Keywords:-
Article Content:-
Abstract
In this paper, we have a bulk arrival queueing Markovian model with two types of services first come first serve and bulk service. This model is also assumed the two servers such as main server and standby server with multiple vacations. If number of customers in the queue is less than ‘a’ then server will provide the FCFS service or goes for a vacation, if number of customers are more than or equal to ‘a’ then server will provide the bulk. After coming to the vacation, when the server will find number of customers are less than ‘a’ then he will provide the FCFS service to the customers. We have obtained the queue size distribution of this considered model and also obtained the performance measures such as idle time for the server, queue length, busy period by using the supplement variable technique.
References:-
References
F. Neuts (1967), A general class of bulk queue with Poisson input, Annals of Mathematical Statistics, 38, 759-770
Bong Dae Choi and Dong Hwan Han (1994), G/Ma,b/l QUEUES With Server Vacations, Journal of the Operations Research, 37( 3), 171-181
A. Krishnamoorthy and P. V. Ushakumari (2000), A Queueing System with Single Arrival Bulk Service and Single Departure, Mathematical and Computer Modelling, 31, 99-108
N. Bansal (2003), Analysis of the M/G/1 processor-sharing queue with bulk arrivals, Operations Research Letters, 31, 401 – 405
Seok Ho Chang, Dae Won Choi, and Tae-Sung Kim (2004), Performance Analysis of a Finite-Buffer Bulk-Arrival and Bulk-Service Queue with Variable Server Capacity, Stochastic Analysis And Applications, 22(5), 1151–1173
M. Haridass and R. Arumuganathan (2008) Analysis of a Bulk Queue with Unreliable Server and Single Vacation, International Journal Open Problems Computational Mathematics, 1(2), 37-55
Anyue Chen, Phil Pollett, Junping Li and Hanjun Zhang (2010), Markovian bulk-arrival and bulk-service queues with state-dependent control, Queueing System, 64, 267–304
Jau-Chuan Ke, Chia-Huang Wu, and Zhe George Zhang (2010), Recent Developments in Vacation Queueing Models : A Short Survey International Journal of Operations Research 7(4), 3-8
M. Jemila Parveen and M. I Afthab Begum (2013), General Bulk Service Queueing System with Multiple Working Vacation, International Journal of Mathematics Trends and Technology, 4(9), 163-173,
Srinivas R. Chakravarthy (2013), Analysis of MAP/PH1; PH2=1 queue with vacations and optional secondary services, Applied Mathemtical Modelling, 37 , 8886–8902
Tonui Benard, Langat Reuben and Gichengo Joel (2014), On Markovian Queuing Models, International Journal of Science and Research, 3(11), 93 - 96
M. I. Afthab Begum, Fijy Jose P, Shanthi (2014), N Policy For Repairable Bulk Arrival Queueing Model With Setup, Second Multi Optional Service Facility, International Journal of Innovative Research in Science, 3, 14614-14626.
Rakesh Kumar (2014), A Single-Server Markovian Queuing System with Discouraged Arrivals and Retention of Reneged Customers, Yugoslav Journal of Operations Research 24 , 119-126
Rama Ganesan, R. Ramshankar, R. Ramanarayanan (2014), M/M/1 Bulk Arrival and Bulk Service Queue with Randomly Varying Environment, IOSR Journal of Mathematics 10(6) 58-66.
Vishwa Nath Maurya (2014), Mathematical Modelling and Performance Analysis of Single Server Two-State Batch Arrivals and Batch Service Markovian Queue with Multiple Vacations, American Journal of Modeling and Optimization, 2(2), 39-46