A Two-Phase Service System with Bernoulli Vacation Schedule, Setup Time andN-policy for an Unreliable Server with Delaying Repair

This paper studies Optimal NT policies for a k-phase service M/G/1 system with Bernoulli vacation schedule. The system contains an unreliable server with a breakdown period and delaying period. The server determines to start service by the policy: the server reactivates as soon as the number of arrivals in the queue reaches to a predetermined threshold N or T time units have elapsed since the end of the completion period. There are k phases of service in the system. After the completion of k phases service, the server may take a short vacation or may remain in the system to serve the next unit, which is defined by Bernoulli vacation schedule. Moreover, we assume the server fails according to a Poisson process whose repair time follows a general distribution. In final, we analyze the system characteristics for each scheme and obtained the optimal NT threshold to minimize the cost function.

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Steady state analysis of an Mx/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

Applied Mathematical Modelling ◽

10.1016/j.apm.2006.03.032 ◽

2007 ◽

Vol 31 (6) ◽

pp. 1079-1091 ◽

Cited By ~ 22

Author(s):

Gautam Choudhury ◽

Lotfi Tadj ◽

Madhuchanda Paul

Keyword(s):

Steady State ◽

Two Phase ◽

Steady State Analysis ◽

Multiple Vacation ◽

Bernoulli Vacation ◽

State Analysis

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A bulk quorum queueing system with a random setup time underN-policy and with Bernoulli vacation schedule

Stochastics ◽

10.1080/17442500500397574 ◽

2006 ◽

Vol 78 (1) ◽

pp. 1-11 ◽

Cited By ~ 8

Author(s):

Lotfi Tadj ◽

Gautam Choudhury ◽

Chakib Tadj

Keyword(s):

Queueing System ◽

Setup Time ◽

Bernoulli Vacation

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Retrial Queue with Unreliable Server and Second Optional Service under K Types of Bernoulli Vacation

International Journal of Services and Operations Management ◽

10.1504/ijsom.2020.10030918 ◽

2020 ◽

Vol 1 (1) ◽

pp. 1

Author(s):

SUGANTHI POOMALAI

Keyword(s):

Retrial Queue ◽

Unreliable Server ◽

Optional Service ◽

Second Optional Service ◽

Bernoulli Vacation

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Bernoulli vacation model for MX /G/1 unreliable server retrial queue with Bernoulli feedback, balking and optional service

RAIRO - Operations Research ◽

10.1051/ro/2020074 ◽

2020 ◽

Author(s):

Dr. Madhu Jain ◽

Sandeep Kaur

Keyword(s):

Performance Metrics ◽

Retrial Queue ◽

Maximum Entropy Principle ◽

Approximate Solutions ◽

Bernoulli Feedback ◽

Unreliable Server ◽

Optional Service ◽

Multi Phase ◽

Essential Service ◽

Bernoulli Vacation

The study of unreliable server retrial bulk queue with multiphase optional service is analyzed by incorporating the features of balking, Bernoulli vacation and Bernoulli feedback. On the occasion when the server is occupied with the service of the customers, an arriving customer finding the long queue, can join the retrial orbit and receives its service later on by making re-attempt. The system is reinforced with multi phase optional service along with essential service and joining customer can opt any one of optional services after getting essential service. Furthermore, the essential/ optional service can be aborted due to abrupt failure of the server. There is an immediate support of multi phase repair facility to take care of the failed server, but sometimes repair may be put on hold by virtue of any unexpected cause. If the service is unsatisfactory, the customer can rejoin the queue as feedback customer. Bernoulli vacation is permitted to the server following the respective busy period. For evaluating the queue size distribution and other system performance metrics, supplementary variable technique (SVT) is used. The approximate solutions for the steady state probabilities and waiting time are suggested using maximum entropy principle (MEP). To verify the outcomes of the model, numerical illustrations and cost analysis have been accomplished.

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