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.

Sensitivity analysis of an M/G/1 retrial queueing system with disaster under working vacations and working breakdowns

2018 ◽  
Vol 52 (1) ◽  
pp. 35-54 ◽  
Author(s):  
P. Rajadurai
Keyword(s):  
Queueing System ◽  
Cost Optimization ◽  
Probability Generating Function ◽  
System Size ◽  
Service Rate ◽  
Steady State Probability ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Working Vacations ◽  
Busy Server

This paper deals with the new type of retrial queueing system with working vacations and working breakdowns. The system may become defective by disasters at any point of time when the regular busy server is in operation. The occurrence of disasters forces all customers to leave the system and causes the main server to fail. At a failure instant, the main server is sent to the repair and the repair period immediately begins. As soon as the orbit becomes empty at regular service completion instant or disaster occurs in the regular busy server, the server goes for a working vacation and working breakdown (called lower speed service period). During this period, the server works at a lower service rate to arriving customers. Using the supplementary variable technique, we analyze the steady state probability generating function of system size. Some important system performance measures are obtained. Finally, some numerical examples and cost optimization analysis are presented.

scholarly journals An M/G/1 Retrial Queue with Fluctuating Modes of Services

2018 ◽  
Vol 7 (4.10) ◽  
pp. 762
Author(s):  
P. Rajadurai ◽  
S. Venkatesh ◽  
K. Parameswari
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Single Server ◽  
Supplementary Variable ◽  
Working Vacation ◽  
Variable Technique ◽  
Retrial Queueing System ◽  
Retrial Queueing

In this paper, we consider a single server retrial queueing system with working vacation and two classes of customers, which are priority customers and ordinary customers. The single server provides fluctuating modes (optional phases) of services. Using the method of Probability Generating Function (PGF) approach and supplementary variable technique, the steady state results are obtained. 

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 Transient Analysis of M[X1],M[X2]/G1,G2/1 retrial queueing system with priority services, working breakdown, start up/close down time, Bernoulli vacation, reneging and balking

2020 ◽  
pp. 203-216
Author(s):  
Govindhan Ayyappan ◽  
Udayageetha J
Keyword(s):  
Transient Analysis ◽  
Queueing System ◽  
Variable Technique ◽  
Retrial Queueing System ◽  
System A ◽  
Retrial Queueing ◽  
Start Up ◽  
Set Up ◽  
Number Of Customers ◽  
Bernoulli Vacation

This paper considers  M[X1],M[X2]/G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the pre-emptive priority rule subject to working breakdown, startup/closedown time and Bernoulli vacation with general (arbitrary) vacation periods. After completing the service, if there are no priority customers present in the system the server may go for a vacation or close down the system. On completion of the close down, the server needs some time to set up the system. The priority customers who find the server busy are queued in the system. A low-priority customer who find the server busy are routed to a retrial (orbit) queue that attempts to get the service. The system may breakdown at any point of time when it is in operation. However, when the system fails, instead of stopping service completely, the service is continued only to the high priority customers at a slower rate. We consider balking to occur to the low priority customer while the server is busy or idle, and reneging to occur at the high priority customers during server’s vacation, start up/close down time. Using the supplementary variable technique, we derive the joint distribution of the server state and the number of customers in the system. Finally, some performance measures and numerical examples are presented.

scholarly journals M/M/1 Retrial queueing system with negative arrival under non-preemptive priority service

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
A. Muthu Ganapathi Subramanian ◽  
G. Ayyappan ◽  
G. Sekar
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Arrival Rate ◽  
Single Server ◽  
Preemptive Priority ◽  
Negative Customers ◽  
Retrial Queueing System ◽  
Priority Service ◽  
Retrial Queueing ◽  
Negative Arrivals

Consider a single server retrial queueing system with negative arrival under non-pre-emptive priority service in which three types of customers arrive in a poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers and λ3 for negative arrival. Low and high priority customers are identified as primary calls. The service times follow an exponential distribution with parameters μ1 and μ2 for low and high priority customers. The retrial and negative arrivals are introduced for low priority customers only. Gelenbe (1991) has introduced a new class of queueing processes in which customers are either positive or negative. Positive means a regular customer who is treated in the usual way by a server. Negative customers have the effect of deleting some customer in the queue. In the simplest version, a negative arrival removes an ordinary positive customer or a random batch of positive customers according to some strategy. It is noted that the existence of a flow of negative arrivals provides a control mechanismto control excessive congestion at the retrial group and also assume that the negative customers only act when the server is busy. Let K be the maximumnumber of waiting spaces for high priority customers in front of the service station. The high priorities customers will be governed by the Non-preemptive priority service. The access from the orbit to the service facility is governed by the classical retrial policy. This model is solved by using Matrix geometric Technique. Numerical study have been done for Analysis of Mean number of low priority customers in the orbit (MNCO), Mean number of high priority customers in the queue(MPQL),Truncation level (OCUT),Probability of server free and Probabilities of server busy with low and high priority customers for various values of λ1 , λ2 , λ3 , μ1 , μ2 ,σ and k in elaborate manner and also various particular cases of this model have been discussed.

scholarly journals On a Retrial Queueing Model with Customer Induced Interruption

2020 ◽  
pp. 112-120
Author(s):  
Varghese Jacob
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Performance Measures ◽  
Queueing System ◽  
Single Server ◽  
Finite Buffer ◽  
Preemptive Priority ◽  
State Behavior ◽  
Retrial Queueing System ◽  
Retrial Queueing

This paper presents a retrial queueing system with customer induced interruption while in service. We consider a single server queueing system of infinite capacity to which customers arrive according to a Poisson process and the service time follows an exponential distribution.An arriving customer to an idle server obtains service immediately and customers who find server busy go directly to the orbit from where he retry for service. The inter-retrial time follows exponential distribution. The customer interruption while in service occurs according to a Poisson process and the interruption duration follows an exponential distribution. The customer whose service is got interrupted will enter into a finite buffer. Any interrupted customer, finding the buffer full, is considered lost. Those interrupted customers who complete their interruptions will be placed into another buffer of same size. The interrupted customers waiting for service are given non-preemptive priority over new customers. We analyse the steady-state behavior of this queuing system. Several performance measures are obtained. Numerical illustrations of the system behaviour are also provided with example.

scholarly journals STABILITY ANALYSIS AND SIMULATION OF N-CLASS RETRIAL SYSTEM WITH CONSTANT RETRIAL RATES AND POISSON INPUTS

2014 ◽  
Vol 31 (02) ◽  
pp. 1440002 ◽  
Author(s):  
K. AVRACHENKOV ◽  
E. MOROZOV ◽  
R. NEKRASOVA ◽  
B. STEYAERT
Keyword(s):  
Queueing System ◽  
Stability Domain ◽  
Single Server ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Single Orbit ◽  
Transmission Control Protocols ◽  
Regenerative Approach ◽  
The Stability ◽  
Multi Access

In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.

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