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Paper Information

Journal:   INTERNATIONAL JOURNAL OF ENGINEERING   SEPTEMBER 2012 , Volume 25 , Number 3 (TRANSACTIONS C: ASPECTS); Page(s) 223 To 230.
 
Paper: 

WORKING VACATION QUEUE WITH SECOND OPTIONAL SERVICE AND UNRELIABLE SERVER

 
 
Author(s):  JAIN M., CHAUHAN D.*
 
* DEPARTMENT OF MATHEMATICS, ALLENHOUSE INSTITUTE OF TECHNOLOGY, KANPUR, 208007
 
Abstract: 

An M/M/1 queueing system with second optional service and unreliable server is studied. We consider that the server works at different rate rather than being idle during the vacation period. The customers arrive to the system according to Poisson process with state dependent rates depending upon the server’s status. All customers demand the first essential service whereas only some of them demand the second optional service. A customer either may leave the system after the first essential service with probability (1-r) or at the completion of the first essential service go for second optional service with probability r (0£r£1). The server may breaks down according to Poisson process during the busy and working vacation duration. Both service times in vacation and in service period are exponentially distributed. The matrix geometric technique is used for the analysis of the concerned queueing system. The sensitive analysis is also performed to examine the variation of the system performance characteristics with various input parameters.

 
Keyword(s): WORKING VACATION, SECOND OPTIONAL SERVICE, MATRIX GEOMETRIC TECHNIQUE, SERVER BREAKDOWN, REPAIR, QUEUE SIZE
 
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