Stochastic analysis of a preemptive retrial queue with orbital search and multiple vacations

2020 ◽  
Vol 54 (1) ◽  
pp. 231-249
Author(s):  
Shan Gao ◽  
Jinting Wang
Keyword(s):  
Cost Optimization ◽  
Retrial Queue ◽  
Length Distribution ◽  
Stochastic Decomposition ◽  
Embedded Markov Chain ◽  
Multiple Vacations ◽  
Retrial Queueing System ◽  
Queue Length Distribution ◽  
Retrial Queueing ◽  
Necessary And Sufficient

This paper deals with a preemptive priority M/G/1 retrial queue with orbital search and exhaustive multiple vacations. By using embedded Markov chain technique and the supplementary variable method, we discuss the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state as well as some important performance measures and the Laplace–Stieltjes transform of the busy period. Also, we establish a special case and the stochastic decomposition laws for this preemptive retrial queueing system. Finally, some numerical examples and cost optimization analysis are presented.

scholarly journals An Unreliable Batch Arrival Retrial Queueing System With Bernoulli Vacation Schedule and Linear Repeated Attempts

2020 ◽  
Vol 11 (1) ◽  
pp. 83-109
Author(s):  
Gautam Choudhury ◽  
Lotfi Tadj
Keyword(s):  
Retrial Queue ◽  
Sensitivity Analyses ◽  
Embedded Markov Chain ◽  
State Behavior ◽  
Unreliable Server ◽  
Reliability Indices ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Vacation Model ◽  
Bernoulli Vacation

This article deals with the steady-state behavior of an MX/G/1 retrial queue with the Bernoulli vacation schedule and unreliable server, under linear retrial policy. Breakdowns can occur randomly at any instant while the server is providing service to the customers. Further, the concept of Bernoulli admission mechanism is introduced. This model generalizes both the classical MX/G/1 retrial queue with unreliable server as well as the MX/G/1 retrial queue with the Bernoulli vacation model. The authors carry out an extensive analysis of this model. Namely, the embedded Markov chain, the stationary distribution of the number of units in the orbit, and the state of the server are studied. Some important performance measures and reliability indices of this model are obtained. Finally, numerical illustrations are provided and sensitivity analyses on some of the system parameters are conducted.

The M/G/1 Retrial Queue With Retrial Rate Control Policy

1993 ◽  
Vol 7 (1) ◽  
pp. 29-46 ◽  
Author(s):  
Bong Dae Choi ◽  
Kyung Hyune Rhee ◽  
Kwang Kyu Park
Keyword(s):  
Retrial Queue ◽  
Control Policy ◽  
Single Server ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Virtual Waiting Time ◽  
The Laplace Transform ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Number Of Customers

We consider a single-server retrial queueing system where retrial time is inversely proportional to the number of customers in the system. A necessary and sufficient condition for the stability of the system is found. We obtain the Laplace transform of virtual waiting time and busy period. The transient distribution of the number of customers in the system is also obtained.

scholarly journals Performance Analysis of Preemptive Priority Retrial Queueing System with Disaster under Working Breakdown Services

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 419 ◽  
Author(s):  
Sherif Ammar ◽  
Pakkirisamy Rajadurai
Keyword(s):  
Queueing System ◽  
Cost Optimization ◽  
System Size ◽  
Supplementary Variable ◽  
Preemptive Priority ◽  
Variable Technique ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Busy Server ◽  
The Impact

In this investigation, a novel sort of retrial queueing system with working breakdown services is introduced. Two distinct kinds of customers are considered, which are priority and ordinary customers. The normal busy server may become inadequate due to catastrophes at any time which cause the major server to fail. At a failure moment, the major server is sent to be fixed and the server functions at a lower speed (called the working breakdown period) during the repair period. The probability generating functions (PGF) of the system size is found using the concepts of the supplementary variable technique (SVT). The impact of parameters in system performance measures and cost optimization are examined numerically.

Strategic priority-purchasing and joining rules in a retrial queue

2020 ◽  
Author(s):  
Zhongbin Wang ◽  
Jinting Wang
Keyword(s):  
Retrial Queue ◽  
Dominant Strategy ◽  
Equilibrium Strategy ◽  
Social Planner ◽  
Theoretic Model ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
The Social ◽  
Game Theoretic ◽  
Customer Welfare

Abstract This paper considers a retrial queueing system with a pay-for-priority option. A queueing-game-theoretic model that captures the interaction among the customers, the service provider (SP) and the social planner is developed. We obtain the equilibrium strategy of customers for any fixed priority premium and identify the unique Pareto-dominant strategy. The optimal pricing strategies for the SP and the social planner are derived and compared extensively. Interestingly, we find that the equilibrium outcome of customers is non-monotone in the service reward and the profit of the SP is bimodal in the priority premium. We reveal the fact that the SP’s optimization makes the system more congested than what is socially desirable. Finally, numerical examples indicate that the customer welfare can be improved by providing priorities when the market size is large.

scholarly journals An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

2018 ◽  
Vol 7 (4.10) ◽  
pp. 758
Author(s):  
P. Rajadurai ◽  
R. Santhoshi ◽  
G. Pavithra ◽  
S. Usharani ◽  
S. B. Shylaja
Keyword(s):  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
Multi Phase ◽  
Number Of Customers

A multi phase retrial queue with optional re-service and multiple working vacations is considered. The Probability Generating Function (PGF) of number of customers in the system is obtained by supplementary variable technique. Various system performance measures are discussed. 

scholarly journals M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Tao ◽  
Liyuan Zhang ◽  
Shan Gao
Keyword(s):  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Service Rate ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
The Matrix ◽  
Vacation Interruption ◽  
Necessary And Sufficient ◽  
Vacation Period ◽  
Conditional Stochastic Decomposition

We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.

scholarly journals Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials

2016 ◽  
Vol 53 (4) ◽  
pp. 1098-1110 ◽  
Author(s):  
Tuǧrul Dayar ◽  
M. Can Orhan
Keyword(s):  
Queueing System ◽  
Arrival Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generator Matrix ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Phase Type ◽  
Necessary And Sufficient ◽  
Infinite State

Abstract A multiclass c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multidimensional Markov chain, and a Kronecker representation of its generator matrix is numerically analyzed.

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.

Numerical solution for the performance characteristics of the M/M/C/K retrial queue with negative customers and exponential abandonments by using value extrapolation method

2019 ◽  
Vol 53 (3) ◽  
pp. 767-786
Author(s):  
Zidani Nesrine ◽  
Pierre Spiteri ◽  
Natalia Djellab
Keyword(s):  
System Performance ◽  
Algebraic System ◽  
Queueing System ◽  
Retrial Queue ◽  
Practical Interest ◽  
Extrapolation Method ◽  
Negative Customers ◽  
Multiprocessor Computer ◽  
Retrial Queueing System ◽  
Retrial Queueing

This paper deals with a retrial queueing system M/M/C/K with exponential abandonment at which positive and negative primary customers arrive according to Poisson processes. This model is of practical interest: it permits to analyze the performance in call centers or multiprocessor computer systems. For model under study, we find the ergodicity condition and also the approximate solution by applying Value Extrapolation method which includes solving of some algebraic system of equations. To this end, we have resolved the algebraic system in question by different numerical methods. We present also numerical results to analyze the system performance.

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