽  
The Subject ◽  
Exponential Case ◽  
Number Of Customers

In this work, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Using the decomposition property of M/G/1 retrial queues with breakdowns that holds under exponential assumption for retrial times as an approximation in the non-exponential case, we consider an approximate solution for the steady-state queue size distribution.

Decomposition property in a discrete-time queue with multiple input streams and service interruptions

2004 ◽  
Vol 41 (2) ◽  
pp. 524-534 ◽  
Author(s):  
Fumio Ishizaki
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Single Server Queue ◽  
General Process ◽  
Decomposition Property ◽  
Service Interruptions ◽  
Virtual Waiting Time ◽  
Server Queue

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or to be stationary. This paper shows that a stochastic decomposition property for the virtual waiting-time process holds in the discrete-time single-server queue with service interruptions. To the best of the author's knowledge, no stochastic decomposition results for virtual waiting-time processes in non-work-conserving queues, such as queues with service interruptions, have been obtained before and only work-conserving queues have been studied in the literature.

scholarly journals Pseudo-conservation laws in cyclic-service systems

1987 ◽  
Vol 24 (4) ◽  
pp. 949-964 ◽  
Author(s):  
O. J. Boxma ◽  
W. P. Groenendijk
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Waiting Times ◽  
Service Systems ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Weighted Sum ◽  
Cyclic Service ◽  
The Mean

This paper considers single-server, multi-queue systems with cyclic service. Non-zero switch-over times of the server between consecutive queues are assumed. A stochastic decomposition for the amount of work in such systems is obtained. This decomposition allows a short derivation of a ‘pseudo-conservation law' for a weighted sum of the mean waiting times at the various queues. Thus several recently proved conservation laws are generalised and explained.

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

1994 ◽  
Vol 31 (4) ◽  
pp. 1083-1097 ◽  
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
Recursive Formula ◽  
Setup Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
New Approach ◽  
Service Interruption ◽  
Special Cases ◽  
Stationary Waiting Time

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

A NOTE ON INFINITE-SERVER MARKOV MODULATED AND SINGLE-SERVER RETRIAL QUEUES

2014 ◽  
Vol 31 (02) ◽  
pp. 1440003
Author(s):  
ZHE DUAN ◽  
MELIKE BAYKAL-GÜRSOY
Keyword(s):  
Queueing Systems ◽  
Retrial Queue ◽  
System Size ◽  
Retrial Queues ◽  
Stochastic Decomposition ◽  
Applied Probability ◽  
Single Server ◽  
The Matrix ◽  
Service Rates ◽  
Markov Modulated

We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the single-server retrial queue analyzed in Keilson and Servi [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471; Baykal-Gürsoy, M and W Xiao (2004). Stochastic decomposition in M/M/∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88]. The main contribution of the present paper is the derivation of the explicit form of the stationary system size distributions. Numerical examples are presented visually exhibiting the effect of various parameters on the stationary distributions.

A new approach to the G/G/1 queue with generalized setup time and exhaustive service

1994 ◽  
Vol 31 (04) ◽  
pp. 1083-1097
Author(s):  
Huan Li ◽  
Yixin Zhu
Keyword(s):  
Waiting Time ◽  
Queueing Systems ◽  
Recursive Formula ◽  
Setup Time ◽  
Stochastic Decomposition ◽  
Single Server ◽  
New Approach ◽  
Service Interruption ◽  
Special Cases ◽  
Stationary Waiting Time

We consider a class of G/G/1 queueing models with independent generalized setup time and exhaustive service. It is shown that a variety of single-server queueing systems with service interruption are special cases of our model. We give a simple computational scheme for the moments of the stationary waiting time and sojourn time. Our numerical investigations indicate that the algorithm is quite accurate and fast in general. For the M/G/1 case, we are able to derive a recursive formula for the moments of the stationary waiting time, which includes the Takács formula as a special case. It immediately results in the stochastic decompòsition property which can be found in the literature.

scholarly journals Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Amina Angelika Bouchentouf ◽  
Lahcene Yahiaoui ◽  
Mokhtar Kadi ◽  
Shakir Majid
Keyword(s):  
Queueing System ◽  
Cost Model ◽  
Probability Generating Function ◽  
Steady State Solution ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Working Vacation ◽  
Bernoulli Feedback ◽  
Markovian Queue ◽  
Retention Of Reneged Customers

This paper deals with customers’ impatience behaviour for single server Markovian queueing system under K-variant working vacation policy, waiting server, Bernoulli feedback, balking, reneging, and retention of reneged customers. Using probability generating function (PGF) technique, we obtain the steady-state solution of the system. In addition, we prove the stochastic decomposition properties. Useful performance measures of the considered queueing system are derived. A cost model is developed. Then, the parameter optimisation is carried out numerically, using quadratic fit search method (QFSM). Finally, numerical examples are provided in order to visualize the analytical results.

scholarly journals Discussion on the transient behavior of single server Markovian multiple variant vacation queues

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Manickam Vadivukarasi ◽  
Kaliappan Kalidass
Keyword(s):  
Waiting Time ◽  
Transient Behavior ◽  
System Size ◽  
Time Dependent ◽  
Stochastic Decomposition ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Decomposition Structure ◽  
Important Time ◽  
Time Dependent Solution

In this paper, we consider an M/M/1 queue where beneficiary visits occur singly. Once the beneficiary level in the system becomes zero, the server takes a vacation immediately. If the server finds no beneficiaries in the system, then the server is allowed to take another vacation after the return from the vacation. This process continues until the server has exhaustively taken all the J vacations. The closed form transient solution of the considered model and some important time dependent performance measures are obtained. Further, the steady state system size distribution is obtained from the time-dependent solution. A stochastic decomposition structure of waiting time distribution and expression for the additional waiting time due to the presence of server vacations are studied. Numerical assessments are presented.

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