scholarly journals Mathematical Modelling and Performance Analysis of Single Server Two-State Batch Arrivals and Batch Service Markovian Queue with Multiple Vacations

2014 ◽  
Vol 2 (2) ◽  
pp. 39-46 ◽  
Author(s):  
Vishwa Nath Maurya
Keyword(s):  
Performance Analysis ◽  
Mathematical Modelling ◽  
Batch Service ◽  
Single Server ◽  
Batch Arrivals ◽  
Multiple Vacations ◽  
Markovian Queue ◽  
And Performance

scholarly journals Bulk input queues with quorum and multiple vacations

1996 ◽  
Vol 2 (2) ◽  
pp. 95-106 ◽  
Author(s):  
Jewgeni H. Dshalalow ◽  
Jay Yellen
Keyword(s):  
Poisson Process ◽  
Preliminary Analysis ◽  
Queueing System ◽  
Compound Poisson Process ◽  
Batch Service ◽  
Single Server ◽  
Compound Poisson ◽  
Multiple Vacations ◽  
Queueing Process ◽  
Multiple Vacation

The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less thanrand not greater thanR(≥r). The server takes vacations each time the queue level falls belowr(≥1)in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.

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