A batch arrival multi phase queueing system with random feedback in service and single vacation policy

OPSEARCH ◽  
2015 ◽  
Vol 52 (4) ◽  
pp. 617-630 ◽  
Author(s):  
A. Badamchi Zadeh
Keyword(s):  
Queueing System ◽  
Batch Arrival ◽  
Single Vacation ◽  
Multi Phase

Analysis of a Discrete-Time Geo/G/1 Queue in a Multi-Phase Service Environment with Disasters

2018 ◽  
Vol 6 (4) ◽  
pp. 349-365
Author(s):  
Tao Jiang
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Queueing System ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Service Environment ◽  
Stationary Queue Length ◽  
Expected Length ◽  
Multi Phase ◽  
The Relationship

Abstract This paper considers a discrete-time Geo/G/1 queue in a multi-phase service environment, where the system is subject to disastrous breakdowns, causing all present customers to leave the system simultaneously. At a failure epoch, the server abandons the service and the system undergoes a repair period. After the system is repaired, it jumps to operative phase i with probability qi, i = 1, 2 ⋯, n. Using the supplementary variable technique, we obtain the distribution for the stationary queue length at the arbitrary epoch, which are then used for the computation of other performance measures. In addition, we derive the expected length of a cycle time, the generating function of the sojourn time of an arbitrary customer, and the generating function of the server’s working time in a cycle. We also give the relationship between the discrete-time queueing system to its continuous-time counterpart. Finally, some examples and numerical results are presented.

scholarly journals An M/G/1 Retrial Queueing System with Phase Type Services and Working Vacations

2018 ◽  
Vol 7 (4.10) ◽  
pp. 758
Author(s):  
P. Rajadurai ◽  
R. Santhoshi ◽  
G. Pavithra ◽  
S. Usharani ◽  
S. B. Shylaja
Keyword(s):  
Queueing System ◽  
Retrial Queue ◽  
Probability Generating Function ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Multiple Working Vacations ◽  
Phase Type ◽  
Working Vacations ◽  
Multi Phase ◽  
Number Of Customers

A multi phase retrial queue with optional re-service and multiple working vacations is considered. The Probability Generating Function (PGF) of number of customers in the system is obtained by supplementary variable technique. Various system performance measures are discussed. 

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