Analysis of MAP/PH/1 Queueing model with Immediate Feedback, Starting failures, Single Vacation, Standby Server, Delayed Repair, Breakdown and Impatient customers

2020 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
AYYAPPAN Govindan ◽  
Thilagavathy Karthikeyan
Keyword(s):  
Queueing Model ◽  
Impatient Customers ◽  
Immediate Feedback ◽  
Single Vacation ◽  
Delayed Repair

scholarly journals Maximum Entropy Approach for Un-Reliable Server Vacation Queueing Model with Optional Bulk Service

2012 ◽  
Vol 23 (1) ◽  
pp. 89-113
Author(s):  
Madhu Jain, Madhu Jain,
Keyword(s):  
Maximum Entropy ◽  
Performance Measures ◽  
Probability Generating Function ◽  
Single Server ◽  
Queueing Model ◽  
Time Service ◽  
Server Vacation ◽  
Single Vacation ◽  
Bulk Service ◽  
Essential Service

In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential service, he can also facilitate the additional phase of optional service (OS) in batches of fixed size b( ≥ 1), in case when the customers request for it. The server may take a single vacation whenever he finds no customers waiting in the queue to be served. Moreover, the server is subjected to unpredictable breakdown while providing the first essential service. The vacation time, service time and repair time of the server are exponentially distributed. The steady state results are obtained in terms of probability generating function for queue size distributions. By using the maximum entropy analysis (MEA), we derive various system performance measures. A comparative study is performed between the exact and approximate waiting time of the system. By taking the numerical illustrations, the sensitivity analysis is done to explore the effect of different descriptors on various performance measures.

Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers

OPSEARCH ◽  
2019 ◽  
Vol 56 (1) ◽  
pp. 300-323 ◽  
Author(s):  
Amina Angelika Bouchentouf ◽  
Mouloud Cherfaoui ◽  
Mohamed Boualem
Keyword(s):  
Economic Analysis ◽  
Single Server ◽  
Queueing Model ◽  
Impatient Customers

scholarly journals Performance and economic analysis of Markovian Bernoulli feedback queueing system with vacations, waiting server and impatient customers

2018 ◽  
Vol 10 (2) ◽  
pp. 218-241
Author(s):  
Amina Angelika Bouchentouf ◽  
Abdelhak Guendouzi ◽  
Abdeldjebbar Kandouci
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Cost Model ◽  
Probability Generating Function ◽  
Impatient Customers ◽  
Bernoulli Feedback ◽  
Single Vacation ◽  
Impatient Customer ◽  
Steady State Probabilities ◽  
Random Amount

Abstract This paper concerns the analysis of a Markovian queueing system with Bernoulli feedback, single vacation, waiting server and impatient customers. We suppose that whenever the system is empty the sever waits for a random amount of time before he leaves for a vacation. Moreover, the customer’s impatience timer depends on the states of the server. If the customer’s service has not been completed before the impatience timer expires, the customer leaves the system, and via certain mechanism, impatient customer may be retained in the system. We obtain explicit expressions for the steady-state probabilities of the queueing model, using the probability generating function (PGF). Further, we obtain some important performance measures of the system and formulate a cost model. Finally, an extensive numerical study is illustrated.

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